 OK, atantio'n... OK, we're starting. The real earth has seasons. This is actually the top of the atmosphere incoming solar radiation as a function of obliquity. So, latitude here. Top of the atmosphere insulation for varying obliquities. Earth is not on here. Earth is 23 or something. I'm not very good with the real world sometimes. It's 23. So, of course, zero obliquity is this line here. As you increase the obliquity, it's rather interesting. Perhaps it's easier to understand this one more. This is the incoming solar radiation at solstice when the sun is overhead at the latitude of obliquity. So, if there's no obliquity, of course, you still get the same plot, most incoming solar radiation at the equator as you increase the obliquity. You get more and more incoming solar radiation coming in at higher and higher latitudes. When the obliquity is 90 degrees, then, of course, the sun is overhead at the pole and the pole gets very warm. And you get a reverse temperature gradient. You don't need much obliquity in order. So, here, the obliquity is 30 degrees. When the obliquity is 30 degrees, which is not much more than today's obliquity, then, in summer, you have more incoming solar radiation at the pole than you do at the equator, even though the pole is further from 30 than the equator is from 30. But the length of the day is much longer. So, you have to take that into account. And then perhaps a little bit more surprising is that when the obliquity is actually above 54 degrees, it turns out, then, on the annual mean, you get more incoming solar radiation at the pole than you do at the equator. So, if you've got... So, even with our... I mean, the obliquity is about 23.5 or something like that. And it has varied slightly over the millennia, not so much, but a few degrees here and there. And the variations in the obliquity are thought to give rise to the ice ages. That's the famous theory of Milutyn Milankovic. It's interesting. It's still a little bit of an unsolved problem. Most people think they've solved the problem as to how the actual variations in obliquity rise to the ice ages. But they seem to do so. Mars has had very large variations in obliquity over the past few billions of years. It's about 30 degrees now, I think. A bit less. It may have been as large as 60 in the past because Mars is closer to Jupiter. And it's the other planets that should give rise to variations in obliquity. But nonetheless, even with our current obliquity of 23, we get finished long seasons. So the basic upshot of that is that we get... The highly cell is not centred. The equator, if this arises in the summer hemisphere, is a rising motion, essentially the ICCZ. And you get a much stronger winter cell and a weaker summer cell. And there's a corresponding theory for that. Again, there are many theories for this. The theory most related to the held-how theory for the seasonal case is that Linzen and Howe was a student actually at MIT in the late 70s. Did a lot of this. And of course it becomes... I don't know whether Simone will talk about this or not, but part of it is that this, of course, is not a steady state. The seasons are going back and forth. Essentially, the back and forth of the winter cell in the summer cell are the monsoons, in a sense. We shouldn't separate them too much. But the monsoons tend to be concentrated in various regions like India, Southeast Asia, a weak monsoon in Arizona, even because of the influence of continents. But we probably shouldn't think of the continents as causing the monsoon any more than we think of the convection as causing the hadler cell. But nonetheless, if we didn't have the continents, the monsoons would not be like they are today. But I won't talk about that at all. Good. OK, so I'll lead in to the main events. So, and Helen, sorry, Linsen and Hal, did this various... It's more or less the same kind of theory, except now the air is rising off the equator. And they go through the mathematics and they get the same kind of... This is the temperature in... Well, let me have a look. This is the angular momentum conserving temperature here on the equilibrium temperature. So, it's... I would say this, getting into the off equatorial hadler cell, you're getting into sort of coen research as to... And people disagree about the very similitude of the Linsen and Hal theory. I would say that the coen's opinions of the Linsen and Hal theory is quantitatively wrong, partly because it doesn't take into account the unsteadiness, the fact that the seasons are shifting back and forth. It assumes that we're always in a quasi-steady circulation. But the winter hadler cell is more or less angular momentum conserving. So, you get this much stronger winter cell here and a weaker summer cell here. And, well, at least the experiments, some of the experiments which we've done in our group with Ruth Geane, who'll talk about it next week, tend to show that the winter cell is a little bit more angular momentum conserving and follows the theory of Linsen and Hal, which is a variation of the Hal and Hal theory. But the summer cell, which is this guy, really doesn't behave in any shape or form like an angular momentum conserving cell. It's really, this cell is really, if you will, driven by the effects of biotinicalities as high latitudes. I'm going back and forth over the seasons. So, as the seasons progress, I should really have a movie of this, shouldn't I, if I was adept as Brian is. As the seasons progress, this would shrink and become the summer cell. The summer cell would become the winter cell and the regime would change from being angular momentum conserving to more of an edit-driven cell. And that's the progression of the seasons. Here are some numerical simulations just to show kind of thing. This is with a dry model. Simulations by Alex Patterson, who's in our group in Exeter. This is a three-dimensional model, full model. This is the stream function, the temperature. Uh-oh, I think I have, this is the problem with talking too long. I did something, some batteries. Let's see if these work. Obliquity is zero. This is the stream function and temperature. This is the annual mean. At the high, obliquity, 60 degrees, you're actually seeing warmer poles than you are than at the equator. So it's kind of interesting. But bizarrely enough, surprising enough perhaps, you're still seeing on the annual mean a similar structure with hadler cells close to the equator and ferrule cells on either side. Is that forcing and then you're taking the annual mean? No, no, no. Seasonal forcing. So this is a dry model with a, but a seasonal varying forcing following astronomy. What is this? This is the actual simulation. This is the actual circulation at solstice. So this is the winter hemisphere. This is the summer hemisphere. 30 degrees obliquity, 60 degrees obliquity, very warm at the pole. More or less dominated by a single hadler cell when you get to high obliquity. Hardly any. There's now the ferrule cell, nor is there a summer hadler cell. Just one single hadler cell. Interestingly enough though, the hadler cell does not, still, I'm quite understood this, as to why the hadler cell is not really centered more. It's not centered anywhere close to where it is hottest. It's still concentrated fairly at low latitudes. These are actually zonal isometric runs now. We take the, we get rid of all three dimensional effects and just have a zonal isometric planet, sort of as in the original conception of Hadley. And how and held, I guess if you want to make a contribution to the Hadler cell theory you should change your name to begin with an H. You know Hadley, how. So if there are any H's in the audience, you know what your career should be. This is 60 degrees obliquity. So that suggests a strong inter hemispheric. Yes, strong inter hemispheric Hadler cell indeed. Yes, rising in the summer hemisphere, sinking in the winter hemisphere. But it's still, I mean this is, it's interesting that this is a three dimensional simulation. So this is the zonal isometric simulation at high obliquity. It's not all that much difference because you're not getting middle latitude eddys which give rise to the main differences because you're not getting bioclinic instability. Why don't you go to 90? Oh, we have that, I'm just not showing it here. Sorry. Yeah, we've done it at 92, I just don't have those figures. Sorry. No. The answer is no to all your questions. Well, it would be Linsen and How really in that. Actually, it doesn't work terribly well. We've done some comparisons which is part of the reason for doing it dry between this and Linsen and How and Linsen and How doesn't work terribly well. I don't know. I'd have to... The thermal, well... No, there's no necessary contradiction there because you can imagine rising here, moving that way, and then you will get easterlies because the angular moment... Oh, I think you shouldn't think about the annual mean is the answer to that. Yeah, but Health and Who? Health and Who is an annual mean theory, yes. But when you have high obliquity... Are you conserving any questions? And yes, there's going to be easterly wins. I'm not even going to... going down the annual mean path for high obliquity is... I think you're thinking about it the wrong way. I think you need to think about it separately for the seasons and average them. Yes. Actually, I haven't done that experiment, but it's a good experiment to do. They don't look the same. Yeah, I can imagine. Yeah, I imagine they don't look the same. Yeah. Yeah, okay. Yeah, yeah, I don't... Well, Health and... Yeah, Health and How breaks down, yes. Indeed. It's not going to work. And I think... I'm in agreement with... I would have... Pardon? Yeah. Even with a dry model, I think they'd be different. We may have done that. If we haven't done it, we should do it. It's a good... It's a little bit hard to do it with a dry model. We're not set up for that here. But I'll mark it down. Thank you. Just another little problem with Health and How, by the way, is that the zonal wind is discontinuous in the Health-How theory. It increases, and then it... to the edge of the heartless cell, and then it drops discontinuously until you get the... the radiated equilibrium wind. The... It's interesting if... the Health-How theory, or the angular momentum conserving theory, perhaps seems to actually do better when you slow down the rotation. So this is actually the plots of a fast rotating earth, a fast rotating planet, slower and still slower. And the winds, of course, don't increase as much with latitude when you slow down the rotation because... because omega A is much... is less, the velocity, the angular momentum conservation has the wind going like omega A, so it doesn't... So the prediction of the theory is that the... heartless cell extends much longer, much further, and it's actually quite flat. The temperature gradient is quite flat at low rotation rates, so you don't get baroclinic instability. The planet isn't rotating fast enough to give you baroclinic instability. So that if you actually perform simulations at low rotation rates, this is earth, this is earth with... a tenth of the rotation, this is... I shouldn't say earth. A planet with one tenth of the rotation, this is one hundredth of the rotation, which is approaching Venus. What we're actually plotting is the angular momentum, M, normalised by omega A squared, subtracted by one. So essentially, where it is all white, it's conserving angular momentum. And the three plots, well, look at the top plot really and the bottom plot. This is courtesy of Greg Collier, also at Exeter. The zonally symmetric model is actually conserving angular momentum, and it's all the way to the edge of the heartless cell or nearly conserving angular momentum all the way to the heartless cell. So the heartless cell is pushed almost all the way to the pole here. And there's the overturning circulation. So it is obeying the predictions of the theory qualitatively. The heartless cell is extending further and further. Another phenomenon which then appears in the three-dimensional model is you get super rotation. Super rotation meaning that you get a strong jet at the equator at high altitudes. So here, the air is going around much faster than the planet's surface. In fact, that also happens in Venus. In Venus, you've got winds well over 100 metres per second at high altitudes at the equator. The planet is rotating incredibly slowly. It's a sidereal day, the rotation rate is one-two-hundredth of the Earth. So one can almost wonder on Venus how the winds even know that the planet is rotating. It's going so slowly. But if you take this, it's interesting, again I haven't shown it, but if you take omega A to be, the rotation rate to be one-thousandth of the Earth, it finally collapses. The winds finally collapse. And the heartless cell gets pushed off kind of all the way to the pole and the winds entirely collapse. Maybe I've got a plot here. Oh yeah. The winds still haven't quite collapsed of the rotation, but they're almost there. Anyway, it's kind of interesting to think that these angular momentum conserving theories and going back to Schneider and Venus only has a three degree of liquidity. So it has no seasons to speak of and it's rotating very slowly. It's kind of interesting to think that these angular momentum conserving type arguments probably apply better to Venus than to Earth. So there we go. And here's the overturning circulation. Oh, and here's Venus. Here's the meridional winds on Venus. So say look at this, the left hand picture, meridional wind is zero more or less at the equator. The positive in the northern hemisphere to about 60 degrees and about 60 degrees also in the southern hemisphere. So we've got a heartless cell pushing out on Venus to about 60 degrees where it stops. If you apply the theory in our simulations, it actually, we would expect it actually to go even further forwards than 60 degrees. But it doesn't. The real Venus stops at about 60. And here's another set of observations of the meridional wind. Here going to about 45 or 50 degrees. OK. That's the end of the heartless cell. More or less. I want to talk a little bit about tropical dynamics. Or keep on talking about tropical dynamics. It's rather funny actually thinking about the heartless cell because somehow heartless cellers, there's another branch of tropical dynamics when you go to the tropics, what you think about, if you actually go there, you're not thinking, oh, this is a heartless cell. You know, where is it? In fact, if you look around you, what you see are, you see, towering cumulonimbus, going up 12 kilometers, you feel the moisture. You're sweating like crazy, but it's not evaporating so you're getting hotter so you sweat more. And then you think of the trade winds and so on. So you don't think of the heartless cell. So the whole branch of tropical dynamics, which isn't to do with the heartless cell. OK. Yes, a complete change. I'm going to think about radiation for a minute. I just want to explain why we have a tropopause. And the main thing I want you to get, there are two things I want you to take home at the end of this lecture as to why we have a tropopause, and they're both what it is not caused by. It is not caused by ozone. We have ozone absorbing heat in the sodosphere, so you might think or be told that temperature starts to increase in the sodosphere and it's falling in the troposphere and where it turns around to increase because of ozone. That's the tropopause. No. Ozone certainly affects the tropopause. It doesn't cause it. The other thing which you might hear, you don't really hear it often, so these are kind of straw men, is that convection goes up and where the convection stops, that's the tropopause. Well, it sort of is, but why does the convection stop there? It's because the tropopause is there. It's not. So all of these things have to be consistent, but there's no particular reason why the tropopause should be at 10 km. In fact, we'll look at Venus again towards the end. The tropopause on Venus is at 60 km high. Venus is quite similar in some ways, apart from the rotation to Earth, but okay, so just radiation, just a little bit about radiation. Imagine we've got some incoming solar radiation here, outgoing solar radiation out here, and some of it will be absorbed in here. Radiation is an incredibly complicated subject, but it's fairly well understood, but I'm going to make some fairly... Mainly I'm going to imagine that radiation is not a big spectrum. It's a single band or two bands. We have solar radiation, we have infrared radiation, and that's it. Some comes in, some goes out, some is absorbed, and some is emitted, and the amount that's emitted is proportional to the magnitude of the fourth. How much is absorbed is called the optical depth, and that's tau, so you can imagine without too much difficulty. The I by the tau, which is the change in the radiation, is minus, minus B. So this first term here tells you that it's absorbed, depending upon the optical depth, tau and this B, which I will take to be sigma t to the fourth, and that's a grey assumption. It tells you how much is emitted. So this is a basic equation of radiative transfer, and a lot, but not all, of the radiative forcing on Earth can be understood by taking the atmosphere to be grey. But people actually know about radiation are actually rather reluctant to make the grey approximation. One reason is that you can actually do these equations almost line back, well, band by band with lots of, with a separate equation for each frequency, and then you sum them all up at the end, and different frequencies have different levels of absorption. And that is important for quantitative measurements. But for now, we won't worry about that. So we, furthermore, will just assume that radiation is going up and down, assume that all the solar radiation is absorbed at the surface, and that's not too bad of an approximation. So we get an equation for the downwards radiation, imaginatively called D, and the upwards radiation imaginatively called U. So these are these two equations. These are this equation, but for the downwards radiation and the upwards radiation, there's actually a different sign involved because tau, which is the optical depth, we take to be zero at the top of the atmosphere, and whatever it is at the bottom of the atmosphere, it's about five. It tells you how much radiation gets absorbed as you pass through. So the downwards radiation is going to larger values of tau. The upwards radiation is going to smaller values of tau. You end up with a different sign. Now, tau is a function of the radiation concentration of the atmospheric composition. The main greenhouse gas in the atmosphere is, what's the main greenhouse gas in the atmosphere? Water vapor. Yeah, not carbon dioxide. Water vapor. Carbon dioxide is number two. And therefore, it's a function of height. If we know what the atmospheric composition is, we can imagine that tau is some function of height. And more or less, it again, just for our purposes, we will assume that tau falls more or less exponentially with height e to the minus z over h. And h is the scale height of the absorber. And because it is water vapor, this scale height is about two kilometers. If we didn't have water vapor in the atmosphere, it would just be the scale height of the atmosphere itself, which would be about eight kilometers. But in fact, I don't know if it's about two kilometers. So if we know what tau is, this is a function of z, which we're going to specify here. And we're going to specify, then tau becomes a vertical coordinate. And then the most basic thing you can ask is, what is the radiative equilibrium temperature? Let's say it's a function of height. We're going to say tau is the minus z. And if there is the radiative equilibrium temperature, there is no net convergence of radiation in a given level. Because if there's a convergence of radiation, it would mean that the atmosphere is heating. But we said it's an equilibrium, so there can't be. So in equilibrium, d by d z of u minus d, which is the convergence of radiation, again assigned because one is going up and one is going down, is zero. So therefore d by d tau of u minus d must be equal to zero. So that's a condition for radiative equilibrium of a column. And I'm assuming no solar radiation is absorbed, which would be a kind of a detail at the level of this argument. These equations are called Schwarzschild equations, by the way. Some people call them. I always have trouble with this. Shouldn't even bother, should I? Schwarzschild is an astrophysicist. We also did work on black holes. And the inventorising in a black hole was to the Schwarzschild. OK, so we want to just solve these equations with d by d tau of u minus d equals zero. And we can actually do that. It's not too difficult. This is the solution. Tells us what the up. Wood radiation is the downwards radiation and b, which is b now is not the buoyancy, b is sigma t to the fourth. These are the solutions. A little bit of algebra under the algebra. And what is u of l t? U of l t is the upwards radiation at the top of the atmosphere. The outgoing infrared radiation at the top of the atmosphere. That must now, and we know what that is. Because the outgoing infrared radiation at the top of the atmosphere is equal to the incoming solar radiation. Because the planet is in equilibrium. So we'll take that as our boundary condition. Because these are ODEs, the first order ODEs, so they need a single boundary condition. And then, since we've got this tau equals tau naught e to the minus z, we know that gives us, in fact, this solution for the temperature. So we can calculate analytically what the temperature profile is as a function of height in a column. Yes, that's right. That's right. There's no, indeed, there is no, do I have an l here? Yes, I have an l. That's right. Okay, l here. Subscript l. Thank you. It is long wave. There's no solar absorption. Indeed. Yes, I secretly introduce an l. And that gives us the temperature as a function of height knowing what this outgoing long wave radiation is at the top. Because I'm just going to take that as a boundary condition. Because it's an equilibrium calculation. And I get this and what does it look like? It looks like this. Well, these are various curves depending on what the optical depth is. I'm very, the optical depth here for a given outgoing radiation. So the outgoing long wave radiation at the top is, then determines what the temperature is at the top of the atmosphere. It's at the top of the atmosphere. Oops, a little typo here. Forget this t equals. Finish my talk here. At the top of the atmosphere, tau is zero. So b, which is sigma t to the fourth, is the outgoing long wave radiation divided by two. So if we're specifying what the outgoing long wave radiation is, it's equivalent to specifying what the temperature is at the top of the atmosphere in this radiative equilibrium case. And you can see that what it does is it increases rapidly. This is for increasing values of tau. For increasing values of tau, it just gets warmer and warmer. And that's why, of course, we have a greenhouse effect. If tau was zero, no greenhouse gases, temperature would be 220 here. A larger tau, tau is 360 here. In reality, tau is about three, I guess. Of course, it varies in reality. As water comes and goes in a particular column, it varies a lot. It is just the same curve with different values of the outgoing long wave radiation. So I'm specifying the outgoing long wave radiation, and that's equivalent to specifying really what the solar constant is. Because the incoming radiation equals the outgoing radiation. One thing about global warming, which we can forget if it's easy to forget, is that after we put CO2 in the atmosphere, the outgoing long wave radiation is going to be the same. Still got a balanced incoming solar radiation. So unless clouds have changed, unless there's more clouds, unless the albedo has changed, we've still got exactly the same outgoing long wave radiation as we have now. OK, so this is the radiative equilibrium temperature increasing like crazy at the bottom of the atmosphere. It's really warm at the bottom of the atmosphere. What is that going to give you? It's going to give you convection, right? So that's why we have... That's ultimately, again, why we will have convection. And we'll have more convection where it's hot. And so we tend to get more convection in the tropics. And what's going to happen? Convection is going to give you a lapse rate which is specified by either a dry adiabatic lapse rate or a moist adiabatic lapse rate, depending on whether the moisture is present or not. But it's going to... What it's going to do is this. It's going to reduce the temperature gradients here. And so you're going to get convection until this temperature reaches the radiative equilibrium temperature and then you are no longer unstable. And this break here is the tropopause. So we haven't mentioned ozone. Ozone just causes this temperature to go up again up here. It causes this to go up again there. It doesn't really influence... And much of the absorption of ozone is high up in the stratosphere. So in fact the... Do I have it? My U.S. standard atmosphere has gone. It was right at the back. But the U.S. standard atmosphere has got a fairly isothermal stratosphere until you get up to the upper stratosphere. This is for the tropics, right? What about the extra? The extra tropics, in fact, the same argument applies. Why is the extra tropics in that most... That's a deeper question than that's a rather deep question. I'm not going to answer right now because I'm not sure I know the answer. This same argument applies. Because all I'm... Certainly in the absence of anything... In the absence of any other motion the middle attitudes would still be unstable. If there were no other circulation the middle attitudes would still be unstable. So you'd still have convection. If you didn't have a large-scale circulation you would just be in one of these regimes here. Like this green curve would still be unstable. But in fact, the middle attitudes are less convectively unstable than the tropics because the large-scale motion baroclinic instability is also actually moving heat upwards. So what actually happens in the middle attitudes is that you just get a difference that this lapse rate here is not so much driven by convection but it's driven by baroclinic instability, the large-scale edges, which are shifting heat up. So then we can actually calculate what this height is. You have one curve for the radiative equilibrium. I have one curve for the radiative equilibrium and then I'm going to imagine that it adjusts. Let's say because of convection and convection is specifying a lapse rate. So what specifies the point at the surface? That is the key question, Franco. That is the key question. But let's not do that. Let's assume no matter what this scale height here, H, is going to be of order a couple of kilometres because if temperature falls off, of course it's going to affect things quantitatively. But the amount of water vapor falls off with temperature. So we'll assume that we know that. Then Franco asked the question, what determines this intercept? That puzzled me for a long time and I should give credit here to my colleague, Pablo Zorita-Goto, and we confused each other for about six months before we figured it out, sort of. This is the radiative equilibrium temperature. For my first assumption, let's just assume then we have this red line, which we don't have any red chalk, but let's assume that it starts from here and we specify the lapse rate and then it will go up to there. And then that would be the height of the tropopause. That is what I've actually done in this first calculation. Take the surface temperature equal to the radiative equilibrium temperature. So if I know what this lapse rate is and I know what this temperature is, I go up to here and that gives me this value of the tropopause here. But that's too high. That's too high of a value because, in fact, it starts down like this. Yeah, actually you don't. That was our first thought, but you don't because it's something a little bit like an equilibrium constraint. Let's suppose we make another guess and we take it here and we go up to here. Now, what we've done, we've said, if we do this, we've guessed this fairly arbitrarily and go up to here, we'll get the outgoing radiation correct. The outgoing radiation u would be sigma t to the fourth. But then let's do the radiative calculation backwards and go down from the top with this temperature profile and solve the radiative transfer equations going from the top down. That would give us what the upwards radiation is as a function of height. It will give us some value here, knowing what the temperature is there and the temperature profile is there. It will give us something u at the bottom equals something, something. I don't know what that is yet, but a function of how high this is. This something we know has to equal sigma t ground to the fourth because that's the radiation which is being emitted by the ground. But it won't be if I choose this height arbitrarily. I have to choose it in a special way so that the upwards radiation at the bottom of the atmosphere is equal to sigma tg to the fourth because that's essentially the way of getting the entire atmosphere into equilibrium. So what you actually have to do is do an iterative calculation. You guess where it is, you go down to the bottom. You see if that upwards radiation is sigma tg to the fourth if it isn't to adjust. The atmosphere does that itself. There's many clever iterative algorithms built into nature. So it gets it. This is what we did with Pablo. We can calculate what this height is doing it analytically. It's a rather complicated calculation and it gives you that. Now, that gives you about the various constants in here. I should stop for a break, I guess. Gamma is the lapse rate. Tt is the temperature of the chopper poles which we know is that temperature up there. Tau is the temperature of the surface. Ha is the scale height. So I guess in as a parameter and we get this formula. And just two other quick things. When we are one other quick thing, if we have global warming the outgoing longwave radiation stays the same after we've got to equilibrium because incoming solar is outgoing in for bed. But we know it warms because that's the greenhouse effect. So it goes from... That's our original chopper poles temperature profile. It warms to give us this red line because of global warming. The temperature of the chopper poles has to stay the same. The temperature of the chopper poles has to increase with global warming. I'm sorry, the height, thank you. The height of the chopper poles has to increase and it's one of the most robust predictions aside from the fact that temperature will increase. The height of the chopper poles has to increase. And I'll just skip that. The lapse rate also causes things to change because the most adiabatic lapse rate changes. So if you know about that the fact that the lapse rate changes makes things actually go up a little bit more. If you don't know about the most adiabatic lapse rate, don't worry about that. Just think of this. So you can predict that the height of the chopper poles putting the numbers in goes up about 300 metres for each degree rise in temperature which is actually kind of significant. And this, by the way, my own is C-Mip. I took away all my C-Mip slides after John's talk. Except for this one. This is the little dot. Well, this is the height of the chopper poles in a whole bunch of C-Mip models as a function of latitude. And this is metres per decade. So, you know, they're all varying but on average the C-Mip models are increasing in heights by about 70 metres per decade. And which is kind of not insignificant especially if you're an airline and you want to fly in the stratosphere to get above the weather, you're going to have to fly higher. OK, so let's stop and have a... But let's not have half an hour otherwise we'll never finish. Let's come back in 20 minutes or something. Or less if you can.