 And this is just, which is the pointer? This is the, I can use the screen for advancing, but. Okay, okay, I probably wanted the point. Good morning everyone. What I wanted to give you today, we're starting exactly half an hour like, okay, so that should be 45 minute lecture. I wanted to go over, sort of set some conceptual groundwork for the next two weeks. We'll be hearing a lot about different kinds of interactions between the tropics and exotropics. And so there are some concepts, some ideas which may underlie them, even implicitly they may not even be stated, but just sort of give you some background for those. The first one is, there are some of the language we use when we're talking about how the exotropics respond to the tropics is actually almost subconsciously based in theories of stationary, stationary wave theory. So what I mean by stationary wave theories, if you have an anomalous source in the tropics, which is stationary, it just sits there. Okay, there'll be a stationary response, just a time-independent response in the latitudes. And that's been very well studied, that's relevant on longer time scales, but some of those concepts have been sort of, are used even, we don't realize it when we're describing interseasonal shorter term responses of the exotropics, the tropical forcing. So it's good to know, and to ask ourselves the question, can we use some of these ideas of stationary wave theory? I also wanna just remind us of a topic that may or may, that hopefully will come up, that the tropical forcing can affect not only the mean circulation of the exotropics, but it can change or excite different kinds of instabilities in the extra tropics. In particular, barotropic instability, I'll just remind, talk about that a little bit. There are many ways in which the tropics actually respond to the extra tropics, and some of them, I'm going to give you a couple of examples, okay, actually one of them in which I actually did some computations for this. And finally, there are situations or ways in which the tropics and extra tropics may be more coupled together, okay, as part of a sort of global oscillation than is often realized, and I'm going to at least mention one of those briefly. So to just try to get you to think about the framework for the whole two weeks. So the first topic, the words that I didn't write down here that I want you to think about are rosby wave source, okay, you may have heard of them, and it sounds like, okay, you have some disturbance here and rosby waves propagate eastward from that, okay. In the context of the extra tropical response to the tropical forcing, that has kind of a background, a theoretical background, which I just wanted to sort of briefly indicate. So the first slide, and I'm going to show the slide tomorrow again, okay, in a different context. This actually comes from a recent paper by Grant Branstadder in 2014, and the question was exactly, what is the response of the extra tropics to tropical heating anomalies that are short-lived? What is the response of those to the same tropical heating anomalies if they were to just stay there permanently? So what he did was, he took an atmospheric model, a dry model so that no moisture, so you can just add heating, specify heating, and he put it, for example, in this set of experiments here on the left column, he just put a heating where that red, that yellow circle is, a deep heating, representing anomalous convection there for two days, only two days, that's like a pulse. Put it on, leave it there for two days and turn it off. And that's days two, sorry, this is day three, day six, and day nine, so this is the, what you're looking at actually is the meridional wind at, in upper levels, indicating the, you can see the development and the spread of the Rossby waves, even though at all these times, the heating has already been turned off, okay? So his point was that by the time you get to day nine, if in the same panel, he were to show the result of the meridional wind at upper levels to a stationary heating source, he would get almost the same pattern, okay? So tomorrow I'm going to talk about this in a different, the same picture in a completely different context, but in this context, this gives us some hope that we can at least apply ideas of stationary wave theory to transient perturbations in the tropics. So the first thing I want to remind you of, and maybe the most important thing, is that in some general sense, the exotropical response to tropical perturbations is usually has a barotropic vertical structure. So that's kind of seen very often, and to try to come up with an example, I had to put one together. So what I took was for stationary waves now, I just thought about the El Nino Southern Oscillation, okay? So what I did was I looked at the response to a warm event of 8283, I took the anomaly of the boreal winter mean compared to a 32 year climatology from reanalysis, and I looked at the top panel shows the divergence, okay? Tropical divergence just along the equator from here we have a longitude on the x-axis and we have pressure level. And you can see there is convergence, so negative divergence means convergence, right? The air coming together as you expect for the anomalies in the warm event of El Nino where you have anomalous convection in the east, essentially in the eastern Pacific, and right above the anomalous convergence, there's anomalous divergence, okay? So reversal from above and below. And if you look at the U-wind anomaly in middle attitudes for that same period, you can see that it's, you can see that the vertical structure of it is there's almost no phase shift with height, okay? So we call that theory equivalent barotropic, but it says, well, maybe the barotropic dynamics has a lot to do with this. Maybe somehow we can relate, with barotropic dynamics, we can relate this upper level divergence, right, to the wind that occurs in the latitudes. So this is another example of the same thing, except I now took the stream function, the, what I took was the seasonal mean stream function and removed the zonal mean to get just the eddies, but so really stationary eddies. And you can see again in the tropics, there's kind of the top panelist, average from 15 south to 15 north, you can see the barotropic structure and the bottom panel, you can, I'm sorry, you can see the first baroclinic mode, okay? You can see the reversal right between lower levels and upper levels between 1,000 millibars and 150 millibars here in the eastern Pacific, and in the, this isn't working too well. You can see a barotropic structure here, right? So this kind of motivates the use of the barotropic dynamics. This is the same thing for another warm winter, 97, 98. Again, some kind of reversal in the tropics, but completely equivalent barotropic structure in the extra tropics. So this is again the notion that the extra tropical response can be barotropic. So let me go this way. So this is my simple mode of tropical convection, my simple model of tropical anomalous tropical convection. As you know, you have divergence below with small vertical velocities, strong rising motion leading to negative OLR because the cloud tops are the ones that are radiating out to space and they're cold, and then the upper level winds have a divergence, D, which is positive. So how does this, so how do we relate to this idea of Rusbe wave source? How do we relate, how do we represent this tropical motion, this tropical rising motion? Well, scale analysis and some theory will show you that if you look at the thermodynamic equation, the important terms are this theta here is the potential temperature. So I'm just kind of writing a second law of thermodynamics. It just basically says vertical advection of theta, W d theta dp is balanced by tropical heating. Since, now let's get this straight, theta's got a potential temperature as the increase with height, right? So d theta dp's gotta be negative in the mean and omega's negative. So d theta dp, this is a negative term here. So that's basically saying negative omega is definitely strongly related in the seasonal mean to positive heating. Okay, so again, so that's kind of that absurd, that's that picture. So the strong rising motion leads to large-scale divergence and we get a little bit faster. So now I write down the barotropic forticity equation, okay? And it's just the advection of absolute vorticity which is relative vorticity plus the Coriolis parameter. And then there's this term on the right, this is an approximate version of the vorticity equation, okay? Which is minus the absolute divergence, vorticity times the divergence plus some kind of friction. And that's called S and that's called the Waspy wave source. Now right away, we have a problem in terms of thinking about the exotropical response to tropical anomalies, particularly when you have tropical easterlies because stationary wave theory, and I'm not gonna actually go through that, but there's several different ways you can look at it. Stationary wave theory says that if you have a source in easterlies in the tropics, it won't in the time mean affect the exotropics, okay? So the zero wind line, right? The easterlies in the tropics prevent its influence from propagating to the extra tropics. But that's where the heating source is in fact. The heating source, this source of divergence here which just comes from the heating and the rising motion is in fact very often in easterlies. So what is going on here? That's a paradox. And this is what the term, this is the paper where I think the term Waspy wave source comes from, the start of Schmuck and Hoskins. What they pointed out is that, yes, this is true in this equation, but skip this one. The problem is that before I had the total wind here, in fact, if you wanna use the barotopic model and the barotopic fraticity equation, you can only solve for the rotational component of the wind. Just to remind you, the rotational component of the wind is the part, the component of the wind that has zero divergence. So if you wanna use the barotopic fraticity equation, there's another term that should appear that where you have the divergent component of the wind as part of the advection, that now will appear on the right side of the source. The reason I say that is this is a nice prescription, this equation right here is a nice prescription because for actually solving it with a barotopic fraticity equation, if you have some friction and you can specify the divergence from the tropics as fixed and you can specify the divergent component of the wind, okay, the component of the wind that actually has the divergence from the tropics, then you can solve this equation because the only variable is the stream function, right? The stream function will give you the relative vorticity and that plus F will give you the absolute vorticity and so the stream function will give you the advection, like the rotational winds. So you have a closed system that you can solve. So they pointed out that specifying the Rossby wave source, you really need to keep both of these terms into account including advection by the divergent wind, which you have to specify, and that's actually just in words. So there's a new source, this is traditional source, sorry, the traditional source is just the divergent in terms of vorticity, now there's a new source, advection by the divergent flow and just to give you an example and kind of go a little faster, these are contours of absolute vorticity and that's the traditional Rossby wave source you're specifying a divergence at upper levels in the Western Pacific here in this experiment and so the divergence is right here and the traditional Rossby wave source would be right here and they don't show but this is pretty much in the region of Easterlies. The new Rossby wave source as they run the barotropic model, here's the divergent wind, and in the Northern Hemisphere there's a strong gradient of absolute vorticity, the divergent wind advects the absolute vorticity northwards, okay, and that pulls the Rossby wave source into regions of Westerlies, it pulls it out of the deep tropics. So this paper was a, I think just in terms of simple concepts, an important message, sends an important message that you can think of barotropic model giving a stationary wave response in mid-latitudes, but you have to have the correct Rossby wave source. Okay, so that's one thing just to keep in mind. The second topic I want to move on to quickly is the change in mid-latitude, instabilities due to tropical forcing. So this is this paper by Simmons Wallace and Branstetter in 1983 and they talked about the role of mid-latitude barotropic instability. We're all familiar with baroclinic instability, storm tracks, rapidly developing disturbances, right, that occur all around the world, especially in mid-latitudes. Barotropic instability is less often discussed. They used basic states which had a lot of longitudinal and latitudinal variation and they were able to find for a chronological flow just using the barotropic model. They were able to find low frequency fluctuations which derived their energy from the barotropic instability. They had an e-folding, they had periods of about 45 and also there were shorter periods and e-folding times growth rates were leading to e-folding increased in about seven days. It's kind of slow compared to typical barotroclinic instabilities, but as you'll see in a second, these barotropic instabilities have a lot of geographical variation and locally in space and time they can grow very rapidly. And this mode may play a big role, may be excited by tropical forcing and particularly the Madden-Julian Oscillation which we'll hear a lot about later. So I just wanted to just run through this quickly. So this was the most unstable mode, okay, and basically what happens it's an oscillating mode that propagates and grows. So it's not just the patterns that it goes through or a whole sequence of patterns here starting from the top left, top right, middle left, middle right, bottom left, bottom right. Okay, that's sort of half a period of its growth. So the overall energy only has an e-folding time of about 6.8 days but there are periods in their regions you can find right here where it's growing from this panel to this panel very quickly. Okay, so this mode is kind of, there's a lot of structure going on in this mode and what they pointed out was, and I know I'm jumping ahead a little bit, we'll hear a lot more about the Madden-Julian Oscillation which is related to convection and the tropics that move slowly through the Western Pacific and in different phases of that oscillation these are the mid-latitude responses and stream function. So all I want you to get out of this picture is that, for example, this top right panel here, okay, which shows one of the maps that I just showed you on the previous page has something in common with this response of the MJO in one phase. In fact, there's some of the patterns some of the features look similar and also this map looks much like negative of this map. Okay, you can see a positive, positive and negative here and negative and negative and positive there. So this paper goes through this in a lot more detail. The point is the response to the Madden-Julian Oscillation may involve both actually, it may involve several modes. This is the longest, the mode that takes the longest to repeat 45 days and then there's another mode which is actually, no, this is a similar picture. I don't want to go through all the panels in detail but again, the take home message is simply that this baritope instability can be excited by tropical forcing, okay, but it's an intrinsically mid-latitude phenomenon, okay? And that really can't, we can't forget about that. So let me very quickly switch gears to possible ways in which, or possible way in which the tropics may respond to mid-latitudes. So there's actually been a lot of this in the literature. This is taken from a paper by Knippertz in 2007, okay? And it's basically upper level troughs at low latitudes. So basically disturbances from mid-latitudes, troughs that descend into the tropics, okay, and stimulate tropical convection. So this is an actual satellite picture, okay? So this is on an isentropic level, a level of constant potential temperature. So if the flow is basically governed by 80 batted dynamics, it should stay on the surface, okay? And this is close to the 200 millibars in the tropics. So basically what you have are the streamlines of the flow on the surface, okay? Coming in from here and here's 30 north, here's the tropics, here's 30 north. You can see the streamlines coming down in. This is actually, if you're into this kind of thing, it looks like it's related to an anti-cyclonic rugby wave break, but that's not necessary to know that. The dashed lines are the isotax, how strong the winds are. And you can see this sort of trough coming descending into mid-latitudes. And you can see this is the cloud picture, okay? This is actually the picture on which all these lines are superimposed is a satellite infrared image of a tropical plume, okay? Going, coming out from the tropics here into the extra tropics. So it's a nice sort of, the smoking gun of extra tropics affecting tropical convection, okay? So, and there are lots of examples of this, pictures like this you can find in the literature. Another example, which I don't have a picture of is cold air outbreak in northern winter over Siberia, okay? Extending all the way into the equatorial Pacific, alright, in the middle of the Pacific and leading to convection. So I thought I would do some diagnosis to represent that. And I'm gonna show you pictures that appear in the paper that we've submitted with Highland as a co-author and Christine and I to Highland's lead author to the views of geophysics. The idea here is to do something really simple. So let's concentrate, I know some of you are interested in storm tracks, let's concentrate on fields which vary with time scales of less than 10 days. So could be related or should be related in the middle attitudes to the storms. So if you just concentrate on those fields and you look at the momentum flux, okay? And you average it over a whole winter and then many winters. And this is nothing new, but people know this but somehow it's never commented on. What you find in the subtropics, sorry, the southern hemisphere is that the momentum flux is less than zero, okay, everywhere. And it turns out according to wave theory that relates to a quaterward propagation of waves. The same thing in the northern hemisphere except now the momentum flux is greater than zero, okay? So in both cases it's poleward. In both hemispheres the momentum flux is poleward but again there's some theory that relates a positive momentum flux to a quaterward propagation of waves. The thing I'm having said all those words, the thing I want to point out is look how far this momentum flux extends into the tropics. In the southern hemisphere it's what? It's very well behaved, it stays out of the tropics, right? 26 out of the tropics. In the northern hemisphere it's not well behaved at all, it incurs all the way down to out what is that, 10 more, okay? So that already gives you a hint that there's a quater propagation of mid-latitude kinds of events which are very better clinic in nature can have an effect on the tropics. So I sort of scratched my head to come up with a way of doing that. So what I did is the following and I'm summarizing a lot of work. You can estimate the diabetic heating from modern re-analyses and we can talk about that later, okay at length how to do that. It's just an estimate and just do some temporal filtering, okay? Make sure that it's a nice smooth tropical heating that you're getting. So that you can get day by day at every grid point and you can get the product of these high frequency momentum fluxes day by day at every grid point, okay? And you can just do the covariance of those two. The point being, are there places where equatorward propagation of waspy waves indicated by positive momentum flux are correlated with the tropical heating. So you do that for winter. You do that, then average it together and of course this is a satellite projection. That's the middle of the Pacific there. And you can see nothing, okay? Clonologically there's not anything. But that's climatologically in certain winters you can find, for example, the winter of 1989 and 1990 you can find a strong positive covariance where equatorward propagation of waspy waves is related strongly covariating with heat diabetic heating, okay? So for that season you really did get a strong effect of the extra tropics on the tropics and then to prove this, that this is not to actually show you how this works, I picked one day in a different year just for variety. What you see on the left panel in the contours is just the meridional wind, the high-pass meridional wind, okay? And the colors are tropical heating. And you can see kind of, I indicated just by having an arrow here, you can see kind of a wave train propagating into the, from the extra tropics into the tropics. That's the associated positive momentum flux and in the eastern, here in the eastern tropical Pacific you get heating, okay, where you normally don't get, okay? So this is kind of another, this is similar to the photograph, sort of a kind of a smoking gun of extra tropical incursions into the tropics related to tropical heating, okay? So that's something I hope we'll discuss more and hear more about and think more about in the next two weeks. So how much, how am I doing time-wise? I'm gonna probably, I used to have one more. Okay, I probably won't, but okay. So, okay, the one thing I should mention are these estimates of diabetic heating. It's not so easy to get diabetic heating, right? Because you don't analyze it, you don't measure it directly. So this diabetic heating was obtained if you would just write down the thermodynamic equation, the time rate of change of potential temperature or entropy is related to diabetic heating. And with modern re-analyses you have, you have enough resolution and time and space and good enough data that you can basically estimate that as residual, okay? So just remember in re-analyses what you're doing is every six hours you're getting the best possible state of the atmosphere that's dynamically consistent but influenced strongly by observations, right? So you're going from one state to the next state to the next state. And nevermind what the model is, the final re-analysis, if it's a good model, okay, and a good data assimilation system should be realistic. So I'm just counting on that to back out the diabetic heating as one of the terms in the budget, okay? And the reason I'm mentioning that is it's particularly, seems to be particularly related to tropical convection in the 700 to 300 millibar range. Okay, the last, so, okay, so we have the, we now hopefully have the idea that the tropics can be influenced by the extra tropics. So now I want to present something that's old but sort of weird, okay? That's the way to describe it. It's a paper I wrote with Richard Linsen in 2000. So are these coupled? Are they, sometimes coupled or they always coupled, okay? So this is the idea, okay? This is, people are still asking me about this, but anyway, so if you think of really simple theoretical studies of beryclinic instability on a sphere, okay? Sorry, not simple. Realistic beryclinic instability on a sphere, right? Really good models, correct spherical geometry. They'll indicate that zonal wave numbers eight to 15, sort of synoptic waves are the most unstable. These are the ones that we see every day and these waves saturate relatively quickly. They grow and they mature and they decay in 10, 15 days. But there are more slowly growing longer waves. Longer waves are actually, I think of planetary waves, wave numbers one, two and three. They are beryclinically unstable, okay? They grow more slowly. They're able to achieve higher amplitudes, particularly in this upper troposphere stratosphere, okay? So the ancient theoretical literature, those were called green modes. In the first paper I ever published, the title was Long Wave Beryclinic Instability on the Sphere. And it was exactly about these, okay. And they were already just talked about in the 70s. So okay, so that's one thing to keep in mind. So zonal wave number one, which is a planetary wave, can still be part of beryclinic instability. Now for some theoretical reasons, you can expect a phase speed of the wave, which if let me remind you, which related to the frequency divided by the dimensional wave number, to be in this range. If you believe that if you buy this, or you just blink and say okay, I'll swallow that, then it turns out there's something very interesting that happens. If you take phase speeds in a range of one to 10 meters a second, and you specify that the zonal wave number is, the zonal wave number is m equals one. Sorry, there's a mapping this equation's wrong. There's a mapping between the dimensional wave number k and the zonal wave number, okay. But if you take zonal wave number one, find out what the correct k is depending on the latitude, and evaluate this range of phase speeds, you find that the range of frequencies is almost exactly the range of frequencies that are in the Madden-Julian oscillation. That's pretty, is that a, that could be a coincidence, right? Because in one case I'm talking about some theoretical long wave baryclistic instability. In the other case, we're talking about a well-known tropical, well-known tropical phenomenon, which we're gonna hear a lot more about. So the idea was the following. The idea was to study the coherence. So we're gonna concentrate on eastward propagating waves because the Madden-Julian propagates eastward in these baryclistic instabilities propagates eastward. And we're gonna look at the zonal wind field. And we're gonna just see how coherent they are between different latitudes and levels. So the idea was let's concentrate on planetary waves, just wave number one or wave number two. And there's some theory you can use, which I won't bore you with, that allows you to isolate eastward propagating waves, okay. So we're looking at a real subset of fluctuations. They're propagating eastward. They're planetary waves one or maybe two. And they have these frequencies which are in the range of the Madden-Julian oscillation. They also happen to have a phase speed which are of relevance for baryclistic instabilities. So let me remind you what the coherence means. It's always something that's easy to forget. So we're gonna be looking at two time series, okay, which fluctuate, okay. And I'm not gonna be looking at a single frequency. I'm gonna be looking at a range of frequencies. And the two time series, which will be displaced from each other. So the question is for these two time series will the phase, if you just think of one frequency, have a sine wave at one latitude and sine wave at another latitude, there'll be a phase relationship, right? Is that phase relationship robust if I just move the frequency slightly, okay? So basically you can think of two fluctuating series which have a fairly robust phase relationship with each other, okay? That's what the coherence measures. And it's supposed to be an indication of some physical connection. That's the idea. So the only picture, oh, I can't do it this way. The only picture I'm gonna show you from the paper because they're all similar. So this is Linsen, Strauss and Linsen 2000 is this funny picture. So this is the coherence here, okay? Between basically this, these magnidruy and oscillation range of frequencies for wave number one between the base point here at 32 North and 300. And you can obviously tell that's the base point because that's where this coherence comes up to one. Obviously the coherence is one at every point of perspective itself, okay? And all other, the same time series, the same filtering by the different latitudes at different levels. And you find that there's something going on with some connection between these two propagating waves at high latitudes or either coherence squared or about point greater than point four. But then you get this bullseye at about 12 North of a coherence of point seven, kind of like half the variance in these two time series is related to each other, okay? That coherence is so high compared to what you expect that for one solid month I was convinced I had a coding bug, okay? And so I spent a month checking out the code every which way I could and there was no coding bug, okay? So this is kind of remarkable. This says that, I'm sorry, this was taken over an extended winter period for 39 years, okay? That's, so it's mostly boreal winter but it's really an extended winter, October to March. So what this says is that fluctuations which might be related to the jet instability are here in the upper troposphere, okay? Because remember the jet, this only mean jet is around 30 something, 32 North, are strongly coherent with fluctuations which may very well in the U-wind, okay? And I picked the U-wind because it sort of captures both what's going on in these mid-latitudes and it's important for the MJO, the upper-level U-wind, remember my picture of tropical convection. So you can see that these two are very strongly coherent. Now the interesting thing is the first thing you should, we thought of, well, oh, that's just the middle-latitudes responding to the MJO, okay? Or it could be the MJO responding to middle-latitudes. So what we did was the exact same thing but we tried to put a ton lag between the tropics and the extra tropics. And it turns out the best result, the strongest coherence is a time lag zero. And if you change it five days, either ways, it doesn't matter very much. So this would, on face value, it's, we don't, we totally understand this but on face value it suggests that there are ways in which the tropics and extra tropics are globally coupled. And I don't know if we're gonna be hearing about it in the next two weeks. There are instability models, okay, of, which take into account heating, basically theories of global instability where you can get modes which have both tropical and extra tropical disturbances growing with all the physics in them at the same time. So this is something we also ought not to totally forget. Okay, so I have 10 minutes. I wanna just again be just quickly, oh, I have a conclusion slide, okay. So clearly, if we think about the, just to conclude, and I wanna be happy to take questions, if we can think about a mid-lateral response to tropical forcing, always in the back of your mind when you're thinking about that, think is this something that you can relate to stationary waves or is this something totally, or the mid-lateral is responding in a way which is new because the forcing is transient, okay. And we're gonna be talking about that a lot, especially with the MJO. We also ought to think that tropical forcing can affect mid-latitudes in a more subtle way, which is that it can excite mid-latitude, but it will change the storm trucks. We know that. I haven't actually mentioned that. The tropical forcing will alter the mid-latitude storm trucks. It's baroclinic instability, but in a more subtle way, it may also excite mid-latitude barotropic instabilities, okay. So that's always something to keep in mind. I've tried to show you one diagnosis or one way in which the extra tropical disturbances can actually lead to tropical heating. There are probably more than I've covered. I know that people are interested in this incursion of these russby waves into the tropics to quite an extent these days. And finally, I should keep in mind that there are these bits and pieces of evidence floating around that the tropics and the tropics are not, you can't think of them as separated by a wall, okay. That's actually also true, I think, for the troposphere and stratosphere. We tend to think of tropical meteorology and exotropical, okay. And in some cases, this is not a good idea to think of them as totally separate. Okay, so I'm happy to take questions and discussion, including those from the directors.