 OK. Thank you very much. So, I should say straight away that the stratosphere is not my area of expertise. And so I'd like to thank a colleague of mine at Reading Andrew Charlton-Perez who gave me some of his lecture notes from one of the courses he teaches as a kind of place to start to build a lecture. So thank you to him for that. So I'm going to try and cover some aspects of stratospheric variability and prediction that might be relevant on sub-seasonal timescales. And we'll see how we go as we go along. So in this talk I will try and just give a brief outline of the structure of the stratosphere for those of you that haven't come across stratospheric dynamics and things before. And then I'll talk a little bit about the variability of the stratosphere itself and then how that might be related to the tropospheric variability that we might be interested in predicting on sub-seasonal timescales. And then I'll talk a little bit about the actual prediction aspects for the stratosphere and the relationship between the stratosphere and the troposphere. So the stratosphere is the bit of the atmosphere directly above the troposphere. It's separated from the troposphere by the tropopause. And so on these plots here the tropopause is marked by this dashed line. And in the tropopause the temperature decreases with height as you go up. And then at the tropopause the temperature is or above the tropopause the temperature remains constant or maybe even slightly increases with height as you go up. So this is the zonal mean temperature as a function of latitude. And so you can see that in the tropics the tropopause is around sort of 15 kilometres high. And in the polar regions it gets down to about eight or nine kilometres. And actually in synoptic weather systems it can even get as low as four or five kilometres in the atmosphere. So I've got the winter, the northern hemisphere winter and northern hemisphere summer season here. And you can see that the winter pole is much colder than the summer pole. And that's because basically the stratosphere is in radiative balance pretty much. And so in the summer pole there's lots of heating from the sun and that's balanced by radiative cooling. But in the winter pole it's just cooling to space basically and there's no heating coming in. You'll also notice that in the summer hemisphere the temperature is actually warmer at the pole than it is at the equator as you go above sort of about 15 kilometres. And so that means that the temperature gradient is reversed in the stratosphere compared to the troposphere. And you'll also notice that in the southern hemisphere winter the southern hemisphere stratosphere is much much colder than the winter hemisphere stratosphere. And that's related to the strength of the polar winter vortex at that time which I will come to in a minute. And so the top of the stratosphere as it were is sort of around 40, 50 kilometres which is about here, just above here probably. And that's where the stratopause is and then we go into the mesosphere above that. And in the mesosphere the temperatures start to decrease with height again. And I won't talk about the mesosphere anymore. So consistent with these temperature gradients that we see in the stratosphere the zonal winds in the stratosphere are in thermal wind balance with those temperature gradients. And so we see in the winter hemisphere a strong westerly jet increasing with height which is consistent with warm temperatures at the equator and cold temperatures at the pole. And in the summer hemisphere we have a weak easterly jet increasing with height which is consistent with the fact that the pole is warmer than the equator. So these zonal winds in the stratosphere are in thermal wind balance. The stratospheric jet is slightly poleward of the subtropical jet but is clearly connected to the tropospheric jet. And then, what else have we said here? So again consistent with the colder temperatures in the southern hemisphere, the winter pole is, the southern hemisphere winter jet is much, much stronger than the northern hemisphere winter jet. Have we got anything? Right. OK, so the other thing we haven't said about here is that the jet essentially describes the edge of the polar vortex. So you can, if you think about the vorticity associated with the horizontal gradients of the wind here, then this jet describes the edge of the polar vortex. Are we following so far? So this just describes the mean state of the stratosphere and the winds. What does the variability in stratospheric wind look like? So there are two sort of areas where there's large variability in this zonal wind structure. So one is in the equatorial lower and mid stratosphere where you have quite large wind variability. And then the other is the variability that's associated with that winter polar jet. And there's very little variability in the summer hemisphere. I'll explain why that is in a little while. But you'll notice that although there's much stronger jet in the southern hemisphere, that when you get towards the polar region the variability of that jet is much weaker than it is in the northern hemisphere. So in the extra-tropical regions this variability is largely caused by planetary waves propagating from the troposphere up into the stratosphere. And the propagation of those planetary waves and their influence on the jet is sort of determined by two things. One is the wind structure in the stratosphere and I'll explain that a little bit later. The other is the fact that, you know, the source of wave activity. And in the northern hemisphere in the sort of polar regions or the sort of higher mid-latitudes, there are lots of large mountains and land-sea contrast which drives quasi-stationary planetary waves in the atmosphere. Whereas the southern hemisphere, around 60 degrees north or south even, there's very little contrast in land-sea or in aerography. And so the wave activity, the stationary wave activity in the southern hemisphere is actually much weaker. And so there's very little wave forcing in the southern hemisphere jet. So the reason there's little variability in the summer hemisphere is because the Rossby waves can only propagate vertically if there's westilly winds. And so in the eastilly winds of the summer stratosphere the waves can't propagate vertically and if they're not propagating vertically, they're not then transferring momentum into the jet. And so there's no sort of source of variability on those timescales there. Okay, so let's have a little bit, a little look at some of these modes of variability. So the first thing we noticed here was this strong variability in the equatorial stratosphere. And that's dominated by something called the quasi-banial oscillation, which is this oscillation in the equatorial stratosphere between westilly winds and eastilly winds. And this is an incredibly regular oscillation in the atmosphere. It's probably the most regular oscillation in the atmosphere other than the annual cycle or diurnal cycle. And it's called the quasi-banial oscillation because its period is around two years. It's actually slightly longer than two years on average, about 27 months, but it varies between perhaps two years and two and a half years. So what's the source of this variability? So, again, this is due to waves propagating vertically in the atmosphere. This time it's gravity waves triggered by orography and convection and also a little bit of influence from the large-scale planetary waves, the Kelvin waves and the Rossby waves that you learned about from Fred Cacharski last week, which propagate vertically in the atmosphere. These waves can only propagate vertically in regions where their phase speed, i.e. their eastward propagation speed, has the opposite sign to the mean wind, or if the mean wind is small. So, as these waves break, where they can no longer propagate, they accelerate the mean flow in the direction of their zonal propagation. So, here we have a sort of a westerly state in the atmosphere and these waves which are propagating vertically which have an eastward phase speed, so westerly phase speed as it were, as they propagate vertically, they break and the action of them breaking tends to accelerate the wind towards their phase speed in the region in which they break. So, that causes an acceleration in this region, a westward acceleration in these regions, but these waves that have an eastward phase speed or westward propagation can propagate straight through this region and they actually start to break a little bit when you get into a region where there's an eastward shear as some of these waves start to break in this region. So, that tends to decelerate the wind slightly or accelerate it slightly into the westward direction. So, what triggers the gravity waves? So, most of it is convection and so the gravity waves, but obviously there are some aerographic gravity waves as well which propagate vertically, which are a source of that. And then also there are some influence of the Kelvin wave and Rossby waves propagating vertically. The Rossby waves is a bit more complicated because you have to sort of think about not just the momentum but the kind of influence they have on the zone or sort of the weak overturning circulation in the stratosphere as well. So, equally distributed. So, from convection and aerography, they're pretty much roughly equally distributed. I mean the equatorial waves maybe not quite so much. So, that's the quasi-biannial oscillation. But if we're thinking about predictability on sub-seasonal or seasonal timescales, this ought to be a pretty easy problem. Persistence is going to do a reasonably good job of predicting the phase of the QBO on sub-seasonal or seasonal timescales because the timescale of the oscillation is much longer than any of those. The reason, well, other than the fact that it's one of the major modes of stratospheric variability on any timescale, I'll come back to it a bit later, but the phase of the quasi-biannial oscillation can actually influence some of the sub-seasonal variability in the stratosphere. And from that point of view it's important. Adrian. I think we're going to start with the record. Why do you set the oscillation in timescales? And what's actually the way you... Well, okay, so if we come to the... Actually, if we come to the next slide here, so what sets the timescale is basically the kind of rate of which the gravity waves are fired from the stratosphere and the momentum that's associated with them in their wave interaction. So it's a combination of the amplitude of the wave activity and the timescale for which it takes for them to influence the jets. But in terms of generation, what would you suggest to... Okay, so the green line on here on the next slide is the same as the green line on here. So the idea is that as you... So you have this green state and the waves accelerate the flow here and decelerate the flow here. And so a little while later you have this blue state where you have westerlies lower down in the atmosphere and you start to get easterlies above. And then the waves are now... The eastward propagating waves are now not able to propagate so high and so they break lower down in the stratosphere and accelerate the wind down here. And the easterlies and westerlies and westwards and eastwards are really confusing, aren't they? And we talk about easterly and westerly winds, but eastward and westward moving waves and they are opposite and it's really confusing. So the westward propagating waves break lower down in the atmosphere and cause an easterly acceleration lower down in the atmosphere and so the easterly flow moves downwards. And then the west... The eastward propagating waves break even lower down and cause this gradual deceleration of the jet here. And then this eastward would start to propagate down further and further towards the surface. Plum, I think. So this mechanism for the TBO has been known for a very long time and it's very remiss of me not to put some references in here for this bit. But you can read about this in a standard dynamical meteorology textbook like Hulton's. And this figure is actually... I thought I'd put it in there. But this figure is actually sort of modified slightly from Hulton's book. So this mechanism has been long known. But it's taken a little while, a few iterations to understand what was going on. Originally it was thought that actually it was the Kelvin waves and Rosby waves that were the kind of the dominant source of this propagating the acceleration and deceleration. But when they start to try and do sort of a quantification of that effect they realise that those waves in themselves don't have enough sort of energy to cause this oscillation and it must be associated with the much faster gravity waves triggered by convection and aerography to drive this mechanism. So in the extra tropics there's a very similar source of the variability in that it's dominated by planetary waves propagating from the troposphere into the stratosphere. But in the extra tropics it's Rosby waves that are that wave source. And again Rosby waves can propagate vertically in sufficiently weak westerly winds. So if the wind is between zero and some positive westerly wind called the critical velocity then the waves can propagate vertically. If the winds are easterly or too strong then they can't propagate vertically. And this critical velocity depends on wavelengths in such that shorter wavelengths have a much lower critical velocity and so they can't propagate very high. And they tend to break lower down in the lower stratosphere. So changes in this wave activity and breaking can lead to variations in the strength of the polar vortex. And if we go back to that plot of the variability that's why there's this sort of variability in the polar regions. And this variability in the polar vortex is the dominant mode of variability on sub-seasonal timescales in the stratosphere and the source of variability which gives us the greatest predictability in the stratosphere on these timescales. And so as I mentioned before there's very little variability in the southern hemisphere polar vortex and that's partly because there's a low source of planetary wave activity in the southern hemisphere. And it's partly because the vortex is very strong there and so it's hard to disturb it basically properly. I mean you do get variability of the jet but what you don't see very often, in fact only ever once in history is these sudden stratospheric warmings where you get a very rapid transition from mean westerly flow in the stratosphere polar region to this easterly flow. So the polar vortex is broken down completely here and I'll show you a little animation of that in a minute. Steve, you mentioned a sub-seasonal timescale, where does that come from? So again it's related to the amplitude of the wave forcing from the troposphere and the mechanisms by which that momentum is transferred to the jet. Does that have to do with the timescales and the troposphere? No, not really, no. I guess in the sense... No, the timescale isn't really set by the timescale of the variability. The timescale is really set by the amplitude of the wave. Well, there's variability there going on all the time. What determines whether you get something like this is whether you have strong enough wave amplitude to generate that. And this would be somehow set for you less than 98. What about the fan? Of the variability you're talking about. So what it requires is some variation in the amplitude of the wave. So if you have a fixed amplitude wave, then the momentum transfer associated with that is negligible. So you need to have some variation in the amplitude of the wave. So the shorter timescale, essentially that's a larger variation in the amplitude of the wave. So the shorter timescale waves are more important. Shorter timescale variations in the wave amplitude are more important than long times or slowly varying. This is just one year. This is 2008. I'm actually going to show you this I think in a second. So this reversal of the westerly wind to easterly wind also implies a reversal of the temperature gradient in the stratosphere. The name sudden stratospheric warming comes from the fact that you get a very rapid increase in temperature in the polar vortex during that time. Because to reverse the wind at that height, you need a reversal in the temperature pole to equate a temperature gradient at that time. This is actually averaged at 60 degrees north where the jet is at its strongest. So in the southern hemisphere, the wave forcing is generally not strong enough to create what's known as a major warming where you get a reversal of the jet at the pole. It's happened once in history and everybody got very excited. But it's not happened again. So I think perhaps what I will do now, briefly, is go to here. So this is the polar vortex. It's an animation from January and February 2008. It's this event that I showed before. This is potential vorticity on an isentropic surface, a constant potential temperature surface. It's about 21km above the surface of the earth. So this is the very high potential vorticity air that you see in the polar stratospheric vortex. You can think of this as being very cold air. This is the low potential vorticity air of the equatorial and tropical stratosphere. You can think of this as being the very warm air. This black line here essentially marks the maximum zonal wind associated with the polar vortex jet. If we run this forward, what you'll see is that you've got this vortex. It's fairly stable. There's some movement around the polar vortex. As we go forward in time, you'll start to see that that polar vortex is getting pushed off the pole. You've now got easterly winds at the pole. There we go. So easterly winds at the pole, warm, very warm, essentially subtropical air over the pole. At the end of the animation here, basically that polar vortex has been completely wiped out. Shall I run that again? Let's not run it again. Let's not play it again. But you can see there's a very remarkable turnaround of that. So that event was what's known as a displacement event because the polar vortex has just been shifted off the pole initially. Hopefully, the fact that that animation wouldn't run is not an indication that this one won't do as well. So this is a slightly different type of event. This is what's called a split vortex event. We've got this polar vortex set up at the start. As we run through the animation, what you'll find is that there's a wave event which essentially splits the vortex in two. There are two little vortices or littler vortices that sit either side of the pole. So this is an event from the subsequent winter in 2008. So you can see straight away that the vortex is starting to be disturbed and pinched in the centre. It seems to re-intensify and then it splits. You have these two vortices and again this warming at the polar region. Shall we see if that one won't run again? Never mind. So that's potential vorticity but you can think of it as being... Potential vorticity and potential temperature are roughly conserved in the stratosphere on fairly short time scales. So you can think about the potential vorticity and the temperature being both traces of the flow. You can have more than one event in winter. A major warming like this, they come along on average once every couple of years. In fact, if we go back to Thomas' page... All these animations are available on a web page that Thomas Berner has at Colorado State. You can see there is... I'm sure I saw... Here there's a December and February event that happened in the same winter. It's relatively uncommon to see two events in one winter. That's right, yeah, I've broken them. So let's go back to it. So this was the zonal mean picture of that first event that I showed you. So you can see that sort of in the middle of February we had this change from westally to easterly in the polar vortex. Now one of the apparent characteristics of these sudden stratosphere warming events is this sort of evidence of some downward propagation of the event, certainly in the stratosphere. And that's again related to the same kind of mechanism as the QBO. So these rosby waves can only propagate in westerly flow. So if you have something that disturbs the flow at a particular level and creates easterly flow at that level, those rosby waves then are breaking lower down in the atmosphere and that causes this slight downward propagation of these warming events. And that's kind of characteristic of these. What you'll also notice is that if we look down at the surface, the tropospheric jet seems to have been disturbed at this point as well. And so there's very, very convincing evidence that these sudden stratospheric warmings have an influence on the tropospheric mid-latitude jet. So it's similar to the gravity waves, essentially, that you have these vertically propagating rosby waves that can only propagate in westerly flow. You've perturbed a jet here to create easterly flow here or the westerly flow is so weak that basically the waves can't propagate through it. And you, as a result, the wave breaking occurs at a slightly lower altitude. And then that brings the jet down. And that occurred as a quasi-bionial period in the trop? Yeah, but here, yeah, the mechanism's a different. I suspect there's an F factor goes on somewhere or something like that. It's above my pay grade now. So I've just sort of taken some snapshots from those videos that I showed you previously. Here's the undisturbed vortex from the January 2008 that was the start of the first animation that I showed you. And you can see sort of the vortex sitting over the pole. Here's the displaced vortex event that I showed you. The pole has now got sort of low PV air and the vortex has moved off the pole. And then this is from this split vortex event. And so some of the stratospheric warnings sort of can be classified if you want to make classifications about them. But they're kind of a spectrum of events. So there's two classifications associated with the strength of the warming. So there's a major warming, which is where the zone of wind is reversed over the polar cat and these climatological westerlies are replaced by easterlies. And they happen every two years, on average, every other year or something like that. They're not every other year, but on average, they're once every two years or so. And then there are minor warmings where there's strong perturbation of that polar vortex but not strong enough to actually cause a reversal of the wind. It may occur most years and more than once most years. And then these, you can also categorise them by whether there's sort of this displacement warming or a split vortex warming. And these displacement warmings are sometimes called a Wave 1 warming because you can, if you were to look at the zonal wave number around this region, it would be a wave number, zonal wave number one perturbation to the jet. And these are called Wave 2 warmings because it would be a Wave 2 perturbation on the jet, on the zonal flow. So these classifications you will hear about because to a certain extent the major warming is distinctly different from the minor warming. If you work on the stratosphere you'll hear about these terms and the impact of these two types of events on the troposphere is perhaps slightly different. But I'm not going to say any more about that. Right, so we've had the polar vortex and we've had the QBO. So there is some evidence that the QBO influences the occurrence or the strength of the variability in the polar vortex. So these waves are propagating vertically into the stratosphere and are also propagating towards the equator. And their propagation towards the equator depends on the strength of the flow. And just as they can't propagate vertically in easterly flow they can't propagate meridionally into easterly flow either. So if you have easterly flow, the easterly phase of the QBO at the equator then those waves that propagate or can't propagate so quickly into the equatorial region and they tend to be more confined into the mid-latitudes. And so you tend to get more wave activity in the northern hemisphere winter in the easterly phase of the QBO. If you have the westerly phase of the QBO then the waves can propagate away from the mid-latitudes more readily and so that tends to reduce the wave activity in the mid-latitudes. And this stronger wave activity tends to lead to more disturbed vortex during easterly phases of the QBO. So you can see that in a kind of time mean picture that you have these more displaced vortex events or more disturbed vortex events. If you look at the time mean that rectifies onto that. So this is the difference in temperature at 10 hectopascals between easterly phases of the QBO and westerly phases of the QBO. And so you can see that the pole is warmer on average during easterly phases of the QBO than it is on westerly phases of the QBO. So that's one reason we might be interested in the QBO because it potentially has an influence on the likelihood of a sudden stratospheric warming which we care about on sub-seasonal timescales. So for similar reasons the influence of the phase of the QBO and its influence on wave propagation may also impact the response of the polar stratosphere, that should say, to ENSO. If you look in easterly phases of the QBO then ENSO has very little impact on the stratospheric polar vortex. But in westerly phases of the QBO Laninio tends to be associated with a colder and stronger vortex and Elinio with a warmer and weaker vortex. And so this is a similar plot now of the difference in temperature for the winter between Laninio and Elinio years. And so you can see in Laninio years you have a colder polar temperature and a stronger vortex. That again is likely to have an influence on the likelihood of sudden warming and things like that. So with lots of variability in the stratosphere but if we're interested in predicting whether in the troposphere why do we care. So the variability in the stratosphere of this polar vortex can be described quite well by an annular mode. So it's an oscillation of the strength of the jet. And those annular modes can be found sort of all the way down through the troposphere. And in the troposphere we call those annular modes essentially, well, so there's the northern annular mode which is just the definition of this annular variation of the vortex. But at the surface in the northern hemisphere these are strongly related to the North Atlantic oscillation or the Arctic oscillation depending on where you live and what you want to call it. In the southern hemisphere the variability of the jet even low down is called just called the southern annular mode because at the surface the vortex or the jet is still fairly zonal and so the jet varies sort of in an annular way but because in the northern hemisphere the jet near the surface is broken up by the continents and the land sea and various things of storm tracks. We tend not to refer to it as an annular mode in the troposphere but we talk about the northern, the North Atlantic oscillation or the Arctic oscillation. And so what I've shown here is composite events, composites of 18 weak vortex events so that would be a southern stratospheric warming or a minor warming and 30 strong vortex events. So here we can see, so this is an index of this northern annular mode so we can see the weak vortex event in the stratosphere but it's associated with weak vortex or the weak jet phase of the northern annular mode in the troposphere and similarly for strong events we can see the same sign of this northern annular mode all the way through. And there's also evidence of this kind of downward propagation of this signal although this may, the downward propagation may be a little bit of an artifact in the sense that it might not propagate downwards as a wave all the way into the troposphere. It might just be that it propagates downwards through the stratosphere and then you tend to get this rather uniform response in the troposphere so it looks like it's propagating downwards through the troposphere because you just sort of carry the thing through but it's more like it gets to the tropopause and then it starts to have an influence on the tropospheric variability. So this sort of relationship between the stratospheric variability and the tropospheric variability hints that there might be some predictability in the troposphere associated with these events. So the mechanisms for this stratospheric influence on the troposphere are still not clear so it could be that the stratospheric or tropopause variations influence directly the growth of the baroclinic waves in the troposphere and that has an influence on the jet. So it could just be that you've changed the potential vorticity in the stratosphere and the troposphere feels that potential vorticity essentially and just adjusts in response to those potential vorticity anomalies or it might be that it's actually sort of related to the same mechanism by which the vortex is disturbed in that you get this relationship between the wave propagation and the mean wind and so I said there's some complex wave-mean-flow interaction but there's no consensus on which of these mechanisms is dominant and it's likely that at least more than one of them is playing a role in some way. So I'll now try and sort of characterise the relationship between the polar vortex and the troposphere. So what we've got here. On the left, these are surface pressure anomalies after weak and strong vortex events and so you can see, so unfortunately these are contoured rather than coloured but after a weak vortex event you tend to get anomalously low pressure over the sort of northern mid-latitudes around Europe and high pressure over the surface and that's associated essentially with a weakening of the pressure gradient and a weakening of the jet and after strong vortex events you see increasing pressure over the polar, decreasing pressure over the North Atlantic and a strengthening of the North Atlantic jet. And so if you look at the distribution of the North Atlantic Oscillation Index following, for 60 days after a weak vortex event or 60 days after a strong vortex event you can see a clear shift towards higher North Atlantic Oscillation Indices following strong vortex events than weak vortex events and if you look at the surface temperature anomalies following stratosphere so this is weak minus strong vortex events so you can see that this much colder North American and Northern Eurasian temperatures following weak events compared to strong events. So this is quite a large signal in the troposphere and it seems to be associated with stratospheric variability so that implies there might be some useful predictive capability associated with the stratosphere. So is that predictive capability realised? So Sigmund explored this in the Canadian it's called the Canadian middle atmosphere model because it has the stratosphere and mesosphere in the model not because it's just the model of the middle atmosphere. And looked at a set of hindcasts basically initialised on the dates of 20 sudden stratospheric warmings and compared them to a set of control forecasts where he took the same day of the year but ran the forecast for the year before or the year after. So essentially he's constructed his control that way so that he's capturing the same time in the seasonal cycle but randomly selecting essentially a stratospheric initial condition that may or may not have a warming event in it. And so if you look at the ones initialised following a sudden stratospheric warming you'll notice two things. So this is the north manual mode index at the surface. You see that the the mean north manual mode index at the surface observed is less than zero and the mean forecast annual mode index is less than zero. So we're seeing the signal here and the forecast models in the mean are able to capture that and you actually see that virtually all of the forecasts all of the runs fall in this quadrant here so the observed signal and the forecast signal are in the same quadrant. If we look at the control and there's quite a strong correlation between the observed and forecast signal if you look at the events which are initialised essentially randomly you can see that the forecasts and the observations are actually distributed much more through all of the quadrants. So and the mean signal in the observations and the forecast is close to zero. So there's very little signal the forecasts on average have got the right response but actually there's very little correlation between what was observed and what was forecast. So this demonstrates two things one it demonstrates that there's a signal associated with the sudden stratospheric warming but the other thing it demonstrates is that forecasts are able to capture the response but not only are they able to capture the response but there is some predictability more than there is in the normal situation associated with that. So here the forecast don't do a very good job essentially. So it also has an impact on seasonal predictability. So if we look at things like surface temperature so this is observed and forecast after a sudden stratospheric warming so you can see warm over northern Europe warm over the Middle East cold over North America rather warm over the Middle East and cold over North in Eurasia and the precipitation you can see enhanced precipitation over the North Atlantic region sort of a dipole pattern. And if you look at the conditional skill scores for surface temperature these are essentially correlation skill scores for surface temperature conditioned on whether it's following a sudden stratospheric warming or not you can see that there's higher skill for these surface temperatures or the surface precipitation over the Atlantic following a sudden stratospheric warming than not. And there's a similar signal on some seasonal time scale so I'm aware we're going on a bit on time here. So on Tripathi and colleagues recently looked at the impact of sudden stratospheric warming on sub-seasonal predictability in ECMWS monthly forecasting system so this again is a composite based on strong, medium and weak events at 10 hex plus scales on 60 north I think that probably fits under that figure. And so you can see that the again observed on the top and forecast on the bottom you can see the model is able to capture reasonably well the stratospheric evolution of the vortex but also the tropospheric response to the vortex. And if you look at the surface temperature or sea level pressure and temperature signals associated with that again you can see at week two this picture of warm over North America cold over East Asia and warm over the Middle East is there in the observations at week two after these events and in the model and similarly still the signal is there at week three in the observations and the model is able to capture most of that response and again at week four. And so there's this signal in the stratosphere that is driving variability in the troposphere and the forecast model seems to be able to capture that quite well. But not only does it not only is that signal predictable but for some regions and in some places it actually improves the predictive skill of the model and so we can see some examples of that so or should I say what this is? So this is a temperature anomaly following a weak and strong event and this is observed and forecast and observed and forecast depending on the sign of the anomaly basically and you can see that the model is able to pretty well capture the strength of that observed signal and if you look at the forecast skill for the northern annual mode index in weak vortex or southern stratospheric warming events or strong vortex events you can see that the forecast skill as measured by the anomaly correlation is higher in disturbed vortex situations than it is during the undisturbed vortex conditions. So not only is it a source of variability it's also a source of predictability enhance predictability in these disturbed conditions and this is a similar plot for temperature in following weak or strong events and you can see in some regions so over the Middle East at week 4 much higher predictability following in surface temperature following a weak vortex event than under normal conditions in the stratosphere and similarly over eastern Canada I think we are near the end so how predictable are the southern stratospheric warmings so if you've got a southern stratospheric warming in your forecast then that suggests you've got improved predictive capability over the northern hemisphere for the next 30 to 60 days but if we could predict when those southern stratospheric warming events might happen that gives us even more predictive and even longer lead time of predictive capability so to date there hasn't been an enormous amount to look at those the predictability of the warmings most studies focus on the prediction of an individual event rather than an ensemble of events and that suggests sort of a skill lead times of 5 to 15 days depending on which event you look at which model you look at studies that have looked at vertical or horizontal resolution have tended to show that improved vertical resolution or improved top, higher top, model top or improved horizontal resolution tend to improve forecasts as do forecasts which have a better representation of the mean stratospheric state which is important for being able to predict the interaction between the planetary waves and the jet and if you can improve the representation of the stratosphere in your models then that gives you a better chance of assimilating satellite observations of stratospheric temperature into your forecast so improve your initial conditions in the forecast and that might give you better predictability so one potential source of predictability for southern stratospheric warming is the MJO so this paper by Garfinkel a few years ago explored the link between the manjillionase oscillation and southern stratospheric warming and found that so this is the MJO phase before a southern stratospheric warming event and so between 1 and 12 days ahead of a southern stratospheric warming you're much more likely to find an MJO in phase 7 or 8 than you are climatologically and much less likely to find an MJO in phase 2 than you are climatologically and as you go back in days then what you'll find is that this where you're likely to find the MJO moves backwards in time because obviously the MJO has a kind of time scale associated with it and if you look at polar cap temperatures which is a measure of the strength of the vortex function of lag in this direction following particular MJO phases along this direction again you can see that there's this clear relationship between MJO phase and polar temperature so we've got potential predictability of the vortex warming associated with the MJO for example so if we've got an MJO in our initial condition that might give us more predictability for the polar jet or the polar vortex but obviously also you know if we can predict the MJO phase a few days in advance then maybe that extends our predictability back slightly further in time as well it's wishful thinking by this stage though probably so I'll try and summarise so the stratosphere is characterised by strong static stability with uniform or slightly increasing temperature with height there's strong seasonality in the zonal winds and temperature which are in thermal wind balance with a westerly polar vortex in the winter hemisphere and easterlies in the summer hemisphere equatorial variability is dominated by the QBO which is driven by this interaction between vertically propagating gravity waves in the mean flow there's weak variability in the summer hemisphere and the winter polar vortex variability is driven by an interaction between vertically propagating rosby waves and the mean zonal wind for strong wave forcing that winter polar vortex can break down and you have sudden stratospheric warmings and there's a strong teleconnection between stratosphere and troposphere associated with these annular modes which leads to potential predictability on sub-seasonal to seasonal timescales operational prediction systems are able to capture some of this tropospheric response to polar vortex variability and so strong and weak vortex conditions can not only improve give you a signal to predict but they actually enhance your predictability on those timescales and there is potential to predict the sudden stratospheric warming events that lead times of a week or two as well which might further enhance our predictability thank you