 This is Martin Hanbaum from the University of Reading, and he will tell us about experiments on stone tracks. Thank you very much. Thank you very much. Am I using this? I can also use shouts. No, no, no. I'm quite good at shouting. I'm used to shouting at students. My lecturing style is if I just shout hard, then they will understand better. I thought that this has anything to do with the talk, but it doesn't at all. It's just a nice cartoon. So the talk is on stone tracks, so we're moving a little bit away from some of the themes we've been covering over the past couple of days. There's several people working with me and also several of those in the audience here. I think the purpose of this talk is to try and convince you that there may be other ways of thinking on how stone tracks operate, essentially. We're used to thinking of a particular way about how stones develop and produce stone tracks, but there's actually other ways of thinking about it, and that opens a whole new area of exploration, in fact, which we have started, and for which idealize model experiments and all kinds of things are needed, which I hope will shed some light also on things like climate responses and that kind of thing. So let's just dive in straight away and see what happens. I am aware that some of this is trivial and some of this is new for people, but of course there's several southern hemisphere people here, so I'd better show what the northern hemisphere storm track looks like, which is the main thing of what I'm looking at, so the US is here. So these are tracks of individual mid-latitude weather systems, and if you look at the Atlantic region, which is the main thing I'm going to be focusing on, because it's probably also, well, because it's a very interesting storm track, because you find many storms starting basically on the east coast US over the Atlantic and then sort of their curl, well, into west in Europe, but quite often into the north, really. And that's, and you can see there, they are kind of organized along areas, tracks, and we call that storm tracks, there's an Atlantic storm track, there's a Pacific storm track, and there's a southern hemisphere storm track, which tends to be a bit more zoneally symmetric, but has some very interesting structure as well, actually. So in many ways, for example, I think west in Europe can be replaced by New Zealand, and that's where a lot of interesting stuff happens. So one of the, and so actually there's some minor storm tracks, minor in the sense that they're less active, sort of the Mediterranean is also considered a separate storm track. And it's obvious that this is extremely important for the weather and basically the fact that we have a storm track here, for example, sets the climate in all those areas. So the climate of west in Europe is just there. We have this climate because we have a storm track. You know, it's sometimes, we're working very hard to try and bridge the gap between weather and climate. So sometimes you hear statements like, well, it's the Gulf Stream that keeps west in Europe warm, you know. It's actually a non-statement really. I mean, it doesn't, we're not living in the Gulf Stream. I don't go swimming there regularly. So the point is clearly that we get storms evolving over the Gulf Stream, bringing up warm, humid, subtropical air, or the humidity gets caught into the storm and that is, for example, dragged into west in Europe. And so it's the organization of the storm track that produces the climate in west in Europe and the same is true for all areas that are located around the storm track. So it's absolutely crucial for what sets the climate. Now, given that it's so crucial, it would be great if we could do a good job at simulating it. And of course, in a weather forecast in context, of course, that is what we've been doing for, well, practically since the 60s, I suppose, that's what we do. So we do mid-latitude storms and particularly mid-latitude storms because we're still rubbish at tropical storms. So we do mid-latitude storms and we're very good at this. But then if you look at the climate of how we do that, this is just one example. What is the easiest one here? So perhaps look at this and this one in the middle. So this is winter storm track density and perhaps you can't see it very well, but if you look into us, there is the climatological state of the, this is a collection of C-MEP-5 models and in the colors are the model biases, the mean model, the model ensemble mean biases. And so what you see is that, for example, blue means that the track density, the number of storms, essentially, is too low there and too high there. So the storms, they go in the wrong direction. That's on average, which is a bit unfortunate because that is kind of, you know, a storm goes into, for example, from the UK perspective, goes to the south of the UK. It's completely different from something that goes over Scotland, for example. It completely changes the weather. We sometimes think when you look at the climate, sort of these blobs and the talks that Franco gave, sort of these, well, that looks kind of right. But when you live there, that kind of right is not right enough because it's really wrong. If your storm goes to the north of you, that's different weather if the storm goes to the south of you. So these are important errors. And basically one of the things you learn from this is, of course, we're very good at climate predictions these days in the sense that we actually kind of know what's going to happen in the future climate in terms of global mean properties. But as soon as we start looking at important features that determine a regional climate like the storm drags, we're actually pretty poor yet. Our understanding is pretty poor. Basically, for example, the future projection of the storm drag is really poorly constrained. We're just not aware what we're doing. This is another example. This is, well, there's a few newer versions of this, but from people from Mark Rothwell and an old group of people studying forecast busts in ECMWF. And basically what they find, well, basically it's probably easiest to just say what it is. They find that when they try and put together all the forecast, a set of forecast that went wrong over Europe, that was their particular interest, and put together these are at the verifying dates, I think, the geopotential height fields. I think that's what it is, geopotential height at 500. Basically, the error is due to sort of a blocking-style pattern which indicates that the blocking-style pattern is precisely the kind of thing that steers where the storm drag goes. So in other words, things that go wrong in weather forecasting context typically have to do with ideas that on average have to do with ideas that you don't know where the storm track has ended up, where the storm, so that's kind of one way of translating that. There's much more to that, but that's one way of viewing that. So just to give you the traditional flavor of what is a storm track, this is very traditional. This goes back millions of years, 1990. That's not millions of years, that is tens of years, so by some people in our department. And I know that not that long ago we used to have overhead transparent. So you younger people, do you still know overheads? Sort of bits of plastic sheet that you write on or make a copy on. I remember that Brian, he used to have a copy of this particular plot in an overhead, and that little piece of overhead transparency was so old it was all crumpled and it had foot prints on it and it had lots of text written around it. So that was a widely used thing. This, of course, looks much more fancy. So this is from a paper from 1990, from Oscans and Val. This is where they diagnosed some aspects on how the mean storm tracks come about. The main thing I'd like to point out is that the way to diagnose the storm track. So there's lots of ice lines here. We don't need to look at all of them. I think I'll point out just the one with the dashed lines here. You can see that the maxima of these ice lines, they all are co-located. It basically means you tend to diagnose pretty much the same thing with these properties. So this is northward eddy heat transport. So the heat transport by storms, essentially. And it has a maximum over the upstream side of the storm track. So sorry about the plotting. This is an ancient plot. So the US is here and the UK is here and we are here. There, on that spot at the moment. And so you can see a maximum here. And that's precisely what the storm track does. So this is metrology. It's not metrology 101 because it would be too hard. But what's the purpose of the storm? The purpose of the storm is to transport heat away from where you build up potential energy. That's what storms do. So in some sense this v prime, t prime, and w prime, t prime is precisely what the storm does. It just transports heat and it has the maximum there. And an equivalent maximum in the Pacific. So that's one way. And then we can ask another question. Perhaps we could ask why is the storm track there? Well then you start going back to very classical theories. So this is, I've called it growth rate. But it's basically vertical wind shear. Vertical wind shear is from eddy growth. And Berkeley in the growth theory is the essentially proportion to the growth rate of individual storms. And if you plot that growth rate in a very standard way, as I said, it's just a vertical wind shear or horizontal temperature gradient, which is the same. And you find maximum in these locations. So that's easy enough. So you find, and the reason, by the way, why you find maximum there is why you could argue because we have a warm ocean there, Gulf Stream, et cetera. So that's where that story from the Gulf Stream comes from. But of course the main thing really is that it's not necessarily the warm ocean, but it's the cold continent that you have in the winter here. So you get lots of cold air coming off the continent, hitting the warm oceans. And that's where then the Berkeley in the growth area comes. So this is our standard view of the storm track. So it is high growth rate. And as you saw in the previous plots, there are all the storm track activity occurs. So that's pretty much how we think about this. And there's lots of, I won't, I have limited time. So what's the fifth forward? What's the half past? Is that a? Yeah, yeah, yeah. All right. Okay, so just to make sure. Okay, so I will probably try and skip some of the details here, but the point is that storm growth over the high baroclinic region, this high temperature gradient region, develops and removes some of the potential energy in the circulation and then decays, I suppose. Well, let's not try and go too far into that. So then, so here we start now. So that seems, I suppose that's kind of the standard picture. We have a high active growth region, and that's where all the activity is. So that's where storms grow and then they decay. Fine. That's how we think about it. And then basically you could ask, is that actually true? I suppose you can always ask that, but so this is what we ended up asking some of us. So this is a hint of what might go wrong with that picture, with that standard picture. So for example, the question is does high baroclinicity, so when I say baroclinicity, that is just this growth rate I was just talking about. High baroclinicity always correspond to high wave activity, high storm activity. And I can already give you the answer. The answer is actually no, even though the maps look as if they do, but actually they don't. And I'm going to show you with an example here. So again, I won't go into the details, but this is work that goes back to Tim Woolings and a few others. If you look at where the storm track is, or the low level jet, that is nearly the same at our latitudes, in Western Europe essentially, or the East Atlantic, it turns out that if you find locations of the maximum of the jet that it tends to come in sort of three-ish areas. The jet might be quite far to the north, the jet might be quite far to the south, or somewhere in the middle. And if you plot it in this way, in fact there are three regimes, they are not regimes to be honest, that's a different discussion. But the point is here, you could think of the storm track state, you could carve it up in three broad regimes, if you like, broad properties, where the jet is either further to the south or the jet is either further to the north or somewhere in the middle. And in fact, the climate is somewhere in the middle, on the average. So let's not go into the details here, but I think that makes sense. Now, and you could argue, you could ask the question, so how does the baroclinicity, this growth rate, and this adiactivity look like over these three different regimes? And that's what we've done here. So there's no point in it, so I just need a long arm. So look at the red box only, and we've plotted in the dashed line, again this heat flux, and in the solid line, this baroclinicity, this growth rate. And perhaps it's easiest to look at these graphs here. They basically reflect what's in the pictures. And so it turns out that the S, which means jet in the south, in the middle or in the north, that when the jet is in the south, the heat fluxes in the storm track tend to be weak. And when the jet is in the north, the heat fluxes tend to be strong. In fact, there's a very strong relationship between the strength of the heat fluxes here and the storm track activity, how strong the individual storms transport heat, and where the jet ends up. So if the storm transports more heat, the jet, the storms tend to curl much more to the north. There's actually a reasonably complicated picture, but that seems to be a systematic picture. So that's for these three regimes so far, so good. And if you look at the growth rate that went along with it, the baroclinicity, it turns out that, well, it looks rather more complicated. So when the jet is in the south, the growth rate is sort of middling, and it turns out that when the jet is in the middle, the growth rate is largest. And when the jet is in the north, the growth rate is not at all that large. So in fact, the growth rate does not at all go with the strength of the eddies in time. Baroclinicity, thermal wind here, essentially, it's rescaled with air for, there's a few more things, as you know. I'd like to view it as a rather informal, there's a precise definition, but informally it's just the amount of potential energy that's in the flow, and that you want to release, that the storms want to release. So although they are co-located in space, they are not at all at the same time. So there's something missing. So when the growth rate is high, the adiectivity is not at all that high. Not quite sure how that fits together. I think I'm pretty sure how it fits together now, and that's what I'm going to tell you about. I'm probably going to skip that in the interest of time here. So here is an example. So in the red line, you find how this adiectivity, this heat flux varies over time. It sort of looks wiggly, you know. It's sort of sometimes you have areas where there's not much storm activity happening, and then you have peaks of storm activity in the winter. So no, so far so good. And this is this growth rate, and blue is the growth rate that goes along with it, and that sort of looks a bit even more messy, perhaps. But you can do composites, right? You can select times when the heat flux was large, and that's what you call that time zero, and you can composite around that, and so you can see that heat flux comes in sort of peaks. But if you composite around the same times there, the eddy growth rate is baroclonicity. You find a totally different picture. In fact, when there's a peak, the eddy growth rate goes down. And that perhaps reminds you and starts to sort of form a picture. Now, there's another. We're going back to meteorology 101 again. A simple question with a much harder answer, and it's highly related to the thing we're trying to solve here. What determines the mean flow? And again, I'm trying to be a bit informal here. Think of it thermal wind or mean available potential energy. That's a more precise answer. Perhaps just ask yourself what determines the mean flow or the jet speed. And you obviously say, well, when you do this, when you write this on the board, you say the change in the mean flow, the dot means time, change in time, is forcing minus friction. That's obvious, right? That's how everything works in physics. U dot is forcing minus friction. And so you write down forcing, well, that's perhaps some radiative input or something into the mean thermal wind. It doesn't matter how you want to describe that, some forcing and this friction. And then if we're normally, we write friction, or that's kind of proportional to the mean flow. There you go. That's easy enough, and that's, of course, how it works, except that it doesn't. It doesn't work like that. The real world doesn't work like that. For example, one of the outcomes of this type of viewing the mean flow is that stronger forcing means stronger flow. Of course, that makes sense, right? In fact, it doesn't, right? It turns out it doesn't. There's a big question mark behind it. It's just not true. But that is what would follow from this kind of consideration. Stronger forcing means stronger flow and also stronger friction means weaker flow. Again, let's examine that a little bit. It turns out to be not right. And this is perhaps an indication of why it's wrong and why this apparently very basic observation is wrong. And this is the Lorenz energy cycle. I'm not totally sure how many people are fully aware of this, but you can carve the energy reservoirs in the atmosphere up in, broadly, in four types of energy, namely what is called available energy. Potential energy for you and me. And kinetic energy, which is just motion. And then we tend to carve it up in what is in the mean flow and what is in the eddies. So this is eddies that's mean flow. That's kinetic. This is potential energy. And it turns out I'm blocking that one out for the moment because that is, of course, very important. But let's examine a situation where that is not important just to make life a little bit easy. So we are only looking at potential energy flows here. It turns out that the mean potential energy flow box is being filled by what we call climate forcing. The poles cool down, the equator heats up. That builds up a potential energy in the full atmosphere and it's mostly zone or mean potential energy. So that is the main climatic forcing of the mean flow. It goes into that box here. And energy is energy. Since the 18th century we know that energy has to be conserved. And so something needs to happen, right? It either has to stop filling up, which it doesn't, or it has to go somewhere, which it does. And indeed, what happens, it turns out broadly, is that the mean flow potential energy turns into eddies. And that's where all the energy goes. And that gets dissipated in some way. So in other words, when I put energy into the mean flow, it doesn't get dissipated. I put energy in the mean flow. It gets transformed into eddy energy. And that's where it gets dissipated. And that's precisely why our equation was wrong. If I go back, forcing, yes, you force the mean flow. But the dissipation has nothing to do with the mean flow is not dissipated. The mean flow gets transformed into eddies. So it's that friction term that is wrong. Okay, we'll come back to that in a second. Another one. This is the second. So there's two ingredients to my story here. So that was ingredient one. Now we're going to get ingredient two. Question. Is the mid-latitude flow perically unstable? Ask this to old cultures like Brian Hoskins and he says, yes, it's unstable. We've done the calculations. And well, you can ask yourself, is that right? In fact, it's not right. And it's very hard to tell Brian he's wrong. He will get very angry. But no, he doesn't get angry. But he doesn't believe us very hard. But this goes back to work. Again, this was done by people when they were in Redding, Nick Hall and Prashant Sardashmak, where they calculated using the IGCM, the Redding Simplified GCM, which I think was part of the original inspiration or origin of the original. It's the same origin as the original ECMWF model. What they did is calculate the growth rate of the observed mean flow. Just how unstable is it? Well, it is unstable for a lot of the, often, but there is a little damping parameter which changes how strong the friction is. And the damping parameter is not very well constrained. And these are values that are perfectly sensible, sort of in this range. These are perfectly sensible variables. It turns out that if you tweak the parameter, the friction parameter a little bit, the growth rate goes to zero. In other words, well, perhaps the flow is unstable, but if it's unstable, it's very weakly unstable. You only need a tiny bit of friction to stop any eddies from growing on average. So actually, the flow is not all that. So when we calculate growth rate, we actually forget about friction. And it turns out that the friction rate is pretty much the same as the growth rate. And this is an important observation, I think. Yeah, go. Observations show us that perturbations are obviously growing. Yeah. I hope, yes. Okay, I hope to, can you ask the same question in ten minutes? Because I think you're right, obviously. So in other words, what determines the eddy strength, so the strength of this, so perhaps it's something like this. We need to write F values because it's inspired by heat flux. Think of it as the strength of the eddies. There's a growth rate times the eddy strength minus the dissipation rate. And often that growth rate and dissipation rate are very close to each other. Okay, so let's leave it on that. There's details there. Now putting it all together here, the two three ingredients I've been saying, so this is just a growth rate, the growth of eddies is growth rate minus dissipation rate. And now we're going to write on a mean flow equation, and it turns out that the mean flow or the growth rate is proportional to the mean flow. And the reason for that is that the mean flow is basically the jet strength is mostly proportional to the thermal wind, which is the strength of the shear. The strength of the shear is just precisely the growth rate of eddies. All right, so instead of this growth rate we can also think jet strength. And we've already written down an equation for that. The jet strength changes by the input into the mean flow and the dissipation rate, but we already agreed that the dissipation rate is not just lambda times the mean flow, it is actually the eddies, it's the conversion to the eddies that take away the mean flow. So this is the equation. And so these are two equations, two are known, and we can solve that. In fact, we can't solve it, it's a non-linear equation. We can't solve it analytically, but if you stare a little bit harder and at the equation you will see it's an oscillator. It's a non-linear oscillator. It's a relaxation oscillator, in fact, and it operates a little bit like a predator-prane model where the eddies eat up the mean flow. And these are models that have been studied quite a bit. So I suppose this is some sense the halfway conclusion and then I have about five minutes or so to get the other halfway conclusion and that two halves makes a whole, so they were done. So the halfway conclusion is that storm tracks are perhaps one way of thinking about it, the classical way, if you like, is to think of it as a grow and decay cycle. Eddies grow and decay. Another way of thinking about it is an oscillator which is essentially driven, this is the forcing in the oscillator, driven by diabetic input into the mean flow, which is peculiarly different. However, I know that there's one or two people working on a radiative convective equilibrium here. People who work on convection always think about these kinds of things, these kinds of experiments. People who work on convection, they think, what kind of experiments do they do? They tend to, they might start with a stable atmosphere or something in a cloud-resolving model and then they might crank up the sea surface temperature and then see what happens to convection. They're precisely used to that, they just crank up the instability until the instability kicks off and then you get something called radiative convective equilibrium. That's what these guys do. All I'm suggesting is we should do the same for the storm track. We're kind of used to sort of, we have an initial state and then we put a perturbation in and then see what it goes. Well, that's one way of looking at it. What I would like to look at is, similar to convection, trying to crank up the instability in the storm track and see how the instability grows or equilibrates essentially. Okay, in the interest of time, just to point out that there are sort of much more solid theoretical understanding behind some of these ideas to do with wave-mean-flow interactions and you can sort of argue your way around that this kind of system we wrote out is related to existing ideas about wave-mean-flow interactions. So let's perhaps skip some of this detail. Just show you some pictures here. So that's the observed. And we are writing down an oscillator, a nonlinear oscillator. Oscillators behave very simply, right? So it's simple. So they don't look like that. This is how, what happens if you integrate this system. In blue is the growth rate. It sort of builds up until the eddies sort of become very unstable. They shoot up in activity. You get a spike of activity and the spike of activity eats away at the instability. The instability collapses. And then, of course, when the instability collapses, the eddies can't sort of feed themselves anymore. So they die out. And then when the eddies have died out, the instability can start to build up again. So it's that kind of... Of course, the question is, that's the real world. This is the oscillator. Is there any sort of more strong correspondence between the two? Well, in order to do that, there's one way of doing it, and perhaps Lanker will talk a bit more about it at some point. But if you plot... So this is one of the interesting things we're trying to push here. If you plot the strength of the heat flux here and the strength of the eddies on this axis and the strength of the instability on this axis, the strength of the berycholinicity on that axis, these are the two variables in our model, and you go around like an oscillator. But it's a non-linear oscillator, so the phase space looks a bit deformed. So that's how this oscillator phase space looks like. Sort of at low heat flux, the instability builds up, and then suddenly you get a big spike of heat flux, and the instability dies down again, and you're back. So that's how you go around. Of course, I would at this point say, this is insultingly simple. There's no way that the real world works like that. Of course, we have found that the real world does seem to work like that. There's a way of... These are called the simple kernel average for people who are more aware of that. We can average real-world data by taking kernel averages in this particular phase space, and you can find average tendencies at each point in phase space based on real-world data. And you can try and plot that. And if you do that, you get this. It looks slightly different from what I showed before. I haven't mentioned this because we tend to take the logarithm of the heat flux for theoretical reasons. In fact, all that happens if you take the logarithm, the shape of the egg changes direction. You get an egg to the left-hand side with a point to the left-hand side. And you get this. And so what do we have here? All right, this is from Speedy. That's era interim. So let's just look at era interim, which are realistic data, more or less. And you find, for example, in red, in the colors, is the jet latitude. So we'll just point back to that one. So when the storm track activity is weak and also at low instability, the jet tends to be in the south, which is blue. And at these high peaks, the jet tends to sort of deflect to the north on those kinds of things. But let me just point out, this is real data. There is no data massaging going on. The only averaging happens in the phase space. So in other words, the real world seems to behave like this. It seems to, on average, want to do this relaxation observation. This is kind of a remarkable property. If you write down, I won't go into too much detail there, if you write down a nonlinear oscillator, you will find that the period is proportional to the amplitude. And there's lots of funny theory about that. And you can go to the library and look it up. It's nonlinear oscillator theory. You can all do it. And it turns out that you can fit observed data to that kind of behavior. In fact, when the amplitude of the oscillation increases, the period increases. And it increases precisely as the theory of this relaxation oscillator would let us believe. And so, for instance, this is the kind of work we're looking at. So, for example, do all models behave like that? Because we saw speedy works like that. But speedy was set up in a very idealized setting. But do real-world models, if you like, see the 5-model wave like that. This is one of the things we're working on now. So this is e-range. And again, plot at the face place. This x-shaped thing in colors is the density of points. But for example, you can do this for all models. And you can see that all models behave more or less like that. But you can also at the same time see that they are located in different ways. The shape is slightly different. So clearly, the whole dynamics of the storm track, on average, you remember that the storm track dynamics and location has strong biases in most senior 5 models, on average. And this is, I think, the way of diagnosing this stuff. And you can see this face space has a lot of systematic differences going across all models. I'm sure you can't read all the labels here. But the labels are just a different model, a set of different models. And you can write that as, for example, a difference from multimodal mean here. So those are the colors. And you can see that the multimodal mean is in contours. And then the colors are the differences in that particular face space of the multimodal mean. So for example, this means that for this particular model, there's too much that egg-shaped thing was shifted in this direction. So you can actually see that the errors that are in the model tend to have sort of systematic things as far as regards to the storm track. And I used to be very fond of EOFs. So I thought, why don't we do EOFs of the error field here? But basically what you're doing here is in colors, you see what the main errors are across the whole ensemble of CMIT5 models. And so the main error is that there is a shift towards low storm activity and low instability. But there's other types of errors, which is the second most important error in EOF. EOFs just rank the variability according to importers. Those are the most important errors. Then you get errors that do this, perhaps, that have too high a storm activity but too low an instability. That seems to point to different physical mechanisms. And then there's errors where the density, where the amplitude is perhaps too low. So you remove density or you add too much density at low amplitudes and take away from high amplitudes. So we hope that this is a way of classifying models and their model errors as far as storm tracks are concerned. So I don't have much time to go through. So what I will do is just point one thing. The Antarctic circumpolar current, which is oceans, is a storm track in the ocean. And we've done the same thing for the oceans. This is an idealized model of the Antarctic circumpolar current. Just point out two things and then I'm done. So if you look at the set of equations we wrote out, is that the, perhaps I should, where are the equations? Yeah, here. If I increase my... So if I try and calculate the steady state of these models, it looks like this. It means that the forcing of the mean flow is proportional to the strength of the eddies. So in other words, if I increase the forcing of the mean flow, my climate forcing, for example, temperature gradient between the polar equator, what happens is the mean flow doesn't increase, it's the eddy strength that increases. The other one is here, that the mean flow, or the growth rate, is proportional to the dissipation rate. In other words, if I wanted to change the strength of the mean flow, the thing to do is increase the friction. It just seems to make no sense whatsoever, but that's what these models seem to indicate, this kind of way of thinking. All I'm saying. So it's completely counter-intuitive. This part is called, the oceanographers call this eddy saturation. This is something new we've been putting, trying to sort of talk a bit more about, and we try and call that frictional control. But just to point out here, for example, this is the strength of the Antarctic circumpolar current. And just point to one of these graphs here. So if we increase the wind stress, the strength of the current does not change at all. It just stays flat. If we change the friction, which is a friction parameter in the deep ocean, if we increase it, the Antarctic circumpolar current increases. I have literally minus one minute, so we've done this stuff for the storm tracks as well, which is actually much harder, it turns out, because the storm tracks in the atmosphere can shift as well, so that really ruins everything. And we have a Hadley cell, which is important, which also ruins things. But we can show similar things. So let's just point out a couple of summary points here. That growth decay is perhaps not the most relevant way of thinking about the mean state of the storm tracks. Perhaps we should think about this funny oscillator, a marginally stable oscillator. The time scale of these oscillations has nothing to do with the baroclinic growth rate, which is not a traditional way of thinking about time scales in the storm track. Time scales of these things is diabetic. It has to do with the climatic forcing of the mean flow. It's a completely different thing. Think about climate change experiments or where you change the tropical SST, for example. You increase the tropical SST in your experiments. You think, oh, well, I'm going to increase my pool to temperature, equator to pool temperature gradient. Surely the mean flow has to increase. Yeah, probably not. Probably the time scale of variability changes, but the mean flow doesn't change. The adi activity probably increases. So there's lots of interesting things here. And this is perhaps a bit more general. I would argue that there's actually still quite a lot of fundamental questions about the precise properties of the nonlinear state of the storm track. I mean, this is pretty basic stuff, I think, but basic in the sense that it's kind of fundamental. But I think we still don't really understand how the nonlinear state of the storm track is being set. And so these problems are both fundamental and I think practical because it's obviously related to where we live. And I think, for example, that one of the ways to do this, or perhaps the only way to do this is to have a whole modeling hierarchy. And so one of the things I've been particularly inspired by to come here is one of the things, we have simple models, we have big models, sometimes very hard to make this transition. And I think, for example, this whole open IFS effort is a great way of trying to make this transition from the left to the right here in the model hierarchy. So I hope to have inspired you a little bit on the kind of problems that still live in the mid-latitudes and that there's lots of exciting modeling experiments and modeling questions that we hope to be addressing here. So thank you very much.