 F Frankly, ydych chi'n hwlad o poetsio gwahanol yn Brexit? It's sort of talking about the weather as a bit of light relief really, island that's going on. In fact I thought I would start with a quote from something that amused me when I read it from Thomas Hardy's The Mayor of Lobbyin. Some of you have probably read the book but the protagonist Henshawd is in a really bad way. felly mae'n eisieit i'r byw i gwisio, yw yw'n gweithio nhw'n ddechrau, a oedd mae'r lle i ni yn scwpio'r gwahol. Mae'n gyfrofiad gyda swydd yn ôl. Mae'n gweithio'n gallu maesio'n gweithio. A yn ymdweithio'r gweithio, mae'n gweithio'r eich gallu roi o'r dysgwyr ar y dyfinaill, er mwyn roedd yn ffrwng y cwch. Mae'n gweithio itfain dweud yma'n ei maen nhw y lle maen nhw'n ei gweithio. So, he goes out at the dead of night, you know, with his coat over his head so nobody sees him. And he goes to some, you know, mysterious place outside the village where the weather forecaster hangs out. And so there we go. In a lonely hamlet a few miles from the town, there lived a man of curious report as a forecaster of weather. And he asked him basically what's the harvest going to be like. And the answer is, as you can see here, by the sun, moon and stars, the clouds, the winds, the trees, the grass, candelflame swallows, smell of the herbs, cat's eyes, ravens, leeches, spiders, dung mixon. I'm not quite sure what dung mixon is, but I guess it's something to do with dung. The last fortnight will be rain and tempest. So there we are. So this was in 1886 and probably around the turn of the century people started to think about how to formulate weather forecasting as a scientific topic. And after the Second World War, with the advent of digital computers, people started to actually code up these equations onto computers and actually make weather forecasts. And then in the 1970s, all the satellites started to be launched and we had lots of instruments measuring the atmosphere to provide the starting conditions for the weather forecasts. So you'd think that everything would be just hunky dory compared to 1886, but of course if we fast forward 100 years, it seems like we haven't improved at all. So this is the, I guess a lot of you in the audience will, normally when I speak to students, I have to say, well this was the guy back in dawn of prehistory. Anyway, so Michael Burke famously said, well you chapter a fact like the good last night, if you can't forecast the worst storm for several centuries, just a few hours before what on earth are you doing? Okay, so and in fact, people have, other people have kind of lept on to the bandwagon and here's an article from a few years ago now, but in the telegraph, it's actually reviewing a book from a climate skeptic by the correspondent Charles Moore and basically he's saying, well you know, look, weather forecasts go wrong, they can go wrong like Michael Fish just a few days ahead, they can certainly go wrong a month ahead. So what hope is there for saying anything at all about climate change 100 years from now. So the game is up for climate change believers, it's all, you know, it's all a gigantic hoax, it's a weather forecast for a century ahead and it can therefore have no value as a prediction. All right, so the purpose of my talk is to try to at least answer or attempt to at least to answer these sorts of questions, why do weather forecasts go wrong? What can we do about it if they do go wrong from time to time, which they obviously do, and what are the implications for our understanding of climate change? Is it something that means that, you know, it's a hopeless task or what? Okay, so that's the, that's going to be the theme of the talk. So I just thought I would start since I mentioned satellites in showing you a movie of the earth from space. Let's see if this works. Just it's just a nice animation of clouds from composites of satellite images, basically just kind of showing you it's a real rather complicated system. It's sort of like a turbulent fluid, lots of scales of motion going on. You saw the weather system, the mid-latitude weather systems going across from West to East and those blobs. Well, in fact, if I go on to the next slide, the next slide is an animation over the tropical West Pacific where these sort of things bubbling up are thunderstorms. They're really transporting a lot of moisture into the atmosphere from the warm sea surface. And then occasionally these clouds start forming tropical cyclones and you can see the eye of these two. Okay, so again, no matter what scale you look at, I could have then shown you a blow-up of, you know, one of these cloud systems and you'd see all sorts of turbulent scales within that. So we're looking at a very complex, you know, multi-scale system. And as I say, I do want to talk a little bit about science. I hope to not to, it won't get too technical. I will show you a couple of good equations, but in fact there's already three there. But you can view equations two ways. You can completely ignore them. What I really want you to do with equations is just marvel at them. So there are three branches of physics which goes into weather forecasting. One is stuff, if you don't know any like O-level physics, you may remember from school, Newton's Laws of Motion, there's Isaac Newton. And the second law of motion, force equals mass times acceleration. Hit something with a force and it accelerates depending on the mass of the object. So that's one. The second guy is Max Planck and he was the German founder of quantum physics, which is very much a 20th century physics. Of course, Isaac Newton back in the 17th century, so it's classical physics. Max Planck very much 20th century physics. And that's important for understanding how photons from the sun actually get absorbed by, you know, by the oxygen, by the water molecules. And indeed how they hit the, you know, when they hit the surface how they're absorbed. And indeed then how those photons are re-emitted back to space as much lower wavelength kind of heat energy, infrared energy. So that all has to be coded up into a model as well. And the third one is a guy that probably my guess is nobody will know, but if you think you know, anyone know? Big prize if you get it right. It's a guy called Rudolf Clausius and he actually was the person that invented the term entropy. If you ever heard the word entropy, he did it. But basically what we're looking at here is the second law of thermodynamics. So this is 19th century physics, you know, the original physics to try to understand how steam engines and such like work. Turns out the atmosphere is very much a thermodynamic engine. The fact, the reason we have those storms that track across the Atlantic and I guess what I was hearing often hit Glasgow on a Wednesday afternoon, is actually that is the most efficient way, those swirly things, is the most efficient way of transporting heat from the tropical latitudes to the poles. So you're actually looking at extremely efficient heat engine. The reason why that is is to do with the rotation of the earth and it's two, not enough times to say exactly why that is. But it is a fact of the matter, those weather systems are really transporting heat from, you know, a year or so ago I was on, a couple of years ago I was on the Today programme and they were worried that some storm had increased the temperature of the North Pole momentarily for a day or two. And the interviewer asked me, you know, is this disaster? Is this what the North Pole going to melt? And I said, no, this is what these storms are supposed to do. This is their function in life, is to transport heat to those high latitudes and then it escapes out to space. So this is perfectly normal. This wasn't the answer she wanted actually, but maybe I helped educate a bit. Now, you may have heard about quantum physics, very, you know, Schrodinger's cat and, you know, uncertainty principles and all that. So you might think that quantum mechanics is the most difficult part or the most uncertain part of a model. But actually it's not. The most difficult and uncertain part is to do with that first equation, Newton's second law of motion. So here is that equation again, so I'm sorry, this is getting lots of equations, but this is really, really its one you have to marvel at. Because this is a form of that Newton's law that is applicable to the atmosphere and the oceans and any fluid dynamical system. It's the thing which actually generates turbulence. And with about 23 mathematical symbols, you can describe, this equation describes everything in the world from the scale, the largest possible scales associated with jet streams, you know, which go across the Atlantic. They've got scales of tens of thousands of kilometres all the way down to, you know, the air coming out of my mouth and the turbulence in this room. It's all described these, you know, multiple scales of motion by that one equation. So that's pretty amazing. It's a work of arts and there's a work of arts of Renoir. But actually I'm not going to use Renoir as my analogy, I'm going to use a Russian doll. It's a Russian doll also a work of art. And this is a very special Russian doll, a Russian doll's unpack into smaller Russian dolls. This Russian doll unpacks into yet smaller Russian dolls and yet smaller Russian dolls and yet smaller Russian dolls and so on and so forth. And the analogy is that if I want to actually solve that equation on a computer, beautiful as it is mathematically, I actually have to unpack it. And it unpacks into literally billions of individual equations. And this is why solving this equation is so unbelievably difficult. And it's by far and away the most difficult part of a weather forecast model. The quantum mechanics and the thermodynamics is relatively easy by comparison. So technically all those Russian dolls, the biggest Russian dolls, as I say, could describe, you know, the jet stream, which is fairly, you know, it's kind of trundles across. Jet stream is a very large scale, sort of undulating river of air, if you like, up in the high atmosphere. And it's all coupled together to scales, as I say, it could be almost sub-millimeter scales. So it's a fantastic range of scales described by that one equation. But that's because that mathematics hides the fact that it's really billions of equations which have to be unpacked and solved individually on a computer if you really want a weather forecast. All right, but the problem is that even with today's computers, because they are, you can't represent such a range of scales. We can't go down to millimeter scales. So basically in weather prediction, climate prediction, you have to start chopping these Russian dolls, throwing them away, because it's just they're too many of them to solve. So here we are, I'm throwing the whole lot away. And typically you, well, if I'm running a climate model where I'm trying to predict what's happening, you know, 100 years from now, typically you can, you'll have to stop at about 100, the Russian doll that's about 100 kilometers in scale. Because if you put any more in, the computers just doesn't, you know, is too, isn't big enough. It'll take you, you know, if it takes you six months to do your climate forecast, it's not terribly useful. So, and it's certainly not useful. You're trying to attend a weather forecast and it takes six months. So that picture on the left is one of those big low pressure systems that trundles across, this is part of North America. That's pretty well captured actually by, so that's got a scale of maybe 1,000 or so kilometers. So that's covered by one of these Russian dolls, that's fine. But that's a thunderstorm cloud, and I saw some nice ones, nice angle clouds coming up today on the train. That would be too small. Those things only have scales of tens of kilometers. So we can't, but on the other hand, as I will try to explain a bit later, clouds are crucially important for understanding the climate system. So we have to represent them in some way, and they're represented by simplified formulae. So I've represented a simplified formulae by a rather inelegant block of wood, so compared with the elegant Russian doll. All right, so we're now in a position to have a look at what the world looks like from inside a computer. OK, so this is not a satellite animation anymore, it's a computer solving those equations, the Newton's laws of motion. And you can see on this global scale, it's certainly capturing the irregularity of the atmosphere, it's capturing those weather systems in both the northern and southern hemisphere. Pretty good, but if we blow up now to look again at that area in the tropical west Pacific, where all those thunderstorms were occurring, you can see it looks a bit more like it's sort of blobby, isn't it? It's sort of granular, it's like a puantillist type of painting, rather than you can tell, you know, you can instantly tell you're not looking at the real world here. Nevertheless, it does spin off, it can spin off tropical cyclones like that. But it's kind of not, you know, it's not quite right, and that is purely due to, you know, the fact that the computers are not big enough. OK, good. Right, so let's, with that as background, let's come back to Michael Fish and indeed Henshard of the mayor of Castor Bridge. And there is a Achilles heel, I guess would be the word to say, the phrase to say, in this notion of trying to predict weather in a deterministic sense, in the sense of saying it will be, you know, sunny, rainy, windy, the harvest weather will be good, bad. If you say anything very definite, there is a very sort of intrinsic scientific problem. And we call it these days the butterfly effect, and I think the phrase has now become pretty common currency. It was actually made, the phrase of the butterfly effect came from a book, a popular science book by a guy called James Glick, who was referring to some work which I'm going to talk about now by a colleague of mine from MIT called Edlerence, who's one of the pioneers of this so-called science of chaos theory. So let me introduce you to Edlerence and again some equations which you can just ignore or just marvel at if you like. Ed was, Ed worked at MIT, this is the Massachusetts Institute of Technology in Boston, and he was, he got interested in the problem of long range forecasting, forecasting let's say a month ahead, sort of thing Henshard wanted to do. And he had colleagues in the statistics department, by the way some of whom one person in particular was extremely eminent statistician. And this was in the days sort of in the 1950s let's say when computer models were just starting to be the sort of mathematical equations I was talking about, starting to be thought about and ideas about how to solve them. But these statisticians said look you're wasting your time with all this stuff, all you need to do is get a big pile of weather maps from the past. And if you want to know what's going to happen next month just look at this, just go through your big pile of weather maps and find a month where the weather patterns say around the northern hemisphere look similar to what they do this month. So they would say for example if it was today they would say okay let's suppose, what do we mean now November, so we want to know what the weather is going to be like in December. The statisticians would say okay maybe November 1948 was very similar to November 2018. In that case all you have to do to predict December 2018 is just see what happened in December 1948. So it's a method of analogs. So you know they were on at Lorenz day in day out he was very keen on the more the doing the mathematics solving the equations. They said no no you're wasting your time just use a bit of statistics and based on past data that's fine. And this bothered him because the implications of the statisticians ideas would be that the atmosphere was very kind of cyclical. You know it went what it's doing today is a bit like what it did in 1948. So kind of the ideas that goes through cycles and he had a kind of a hunch a remarkable hunch that that wasn't the way the atmosphere worked. It wasn't cyclical like that or periodic to be the slightly more precise word. So but he thought about how can I prove this and you know because of all the Russian dolls he couldn't solve the exact equations. So he looked for very simplified approximations to these underlying equations and he came up with this set which is basically the equivalent of three Russians. So he's paired one billion down to three Russian dolls and these three so each Russian doll is now an equation in science in the in the science of what's called nonlinear dynamics. These are three of the most celebrated equations that's ever ever happened. So you may not quite appreciate it but but these have sparked it's unbelievable what revolutions they have happened in the only in physics but in biology economics. Engineering chemistry every every branch of science you can think of these equations have triggered a revolution of of of understanding. And the basic property that these equations have one of the key properties is illustrated here. And what I'm showing you are two solutions of those equations which have almost identical initial conditions and starting conditions. And you see for a while they track the two solutions track each other but then eventually they completely decorrolate. Now people have thought that that sort of behavior could be simulated if you had a sufficiently complicated system. But nobody had imagined just with those three equations one could generate such behavior. So this is the phenomenon of chaos the idea that tiny tiny tiny infinitesimally almost infinitesimally small initial uncertainties can completely amplify and sort of destroy any confidence you'd have in what the system is going to do. So that was Laurence's work and he went on to I'm just going to show this because I need to refer to this later he but without again getting technical about it. One of the remarkable things he did was he realized I'm just going to let this animation go that within a sort of abstract space the space of the three Russian dolls the three equations if you like. The system traces out a remarkable kind of geometry which we now understand to be a fractal geometry. The fractal means whatever structure it has on a large scale and you zoom in it has that same structure on a smaller scale. And this shows the system kind of evolving around on this geometric structure. It turns out that this fractal structure is you know relates a lot to a lot of modern ideas in 20th and 21st century mathematics. And in some sense what Lorence did was bring he joined together the work of Newton because Newton had discovered the calculus Newton would have understood what those three Russian doll equations were very well. But he would never have guessed that they had this underlying intrinsic fractal structure. So that was actually one of them also one of the most important things that Lorence did which again has had enormous ramifications in in mathematics of its applications. But I want to go back now to Michael Fish because I just want to show you so that was with a with a rather idealized system but let's see what this means in practice. So what I'm going to show you now are two or the evolution of weather the weather from a kind of modern day computer model run from two. So you're going to see an animation of two weather forecasts run from two different initial conditions which are very slightly different from each other. So if you look very carefully you'll see differences. So these are pressure isobars constant pressure at the surface. And it's a couple of days before the famous Michael Fish hurricane. So that's a big low pressure system to the west of Ireland which is not you know I mean that's that's that's not an exceptional weather. That's that's a fairly I mean it's a kind of windy day but nothing exceptional. So we're looking a couple of days beforehand and we're going to run our weather forecast model from each of these initial conditions if I can get it to. Okay so here we go. So the model is taken those initial conditions and move them forward and now we're and now we're the day of the of the Michael Fish storm. So the top one if you look sort of the tip of bottom tip of Cornwall that's a little ridge of high pressure. Anyone making a forecast for that day would say oh it's going to be a pretty nice day. Certainly no strong I mean there's almost no gradient in pressure which means the winds are very light. But the bottom one has this you know these these several concentric isobars and just to the south of the center these are very very tightly packed which means very very strong winds indeed. So poor Michael Fish you know in those days he just had the one weather forecast from the Met Office and it more or less looked like the top one. So he he said everything's going to be fine. And of course if he'd had the bottom one you know which which but for a flap of a butterflies wings so to speak he might have had. He would have been a national hero and so on. Now actually the truth of the matter is you shouldn't feel sorry for Michael Fish. Because I met him a year ago at the Cheltenham Science Festival and I realized he's made an extremely good living from after dinner speeches on this storm. So don't don't feel bad about him at all. He's he's done absolutely fine. Okay so all right so what what could we do in that situation? Well let's imagine instead of running our model twice we ran it 50 times from 50 very very slightly different initial conditions. Each one consistent with whatever the observational network was at the time. So these are pressure maps of two basically two day weather forecasts from that done if you like retrospectively in 1987 using a modern weather forecasting system. And you can see maybe the British Isles are you can see the British Isles right there in each one of them. You can see there's a phenomenal sort of range of of of weather maps. Is this a doesn't look okay. Well let me take the very first one the top left. I mean there's not much going on there. The second one. Oh great. So that one that's our ridge of high pressure. That's a really nice day. Certainly I don't know. In the south of England it's a nice day. Maybe not. Anyway you know what I mean. Whereas these ones of course all these ones with these enormous great low pressure systems are horrendously awful days. So this is actually a remarkable range of situations. So how the question is how would you synthesize all this into something because you can't give you know if the weather forecaster had to give 50 weather forecast. You need a half an hour slot instead of like a minute before the news. Well one way to do it is to is to try to calculate probabilities. You can think of this as a distribution of 50 possible potential realizations. You could say well how many in how many of those were the winds of hurricane force. And if the answer was well as you see here it's 30%. So 15 or something 15 out of 15 out of 50. If 15 out of 50 had hurricane force winds then you would say there was a 30% probability. So these are actual now maps. This is a contours rather of colors if you like showing not wind force but the probability that the winds will exceed hurricane force on the 16th of October 1987. So that's what he could have had had we had that technology then. This is what he could have said that there was a significant risk of a hurricane. I mean again we don't can't say for certain. So what would you do with this information? I mean let's say some of you maybe if you were living down in Kent at the time and you just cashed in your pension saving to buy a new Lamborghini. Which I hear is what people do these days. Then perhaps it wouldn't be a good idea to leave it parked outside under a big oak tree for example 60% probability. Or if your wife had just bought you a yacht and you were planning to sail across the channel. 30% probability of a hurricane may be a good idea to not do it right. Wait a few days and see what happens. The important point here is that the decision well let's make so that was a bit facetious. Let's suppose this was a hurricane. Well it is a hurricane actually but in the sense of a hurricane about to hit the Caribbean or Florida or something. How high a probability and you're the town mayor. How high a probability does it have to be to before you evacuate people. Now obviously that's not a decision a meteorologist can make. But a meteorologist can give the town mayor the information to make that decision objectively. So having a probability, I mean if the probability was 1% you probably wouldn't evacuate because it means 99 times out of 100 the event wouldn't hit. But if the probability was 99% then you probably would evacuate because 99 times out of 100 it would occur. But the question is where is the dividing line between recommending evacuation and not recommending evacuation. I don't know as a meteorologist I don't know where that dividing line is. It's something which you have to discuss with the person who has to make the decision and they have to know about what the upheaval is for evacuating. But at least this type of method provides the objective information to make that kind of decision. In other words it's an objective method of formulating the uncertainty in the prediction. I just want to go back to this more abstract Lorentz model just for a minute because it makes the point that you might get the idea that therefore okay forecasting, whether forecasting is hopeless because you're always having these butterflies which amplify and ruin forecasts. It turns out that actually the situation where they grow so rapidly that within two or three days they destroy the accuracy of a forecast is extremely rare. Actually that point is demonstrated even with that simple Lorentz model with the three Russian dolls. What we're looking at here is a kind of little ball of uncertainty in the starting condition. For some starting conditions like this one there's actually no growth at all in that uncertainty so it remains remarkably predictable. You move down a little bit and then you start to see some indication of uncertainty. It's this one where the uncertainty just explodes. For any sort of cognoscent in the audience this is a consequence of what's called the non-linearity of the equations of motion. Now the point is when you have this ensemble idea, when you run these 50 forecasts, which is basically what we do today in a weather forecasting organisation like the Met Office or European Forecast Centre where I used to work for a number of years, so we run these forecasts every day and if you look say a week ahead in many situations it's actually like this and you can say with some confidence what's going to happen a week ahead. Some of the time it's like this where there is some significant uncertainty and other times you can say virtually nothing if you like or very little because the uncertainty has exploded. Now they don't tend to show these ensembles very much on the TV but you often hear the forecasters talk about uncertainty which is I think a great step forward since Michael Fisher's day. They say when things are uncertain and when they say they're uncertain it's basically because these 50 forecasts are not giving a consistent picture, the front has moved on in some of them or stayed behind in other ones so the forecasters just don't know exactly what's going to happen. If you were a fee paying customer to the Met Office you would get more tailored probabilistic information and indeed for a lot of users these days that actually turns out to be quite important information. So ensemble forecasting has now even got its own, I mean this is basically something I have worked on for many many years now and I was pleased to see nothing to do with me, it's got its own Wikipedia page. And of course it's not just storms hitting the UK, this is an ensemble of 50 forecasts of Hurricane Sandy. This was an important forecast because you can see some of the ensemble members had the tracks going out over the ocean which is the normal way a hurricane does move if it goes up from the Caribbean due north it tends to get steered out to sea but in this particular case this is like over a week ahead from the actual landfall. You can see a significant number of the ensemble members had it tracking back over the east coast. Again a lot of uncertainty where actually it would hit at this range when it was in the Caribbean but it gives the people on the east coast the first warning that this is something they may need to start preparing for. By contrast this is Typhoon Hyann which caused utter devastation. It actually broke some records for the strongest wind strength for a typhoon after it had hit land and caused utter devastation for some areas of the Philippines. Indeed it was a frustration to me having seen how predictable, this was known about, again this is a forecast from a week or so ahead that it was hitting this area. It's a frustration to me when I see emergency services only start reacting to these events once the hurricane has hit and certainly something I'm trying to get disaster preparedness agencies to really change is the way they work and where things are pretty certain like this to start becoming proactive, getting emergency food and medicine and shelter and so on and water in place before the damn thing hits. Then those of you who may have heard of this thing called the El Niño it is an oceanic phenomenon in the Pacific Ocean and it allows us to make forecasts of the general patterns of weather particularly in tropical latitudes on seasonal timescales so three to three, six months ahead. This is a so-called El Niño index, this is right up to date. It's nothing actually very interesting but it just shows that the El Niño sea surface temperatures in the eastern Pacific are going to remain probably above average but there's some uncertainty about whether, if they get up to two degrees that's quite a significant change from the normal climatological sea temperatures but it just shows again a plume if you like of possible outcomes. With that under our belt I want to move to the climate change issue and address the Charles Moore question about does uncertainty in weather prediction invalidate our use or our ability to predict climate change? So climate change as you're probably aware I guess is the question about what is the consequence of this curve and this curve is a measurement of the carbon dioxide content of the atmosphere. It's done at an observatory in the Hawaiian islands but carbon dioxide is a unlike say water vapor or something, carbon dioxide is a very well mixed gas so if you measure it here in Glasgow it'll be almost the same anywhere else in the world. So measuring it in Hawaii one can infer pretty much where it's going to have the same value pretty much everywhere. First of all there's this wiggle up and down which is the annual cycle so it's the fact that in summer plants take in carbon dioxide from the atmosphere to grow so atmospheric concentrations dip a little bit and then in winter it goes out again. So this is winter to summer cycle but on top of that there's this gradual upward trend and this is due to our mankind's emission of carbon dioxide due to burning of fossil fuels so fuels of carbon that was laid down millions of years ago typically below ground. And if you go back to pre-industrial times so to back into the 19th century the value is at about 285 parts per million and we're now significantly over 400. This is actually not completely up to date, this is only 2016. So it's up, it's well above 400 parts per million. And the question is what is the consequence of that? Now let me first of all show you a couple of analogies to climate change. I'm going to first of all go back to this model that Edelorentz came up with to demonstrate the chaos theory if you like. And I think I forgot to put a slide in. I should have first had a slide which showed what would happen if you ran the model. What I'm doing is I'm putting an extra term in here. This F stands for sort of a climate change term. Without that term what I should have shown you is that this model, the time series I guess I showed you a little bit when you ran the model just for a little while it jiggles up up here or goes down here. If you run it for a long period of time then the time it spends up here is the same as the time it spends down here. But when I've added this term here it kind of biases the system so it's spending more time up here than down here. Now I'm going to show you, because I forgot to show you an important slide I'm going to now move very quickly to another analogy which makes it exactly the same point as the Lorentz one. This is a much more mechanical analogy. This is the executive decision maker as it's often called. It's a pendulum which I'll show you the animation. It's a magnetic pendulum and it oscillates irregularly around these four magnets. The idea is if you have to guess which magnet it will eventually stop on and you buy a million shares if it stops there and you sell a million shares if it stops there or something like that. But what I want you to think about as it's oscillating is that this now represents the state of the atmosphere if you like and it's going between, it could be warm or let's say warm or cold states or wet or dry states. So these four magnets, think of them as definite types of weather states. What we're going to do is animate. So it's actually an example like the Lorentz model of a chaotic system in the sense that trying to predict the motion of that pendulum bob depends very, very critically on knowing the initial conditions. So a very slightly different initial state will lead to a completely different trajectory of the pendulum. So it's kind of a mechanical analogue of a chaotic system. It happens to have stopped over the yellow magnet. All right, so that illustrates in a way why it's quite difficult to predict the sequence of weather states for let's say a few weeks ahead, whether it's going to be warm, dry, wet, cold. Because if I started the pendulum bob very slightly differently, it would track in a different way. However, if I looked at this long enough, I would realise that on average the pendulum isn't favouring any of those four magnets. It spends on average a quarter of the time over each of the four magnets. The probability, you could say at any instant in time, the probability of being over the blue magnet is 25% over the yellow one 25%, white one 25%, red one 25%. So they're all equally likely. But what I'm going to do now is I'm going to sort of bias the system by sliding a little wedge underneath. And now off it goes. Now again, as before, it's completely chaotic in the sense that the trajectory would be very difficult to predict because it depends very, very precisely on the initial condition. But you can see how it's favouring, even though it makes an excursion to that white one, it's clearly favouring the yellow magnet. But in fact, does it stop there? So what I've done is to bias the statistics by sliding the wedge. And in this analogy, the wedge is our emissions of carbon dioxide. So we're biasing the statistics of weather in some way that we have to determine by the emissions of carbon dioxide. And the fact that the system is chaotic, the fact that you can't predict the detailed like here, you can't predict the motion of the pendulum, doesn't stop you from estimating the changes in the probability of each of those magnets, the occurrence of the pendulum bulb over each of the magnets. Now, so what I'm trying to say here is that climate change, in a way it's not, in the some sense, it's not any different to predicting the difference between winter and summer. The difference between winter and summer is due to the orbits, the tilt of the earth as it circles around the sun. So the sun provides a well-known, a completely predictable forcing to the atmosphere. And in some sense, you can say that the changes in the statistics of weather between winter and summer are pretty robust, even though we can't necessarily say what any one particular summer will be like if we start from a wintertime initial condition. And indeed, as you transition from winter to summer in a particular year, you might actually go into, in February, or something into a cold snap where you think your sun's had two months of coming up higher in the sky, and then suddenly we've gone into this cold snap. Well, okay, that's one particular year. But if you took 100 years and put them all together, put all the temperatures together, say for Glasgow or London or anywhere, you'd see a very nice smooth curve of the transition between winter and summer. And it's really that, you know, it's what that sort of expected change in the statistics of the weather. This is the nature of the climate change problem. And it's not something, therefore, that is sensitive to initial conditions. So Charles Moore, unfortunately, got it wrong. He misunderstood, if you like, the nature of the problem. But that actually doesn't make predicting climate change an easy problem. And you could say, basically, the problem is how thick is the wedge. And I want to say what I mean by that in a bit more detail. Because there are things which can amplify or indeed damp the effect of increasing carbon dioxide. So carbon dioxide, I think you will know, is this greenhouse gas. It traps, it's transparent to the visible and indeed ultraviolet light that comes in from the sun. But it's opaque, relatively opaque, to the infrared energy that the Earth radiates back to space. Because the Earth's temperature is much lower than the temperature of the sun. So it radiates photons at a much, with a lower temperature, longer wavelength. That's the quantum mechanics. But it's not as simple as that, because there are certain processes which can and do indeed feedback. So one example is water vapour. So water vapour, just to be 100% clear about this, water vapour is the gaseous form of water. So when you look at the atmosphere on a nice clear day with no clouds, there's still water vapour in the atmosphere. But water vapour is also transparent to incoming sunlight. It's not blocked by incoming sunlight. But it also is very opaque to the outgoing infrared energy. In fact, the Irish physicist John Tyndall back in the 19th century realised that without this greenhouse effect from water vapour, human life and indeed biological life would not exist on the Earth. The warming from water vapour is crucially important in keeping the Earth at an equitable temperature. Now, as I guess everyone knows, if you warm the atmosphere, you can evaporate more water into it from, say, the oceans. Or conversely, if you cool the air, its ability to hold water vapour that has been evaporated from the oceans becomes less. So that's why in the autumn you get very foggy days, because it cools enough overnight that the water vapour condenses into small droplets of water, which are the fog. So if you now increase calm dioxide, which has a warming effect, that can be amplified by the additional effect of the increase in water vapour. So you get additional evaporation of water, and so you've increased water vapour. And now water vapour is the greenhouse gas, so that will add, if you like, to the already warming effect of carbon dioxide. So that's a pretty well understood what's called positive feedback process. So it's something that will amplify, and it's probably one of the most important amplifiers. There are other things I've shown, for example, this little piece of melting ice in the Arctic. And that's, again, another well-known positive feedback, that if you have a region of the Earth covered in ice, which is basically white and reflects sunlight back to space, and then that ice melts, it leaves a much darker water, the surface of the water is much darker, and that water can absorb sunlight. So the melting of ice will also amplify the warming effect. You've probably heard about methane. Methane is another greenhouse gas that could be released from things like tundra and permafrost if it melts. But the carbon cycle, carbon is absorbed, carbon dioxide is absorbed particularly by the oceans, and if you start to warm the oceans, their ability to absorb carbon dioxide decreases. A bit like a bottle of Coca-Cola, if you warm it up, suddenly it can't hold all that fizz and it spills over. But the 64, I would say, trillion dollar, literally trillion dollar question, which we don't understand well, is the role of clouds themselves. And that's because clouds have a kind of two different roles, depending on how high in the atmosphere they occur. You're probably familiar with what are called cirrus clouds. So these are the very high-level, wispy, basically ice-type clouds that you typically have if you have very anti-cyclonic weather. These cirrus clouds actually trap heat. They act, again, as a kind of blanket on trapping heat. Very often, if you have a night where you have cold temperatures and it looks like there'll be a big frost in the morning, and then actually a layer of cirrus cloud comes overhead, that will actually stop the frost from forming. So it has a kind of blanketing effect. So if climate change is to will increase cirrus clouds, that's bad news, because that will be a positive feedback that will further amplify this blanketing effect. On the other hand, low-level cloud, what's called stratus cloud, which is very common of course in winter, blocks of sun completely, stratus cloud reflects sunlight back to space from the top of the cloud deck. So increasing globally the amount of low-level stratus-type cloud will actually have a damping effect on climate change. I have to say, unfortunately, most of the models are going in the wrong direction. So they have cirrus cloud increasing and stratus cloud decreasing, which is really absolutely the wrong direction for what we would like. But having said that, because all of these cloud processes are represented not by the beautiful Russian dolls, but rather in elegant approximate formulae, there is considerable uncertainty about this, and I would say that is the single most important element of uncertainty. I spend a lot of my time trying to persuade the government, well, EU government, so I don't know how long that will last, but anyway, to invest in yet bigger supercomputers because if we can really get these Russian dolls down to the scale of clouds, then that will really help understand this majorly uncertain process in the climate system. OK, so I'm going to... I've just got... I can't remember what time it's at, but if I can just give a few more minutes. Actually, I need to take some advice from whoever my introducer was. Oh, you're there. When would you like me to stop? About 10 minutes. 10 to? OK, great, fantastic. Right, so that just gives me time to just do a couple of quick things. So I just want to talk about the word consensus because you often hear, perhaps you hear on the media and so on, that there is a scientific consensus about climate change, and people often misunderstand what that word consensus means. What is it scientists are agreed about? Because what they're not agreed about is a specific amount of global warming. So this is a graph, or a sort of distribution, if you like, which tries to estimate how much warming there will be, global temperature, if you double the amount of carbon dioxide in the atmosphere. So if you went from 285 to 560 parts per million, we're sort of well on the way to 560, we're over 400, so by the end of the century we're probably up to 500 or more parts per million. How much will the earth warm to get back into some equilibrium with that doubled amount of carbon dioxide? And because of these uncertainties that I talked about, particularly clouds, the answer is actually not a particular number, but a probability distribution. So along the x-axis there's an amount of warming, 1°, 2°, 3°, 4°, 5°, 6°, 7°, and the vertical scale is a probability. So the most likely warming from a doubling of carbon dioxide, you probably can't read the number, is about 2.5°, but the really important, I think, point is that there's this tail, if you see it, the distribution is not symmetric about the maximum, it's what's called skewed, and there's this tail out to 4, 5, 6, even 7°, which can't be ruled out. That's where all these feedbacks line up in a bad way. Now, if we... I mean, the consensus is once you get past about 2°, then you're in the region where things really are dangerous. If you're talking about 4, 5 or 6°, this is utterly catastrophic. This really is catastrophic climate change. In every sense of the word, sea level rise, storms, droughts, the ability of the human body to actually lose heat, places most large parts of the world with that sort of warming, human beings literally cannot survive because they can't lose heat. But the point is that the consensus is not about a particular value, it's about that distribution. It's about the fact that we can say quantitatively what we think the probability is that the warming will be, say, greater than 2° or greater than 3° or greater than 5° or between 3° and 4°. Whatever you want, there's a probability. That is that probability distribution that is where there's this consensus. So you see the theme of my talk, whether it's weather forecasting or climate, is about thinking in terms of probability. Now, the point about saying this is that people who will claim... Now, it could be at one end, it could be an environmentalist who say climate change will be catastrophic. It will be catastrophic. If somebody says that, they're not being scientifically rigorous, they're not being credible. But similarly, somebody that says, I don't know, it's a hoax, or, well, you know who says it's a hoax, but... Although apparently he doesn't say this anymore, but anyway he used to. But more seriously, there's a group of people, Nigel Lawson, Matt Ridley, others from the so-called Global Warming Policy Foundation who will say, oh, yeah, well, yeah, yeah, yeah. I understand, you know, the greenhouse effect and all that stuff. But it's not, you know, in the big scheme of things, it's not a big deal. It'll be, you know, Luke... It's Lukewarm. It's a Lukewarm problem. So they're banking for something on the far left-hand side of that distribution. Well, again, that is just being inconsistent. It's not scientifically rigorous to say that. I'm just as critical of the, you know, it's going to be a catastrophe as it's going to be Lukewarm. But the point is, whatever, if you say something specific, then you're wrong. That's not, at least that's inconsistent with our understanding. All right, so just in three minutes, because I'm desperate to get this last point out, how do you actually make decisions under uncertainty? So I want to just think about for a minute. You are adviser to Fred, the ice cream seller. And the amount of ice creams that he sells is proportional, well, it depends on the temperature of the next day. Now he has to stock up the day before with ice cream. So you have to advise, your job is to advise him on how many ice creams to stock up. So there's what an economist would call a utility curve. It tells you, for a given temperature, this is the number of ice creams or the expected number of ice creams sold. So for example, if it was 25 degrees, you'd sell 70 ice creams. But notice how the shape, it gets steeper on the right-hand side. So as it gets above 25 degrees, the number of ice creams really takes off in a big way. But as it gets less than 25 degrees, the number of ice creams is not quite so sensitive to temperature. OK, so on a day, though this is now the forecast, and that blue line is a... See, I'm trying to educate you about probabilities, the probability distribution, right? So it says that the most likely temperature forecast is 25 degrees, but it sort of could be a degree or so either side of that. Well, that's quite easy because you can estimate where the uncertainty is very small. It's pretty much the same as just reading off the value at the maximum probability, which is 25 degrees. So in that situation you can sell, Fred, you're probably going to sell 70 ice creams. But consider a situation where there is a lot more uncertainty. So now we have a distribution, again, the most likely temperature is 25 degrees, but it could be as much as, I don't know, 30 degrees or as less as 20 degrees. So now what do you advise Fred to do? If you're just going to tell what's very uncertain, you'll be fired. So you've got to do something a bit more positive than that. So if you're a statistician, you can actually calculate how many, given that distribution, how many ice creams you can expect to sell. But the important point about this is that because of the shape of that curve, the red curve, for every degree to the right of 25 degrees, you're going to sell a lot more ice creams than the number fewer that you would sell if it was one degree cooler. So there's a kind of an asymmetry. So the fact there's a chance of it reaching 30 degrees means there's a chance of a really phenomenally large number of ice creams sold. But on the other hand, if it's less than 25 degrees, that's not going to have such a radical impact on the number of ice creams sold. And in fact, what you can do is estimate the effective temperature. Given that uncertainty, you can say actually the amount of the expected number of ice creams sold is as if it was 28 degrees. So you can tell Fred, what you can tell Fred in that situation is, although you know the most likely temperature is 25 degrees, because of this big uncertainty, you can say plan for it to be 28 degrees and that will give you 120 ice creams sold. So you can actually make a sort of rational decision process under this situation of uncertainty. And when you have this sort of skewed nature where there's much more, the rate of increase is much larger when you get to the right of 25 degrees and 20 degrees, telling him that he will sell 70 ice creams, which is the most likely value, is actually not the right information to give him. Now, the reason I'm telling you this is that this translates directly into issues about climate change. The most likely effect of a temperature rise to a doubling of carbon dioxide is about, as I say, about 2.5 degrees. And based on econometric models, I've been working with Chris Hoek from Cambridge. You can estimate global impact of global GDP is about $120 trillion, which is quite a lot, but it's much less than taking the whole distribution into account. And again, the reason is that when you reach four or five degrees, the impact of GDP is so much more than going on to the colder side. There's a kind of an asymmetry. Those are the utility curves. It's a bit like the Fred's ice cream, but of global GDP impact and temperature rise on global GDP as a function of temperature. And in fact, you can say, I mean, one way of saying this to a politician is to say what we should really see the effective temperature, what you should plan, even though the most likely is 2.5 degrees, you should be planning as if it was almost four degrees, because the impacts are so much larger to the right of that curve. All right, so I'm done. So I've rushed a little bit that last point, but I hope you just get... So why do weather forecasts go wrong? Well, the weather is chaotic, and sometimes, but certainly not always, sometimes can be very sensitive to small initial errors. So what can we do about it? Well, we've developed this idea of what's called ensemble prediction. We can do it because computers are big enough to allow us to run 50 forecasts every day. And so now we can know ahead of time when we can be confident about the future weather and when we can be cautious. And as I say, you hear that on the BBC weather now. They say there's uncertainty. There's uncertainty because the ensemble has got significant spread. Does this all mean that reliable climate change predictions are impossible? No, predictions are not chaotic like weather forecasts, but they are uncertain, and they're uncertain because of these feedbacks, particularly with clouds. So the issue for people like you to decide on is whether you think the risks of dangerous changes to climate are large enough to warrant mitigating action now. It's no different to deciding whether to park your Lamborghini under the oak tree or not. Seriously, it's absolutely no different. Mitigating action means, you know, mitigating action means cutting our carbon emissions and that comes with some economic costs. So the issue is, is it worth taking those economic costs now if it will reduce the risks of dangerous climate change? Just as I can't tell you whether to park your Lamborghini under the oak tree, in a way I can't tell you either whether you should, whether these risks are large enough or not. However, I would say this, uncertainty should actually make us be more cautious about the future and not less so. And the reason for saying that is that tail, the fact that we cannot rule out this tail at four or five, six degrees. And this is the tail where, you know, the Greenland ice sheet completely melts, completely disintegrates. It's where humans in large parts of the tropics physically cannot survive because the combination of temperature and humidity is too large. It's where storms just become unbelievably intense due to the extra water in the atmosphere. So that is the risk of doing nothing. But ultimately it's of course individual's decision about whether that risk is worth taking or not. So that's my talk. Thank you very much indeed.