 OK, just first up, a couple of references and resources. So after my talk on Monday, I realized that the theoretical ideas behind resonance and all of these types of things were sudden warments. I gave you the literature, but I won't lie. It is a non-trivial literature, mathematically. And often, those authors are very good at doing the clever math, but perhaps not so great at translating that into physics. So in this paper of mine that I've cited, there are three sections that if you want background on kind of the theory, but you want it written in English or more simple language, the introduction in those two sections in 4A and 4B will give you background that really translates. The paper is sort of long, but the reason why it's long is because I tried to translate the theory into physics. So you might find that helpful if you're interested. Second, I know a lot of the talks have been making use of like RMM and all those various MJO indices. And I just wanted to point out that in my section at NOAA Ezraal, we have an MJO indices web page. And that has links to Matt Wheeler's website that will give you time series of RMM. But in addition, no one has mentioned the OMI index. And that is a index that's maintained locally at NOAA. And you can get time series of that there. And I should just point out that in some sense, the way to think about those two indices is RMM takes circulation and OLR. But for the most part, it's really just a circulation indices. It's not to say that it's not related to OLR. But if you remove OLR from RMM and you correlate it with and without OLR, it's correlated at like 0.9. So it's really a circulation indices. The OMI, on the other hand, is purely based on OLR. So if you want to look at those two types of things that circulation OLR indices, this is a great resource. And then the paper by George Coladas, I put the citation for that down there. So that might be useful to some of you. That's got nothing to do with my talk. I don't work on the MJL, but here you go. OK, so folks, my talk will be on stress for troposphere communication, and in particular, in the context of extra tropical tropical communication and sudden warmings. So I'm just going to briefly go into a little bit of the mechanistic understanding, which has been around for 30 years, but is still poor. But I'll try to give you an overview of that. And then I will talk about predictability, probabilistic predictability, not deterministic like in my previous talk in the context of, and so, QBO and sudden warmings. OK, so most of the talks that we've heard, OK, all of the talks, have focused on things like tropical SSTs and the tropospheric teleconnection pathway. So that's like, say, the jet stream response, and then you get a raw speed response and those types of things, all within the troposphere. However, there's also what is called the stratospheric pathway. And kind of a broad leeway to think about this is like, so say you have an El Nino going on and that SST anomaly drives stationary planetary wave response. And that wave response goes into the stratosphere and it affects the stratospheric polar vortex as opposed to the tropospheric vortex. And that signal goes up, does something to the stratospheric polar vortex, and then that signal comes back down. So that's kind of in a very broad sense, a two-way process. First is you get the signal that goes up, but then you've got to communicate it back downwards to the trouble pause. And I've listed out a set of ideas that are kind of theoretical constructs that have proposed how this might work. I won't lie to you. There isn't a smoking gun at this point. I'm going to go through one of them that I find to be more compelling, but you shouldn't forget that all of these exist. That response then is amplified. And I'll kind of show in the next slide how that might work. But essentially, you imprint something on the trouble pause. And then there's a synoptic eddy feedback that amplifies that response. OK, so I'm going to focus on just so you can get an idea of how this might work on the remote response to the stratospheric PV anomalies. So I just wrote the perturbation QG PV equation and kind of this middle piece. You know, it's got all these geometric terms and whatever, and it looks sort of complicated maybe. But really, you could just distill it down to the fact that it's a three-dimensional elliptic operator. And anybody, I don't know if anyone's worked on partial differential equation theory, but an elliptic operator, this is a linear operator, what it means is when you invert that. Once you have the PV, you can invert that to get things like geopotential and the winds and things like that. And that invertibility is non-local. So what that means is if I have a PV anomaly in the stratosphere or the troposphere, I invert that. There's a wind and geopotential response that is a broad field response, and it's not just at that point. It's also a linear operator, so we can do what's called piecewise PV inversion. So this is from a paper. I think I gave the wrong, no, that's the right reference. I was thinking that was the black paper. Anyway, essentially what you can do is you can say, OK, well, I'm going to take a PV field, and I'm going to invert it and get a zonal wind profile. So this box right here on the far left, in the upper corner, is a zonal wind profile in latitude and pressure for tropospheric and PV field in its entirety. Then, as I said, it's a linear operator, so we can split that into, OK, let's look at the tropospheric and stratospheric portions of that PV anomaly separately, invert them separately, and then figure out what their implied wind response is due to those two PV anomalies. And what you see is that the tropospheric PV anomaly gives you this wind response that's largely lower most stratosphere down to the surface. And if we invert the stratospheric PV anomaly, we get something that's largest in the stratosphere. But you, again, you see this large scale structure that leads all the way down in the troposphere. And so if you look at that on, say, the 215 hectopascale geopotential in terms of the 215 hectopascale geopotential height anomaly, this is the full field, tropospheric plus stratospheric PV. This is the geopotential that results from the tropospheric portion of the PV inversion. And this bottom piece is the stratospheric PV inversion. So kind of what you can broadly, qualitatively interpret here is something happens in the stratosphere, changes the PV polar vortex strength in the stratosphere. You get this kind of large scale imprint on the upper troposphere. And then the tropospheric part is this higher wave number kind of pattern. And that's the contribution there. There's no causality there, but you just kind of keep in the back of your mind that something happens in the stratosphere. It imprints something on the troposphere, and then there's probably some sort of feedback with tropospheric anomalies. So any of these theories, whether it's, I mentioned, wave reflection, downward control, any of these are you have to take that, translate that polar vortex anomaly in the stratosphere, get it to the tropopause so that you can then alter tropospheric weather. So anything, heat anomaly, anything that's going to alter PV. So drive a planetary wave from anomalously large planetary waves from, say, an El Nino event, drives a stationary planetary wave into the stratosphere, weakens the polar vortex. That's a PV anomaly that's going to then imprint something non-locally. So this left panel is what's called the nominally the dripping paint diagram. And this goes back to Baldwin and Dunkelton in 1999. And what they did was, is they calculated the northern annular mode, which is just, and they did this in the stratosphere, I believe, but it doesn't much matter. Essentially the way to think about this is that when you have the polar vortex, when it's strong, and there's not a lot of wave activity in the stratosphere, the vortex is very broad and strong. There's a lot of wave activity and a lot of wave drag, it slows down the vortex and you get a contracted and weak vortex. And essentially what they did was they composited, this is at lag, plus and minus, for, I forget what the time series, maybe went back to 1979 or the 50s or something like that. The point is, is that they composited 18 week vortex events and 30 strong vortex events. And there's been a lot of discussion this looks like some sort of downward signal propagation. Something starts in the stratosphere, at zero lag and then it bleeds down in the troposphere. There's a lot of argument about whether that's the correct interpretation of that. Yes? Yeah. Because it's extremely low. Yes, that is accurate. And there's, but Dave Thompson and Mark Baldwin recently, not super recently, but wrote a paper on all of these various indices. And if you go into this stratosphere, all those indices, whether it's the NAM, they owe whether you use geo-potential or EOFs or whatever you essentially get, get broadly the same result. And this, this is a recent plot and instead of just weak and strong vortex events, this is for sudden warming events, right? So in a sub, some sudden warming event is just a subset of weak events. It's particularly very strong events, right? So that's when the vortex breaks down and you get a very similar pattern. So if you look at this at, say, various surfaces in the troposphere in terms of mean sea level pressure, surface temperature anomalies or precip anomalies and the hatching shows where things are significant, you see what those patterns, this is 60 days out from a central warming date, right? So sudden warming happens and then 60 days and you integrate and to find out what the anomaly patterns look like and this is what you get. In particular, for a sudden warming, you get a negative NAO pattern. You can see that when you look at these structures. Okay, so those are just kind of the broad basic characteristics of what happens when you strong weak vortex events and sudden warmings. What does that mean in the context of other previously kind of thought of as tropospheric teleconnection patterns? Okay, so I'm gonna show a series of plots from model results, all these model results that I'm gonna show you, they're various. This is Ekken from Max Planck and they're all very long runs, a lot of ensembles and so there's a lot of statistical power in these but they are all model runs. So this is plots in the top row of 500 hectopascal geopotential height anomalies. On the left we have the model predictions and on the right we have error interim and so this is the two months after a sudden warming and what we did some, no, I'm just hearing things, okay. In the two months after a sudden warming you get this negative NAO pattern and that shows up both in model and in error interim and on the bottom panel, what they plotted is El Nino both in the model and for error interim and again you get kind of this similar pattern. Okay, so what happens if you try to separate out the effects of kind of the sudden warming from just pure El Nino? Yes, sudden warming can only happen in DGF so yes, all these plots are, for the stratosphere primarily only has an influence on things in the winter because the Charney-Dresden condition says that you cap wave activity during other parts of the year so you really have a boring stratosphere during summer. So okay, so then they took this and they sliced their data into time periods with El Nino with a sudden warming and time periods of El Nino without a sudden warming and part of the problem with looking at just reanalysis status, by the time you chop it all up, right? You only have a few El Nino cycles, you only have a handful of warmings, by the time you chop it up you do it left with essentially nothing so that's the whole point of trying to do a lot of these simulations with a lot of ensembles to get more statistical power. Now interestingly what happens is we get a, when you look at El Nino with sudden warmings you get this kind of similar pattern that we looked at before, right? And that's not surprising. However, if you look at El Nino without sudden warmings you get a very, very different picture, okay? So what this is and the El Nino with sudden warmings if you notice looks very similar to all sudden warming periods or all El Nino periods. And I think one of the messages they're trying to take away there is that yes, El Nino in the tropospheric pathway gives you something strong but a good portion of that is likely due to the fact that you also have in the data record you have sudden warmings going on during those years and when you collect them all together on aggregate you're seeing a big imprint from the stratosphere and it's not just the troposphere pathway from El Nino. Okay, so what about El Nino versus La Nino? And as I said, when you have a sudden warming it imprints typically a negative NaO pattern and if you take, these are again 500 hectobascale anomalies, height anomalies and the top row is El Nino, the bottom row is La Nino and you have for all years and again these are N-CAM5 simulations you get these kind of opposite pattern for El Nino versus La Nino and if you look at with sudden warming it looks essentially the same for El Nino perhaps a bit stronger and for La Nino it's slightly weaker than the all case and then if you look at the no sudden warming and you subtract the with minus no sudden warming what you see is this identical pattern and that's that imprint of that negative NaO pattern so whether or not you have essentially the way to look at this is I think in a simplified sense is that you have the tropospheric pathway that's going on that El Nino versus La Nino but if you then imprint on top of that a sudden warming you're gonna get the aggregate effect of that tropospheric pathway plus the stratospheric pathway which is a negative NaO effect. Obviously that's a simplified linear way of thinking about this but broadly if you're trying to get a conceptual handle on these things that's maybe the way to look at it. Sagan? No, it's not. La Nino when you find some sudden warming and of course if you pick it up then you see the difference. No, I probably wouldn't interpret it that way. Just here as I said I have a linear and a positive NaO it's clearly different from a linear and not positive NaO the structure is different by definition right? It's also saying what I do here they have to look different by different conditions. Sure. A sudden warming produced negative NaO. That's the, I mean that's the, this is not a, I mean I wouldn't argue that that's a noise imprint of noise. No, but it's just saying that it's not noise. It's just saying okay if I have a negative NaO or a negative NaO then this sudden structure is warming then I get the signal that can be superimposed to a linear and then or not superimposed to a linear that gives me the response. It's just saying that the acceptable atmosphere can have this noise pattern or whatever you want to call it I guess I'm not following. We'll have to, what's that? That's an open, that's sort of an open, yeah well I mean the argument is as I'll show that sudden warmings have a tendency to occur more during both on linear and on linear why that occurs. That's sort of an open question but I mean, sure? Let's talk afterwards. This is, I mean this is at lag so that's unlikely. I don't think the NaO is not causing a warming but all right I'm not going to go through this. I just wanted people to have this reference. It looks at central Pacific versus east Pacific and I'll only know and there's some I guess some more rich behavior depending on how you chop up the data. Okay so that's kind of the broad understanding of and so what about the quasi-venial oscillation? So I'm not sure whether people, how familiar people are with it but broadly the equatorial QBO is an oscillation in wind and up here I've just shown time series and these are easterly versus westerly downward propagating zonal wind anomalies and this is a wave driven effect. Essentially what you have here is if you look, this is height versus latitude and you have generation of Kelvin waves, mixed rock and gravity waves, gravity waves. Those propagate up into the stratosphere and those are differentially filtered dependent on whether it's whether you have easterlies or westerlies and so one spectrum of waves are allowed up during easterlies while the others are capped and they drive one descending branch then when that branch is ascended you switch and the other spectrum of waves are allowed to propagate up and they drive the reversed cycle. So you get this alternating wind anomaly pattern. Now in addition to that over the tropics what that does is this is a zero wind line it essentially takes that zero wind line and ends it in and out in the latitudinal sense. So when you have the way that that's important is broadly speaking you have planetary waves that propagate out of the troposphere into the stratosphere and as you move this zero wind line in and out you constrict that wave activity to stay more towards the pole or allow it to escape more towards the equator. It's a bit more complicated than that but in a very kind of schematic broad sense that's the way to think about it. Okay so what might that look like? So just so that we understand during the westerly phase this line is moved more equator-ward and in the easterly phase the zero wind line moves more towards the pole. So when it moves more towards the pole you kind of hold more wave activity in and if you look at the difference between the superior west minus east this is co-authors mind I prefer to look at the east minus west because the west is sort of like a non-signal because climatologically wave propagate up and they go equator-ward it's really during the east when you're pinching it that you're changing things. Nevertheless this is error interim and error 40 and this is for a very large ensemble of NCARC-CAM-5 runs and you essentially get the same deal and essentially what happens is during cubio-east as I said you kind of constrict things you hold more wave activity in and you get a weaker polar vortex. Okay well what does that look like in terms of sea level pressure so you can see that you get this kind of similar pattern those contours are they're like a half a hexapascal or something like that so it's from my perspective it's kind of shrug meh you know that's not a big effect okay why might I be bringing up the cubio then if it has such a weak if the cubio itself has such a weak surface anomaly well it's because the cubio has the two phases have some preference as far as sudden warments so what this is a plot of here is this is on the vertical axis this is a measure of what is called the Holtman tan effect that breathing in and out is what's called the Holtman tan effect that's due to a paper that was written in 1980 by Jim Holtman and what we're doing here is correlating the strength of that that Holtman tan effect with the frequency of sudden warments and you see that it's very very well correlated down at the bottom what we've done is we've done it for both phases and what you see is during the cubio-west there's essentially a non-significant correlation of 0.35 and during east there's an extremely high correlation right so that's 0.91 and so essentially what this is telling you is that when that zero wind line is very is encroaching strongly poleward you're getting more sudden warments so and as I said that's consistent with the idea that the easterly phase is really a signal and the westerly phase is largely just a weak okay so the cubio is a 28 month oscillation right and that period that's plus or minus a few months this except for this last year where we had disruption of the cubio this looks like this and will continue to look like this barring some sort of catastrophe so it's very predictable so you can imagine that if we know what phase of cubio we're in and we knows probabilistically what that means in terms of sudden warments that might give us some sort of seasonal predictive skill on the NAO provided the NAO doesn't trigger warments or any of the questions notwithstanding what about ENSO so what I've done here is I've taken these are I created tables from two different papers and essentially the takeaway message here is that El Nino and La Nina typically compared to I didn't include neutral I think neutral is like about .6 sudden warments per decade like 6 sudden warments per decade during El Nino and La Nina there's an elevated number of warments it is a open question why that is I should point out that El Nino it has been strongly shown that it generates more wave activity that goes into the stratosphere versus La Nina so as I mentioned the other day it is likely that it is not just a generation of wave activity issue that's driving the sudden warments there's something more subtle about the geometry of the stratospheric polar vortex that's occurring in both La Nina and El Nino why did I put up this second box because you'll notice that the El Nino and La Nina for the top box are largely close in the second set they're farther apart that's because NOAA's SST version 4 dataset is problematic so if you were going to use that for something don't I don't know if they I think they may have put out version 5 in the last few months use that because this version 4 they were trying to do a lot of data correction in the end what it did was it smoothed things and the inter-annual variability is much weaker than it should be and for example a whole bunch of La Nina has just disappeared so I would say that this most recent paper that relies on that dataset is keep that in the back of your mind if you believe that this kind of thing has been in huge ensembles there's been yeah this is data I like data but I didn't do a model yeah so provided models are doing some warmings correctly which depending on the model open question but yes this is a consistent result okay I threw this in here we may have looked at this the other day essentially I just wanted to point out to people that this is a set of nudging experiments and it's just showing enhanced predictability different types of forcing so for example this is another one of these nudging schemes where you nudge sea surface temperatures you nudge the tropics and then you see what kind of skill you get and for example this experiment takes climatological SSTs and this is for DJF and they nudge the tropics so that's why the correlation in the tropics is essentially perfect so really what you want to look at is the extra tropics and you see that when you do that you get a lot of enhanced skill in the extra tropics right if you do the same thing where you take climatological SSTs and you nudge the stratosphere again you get a lot of skill and arguably again you have to ignore the perfect part that you nudge and look at the extra tropics and you know if you look at the two so the takeaway message that a lot of these studies have been looking at and this doesn't even include warmings this is just kind of average behavior so this is just the vortex in the stratosphere being strong and weak with the occasional sudden warming thrown in there so noise wise what does this mean in terms of prediction so this is another series of nudging experiments but this takes a Canadian model and essentially what they did was is they nudged to two types of warmings the displacement and the split and then they did a ton of ensembles where the stratosphere was nudged to that state and then they let the the troposphere be free run and looked at the result so if you look at the daily NAMM to see for JFM for the control and the two types of warmings splits and displacements what you see is as I mentioned towards negative NaO and essentially what you see here is this is the warmings are triggered I guess they were late December here and what you see is in the ensemble mean you get a tendency for there to be a negative NAMM or a negative NaO event however if you look at all those gray lines those are the ensembles so that's your noise so in a probabilistic sense you get something but you have to be careful because there's a lot of noise but that's no different than looking at tropospheric teleconnections if we look at the most recent El Niño that embarrassed all of us at NOAA you had this what was supposed to be a Godzilla El Niño and there was a lot of noise so a lot of the signal that we were expecting to see was in particular the beginning of the season was largely obscured so that's just kind of the nature of probabilistic seasonal forecasting but I think this kind of gives you an idea of looking at the noise versus the signal okay how we doing on let's see what time what time are we okay very good there's nothing I get to talk about stuff that I've actually worked on alright so so far I've talked to you about this stratospheric teleconnection pathway and kind of looked at the difference between that and the tropospheric I kind of subscribe most of these views are predicated on the notion that you have two regions and you take the tropopause and you draw a line through it and depending on your view if you're Nick I'm the stratosphere is a sponge layer that's just absorbing things if you are what's that this is George he just humbly laughs along if you're a stratospheric dynamics the tropopause is a lower boundary condition it's just a noise maker that helps produce variability because no one cares about the troposphere anyway right I don't take that view I really think and I mentioned in my last talk that there were I didn't really talk about his theories but I told you to go read a bunch of Alan O'Neill papers and one of the things that I like about his set of papers is he thinks about sudden warmings in a more vertically deep sense okay so there isn't this this tropopause yes it's a big change in stability and all kinds of other things but these vortex structures are very vertically deep right PD anomalies are very vertically deep so I like to think of these things in a more organic integrated sense and I won't tell you what I mean by that but just let me set the table a little bit here knowing two things and why this might be important so this is a plot from Sardis Muck and Hoskins and essentially all you want to take into account here is if you look at the black dot she just took divergence forcing and he just moved it and you can tell that these are the Rossby responses right so same basic state that you start with but if you just move the divergence forcing you get a very different Rossby response right so where we imply divergence forcing makes a big difference two the basic state also matters here if you take December, February basic state or June, August basic state leave the divergence forcing in an identical place again you get a very different Rossby response right so those are two ingredients that if we alter them basic state or the location of the divergence forcing we're going to get a different tropospheric teleconnection pattern Rossby response alright so you know what are we basically we've been talking about ENSO MJO things like that that cause tropical heating and then there's divergent outflow and we get a Rossby response what might other types of forcing be um this is from a paper from George Pilatus in 98 and essentially at the top level we see PV on the 350 k isentrope and essentially what you're seeing here is he did some regressions what you're seeing is you know waves that are coming they come off the the Asian jet and they propagate out into the pacific basin and they propagate down into the subtropics where they break right so these are these are extra tropical to tropical waves and with that way breaking we get this is the divergence and this is the divergent wind so if we have extra waves to propagate into the subtropics and tropics with it comes comes a divergence forcing okay so where do they occur this is the 350 k isentrope that's about 200 millibars zonal wind and here we see the two jets over Asia and North America and we see easterlies over South America and most of the maritime continent and Ross linear Rossby wave theory tells you that waves are able to propagate where we have so essentially what happens is you have waves that propagate along the southern edge of these two jets where the elasticity due to the pv grading kind of holds them together they propagate out over the ocean and they often then propagate into what are called these westerly ducks and they're called ducks because we have mostly easterlies and then we just have these two openings right and here's a pv back on the 350 k isentropic surface that shows you know kind of what we what you're looking for when you see one of these wave breaking events going on right okay so why are those westerly ducks there you'll see a lot in the literature I'm not gonna go through this deeply but I just wanted to throw it up there this is a this is from an article that Peter Webster wrote in a cool book that was edited by Brian Hoskins and essentially what he talks about there that these westerly ducks are there from you know in the maritime continent you have a lot of precipitation and that causes this mass circulation this Walker Lake circulation that that drives easterlies and that's what he says the reason for that is that's that may be part of it but the fact of the matter is that when you this is what I've taken here is error interim winds and broken it into the rotational and divergent component and this is trim precipitation what you'll end up seeing is that it doesn't quite match up right where you have the maximum in precipitation and you would expect outflow like this the winds actually the other direction right where you would expect the largest part of the mass circulation and you can see that and it's hard to see here but you guys can take a peek at my slides on your own time what you'll see is that the divergent component is part of it but really it's the Rossby response that sets up these ducts you can see that in the rotational wind component alright so what does this all have to do with sudden warmings as I said most when you look at wave breaking it really occurs in these ducts those occur out of the Pacific and the Atlantic while I was reading a paper and there was local station data over India and we were seeing intense gravity wave activity during the sudden warming of 2009 and they were saying well this is from a PV intrusion there's a wave breaking and it's emanating gravity waves and I thought about that and I thought well sudden warmings have a geographic preference right so when you have a split sudden warming those two lobes always end up in the same spot when they break right and there's some sort of geographic locking probably to do with the fact that largely a big component of their forcing is stationary topography and land-sea contrasts so I just thought well is there a systematic connection between sudden warmings and deep extra tropical tropical PV intrusion so the first thing I did was go on a little bit of a fishing expedition and I this is the climatology of wind on the 350K surface and this is the time period before that warming and what you see is that where you normally have easterlies there's this huge new duct south of India that's opened up and I was like oh that's an interesting effect so let's see if we can quantify this for all sudden warmings okay so just to get an idea of I mentioned that I like to be giving these things as very vertically deep vortex events this is the PV field for the split event in 2009 and you can see you know there's you can see this is prior to the event you can see the two low pressure systems this is that the vortex getting stretched into that peanut shape and it's about to rip into two and these would be the two lobes that are being torn apart you can see that this is up in the mid stratosphere this is down at 350K right along the tropopause and this is down all the way at 320K which definitely dives down deeply into the troposphere and what you see is that this wave number 2 structure is really deep you can see it all the way from the upper troposphere all the way into the deep stratosphere so it's I'm not making any sort of causal argument about where the source of this comes but when it does happen you get these very beautiful deep vertical structures okay you'll notice that there are wrapped up of waves breaking into locations so we did some composite building and bootstrapping to try to establish significance of this and what you see is you see these two dipole patterns that occur in those two specific locations and those are really significant so what this means is the dipole pattern what is that well when one of these waves break you have high PV to the north and low PV to the south is you're transporting that wave breaks and you're transporting high PV from the north to the south and low PV to the north right so this is the mixing process and it occurs in two very specific locations so what is the kind of idea that's going on there well as I mentioned before typically these waves that like George Klaus was looking at are synoptic scale waves they're propagating along the Asian jet out over the ocean and into the duct so that would be equivalent to having these small scale waves right on, breaking right along the tropopause well the thing that I thought about is you see this very deep vertical structure and these waves that are breaking in the stratosphere is what Michael McIntyre calls the stratospheric surf zone so these are breaking waves but they're not synoptic waves these are part of the large planetary scale structure now most of the time when the polar vortex is contained to the pole that surf zone wave breaking dynamics is fully in the stratosphere however when you start ripping the vortex apart you start pushing the vortex towards the equator and when you do that this wave breaking that used to be fully contained within the stratosphere starts impinging on the tropopause so it's possible that the aggregate effect of this you have these two lobes moving southward is you cause this bulging in the material pv surface that does two things one is is that in these two regions you've got this very vertically deep large scale planetary wave breaking that is contributing to these anomalies and the other is is that this bowing of the material pv surface you can kind of think of that that's the wave guide the strongest pv grading is where Rossby waves live and so what you're doing is you're warping the wave guide structure for the synoptic waves so the idea here is is that those two dipoles that we see are the function of both vertically deep planetary wave breaking and warping of the ways in which synoptic scale waves propagate and break so we tried to split this into synoptic scale wave breaking by taking a high pass filter and then the large scale low frequency wave breaking by taking a 30 to 120 day filter and what we found is depending on the event and even the daily you know you get a mixture of both so for the 2009 warming what I've done here is this is the low frequency stream function and this is the synoptic stream function and if you look here at the bottom you see this is where we get those two wave breaking centers of action and associated with the pv and if you look at the synoptic scale on the right first you'll notice I've taken these two agents for the synoptic waves and I've imprinted that on here and it'd be really hard to argue that this wave breaking has much to do with the synoptics however if we do the same thing with the low frequency variability we see this nice tilt so we see that that's likely the effect of the large scale wave breaking so kind of the idea here is that these are two different events and this is a vertical cross section of pv climatology but when you have this the colors are pv on 350 and I've taken this dashed white line is pv at a much higher surface so essentially what that's just showing you is showing how vertically stacked and vertically deep this pv anomaly is this wave breaking if we look in the vertical cross section essentially what you see is you can see that these anomalies these are essentially what's going on I'm not going to do this deeply because it may take you some time to see this but essentially what's going on here is this b that is this pv wrapping down and through in the cross section sense and you see this the stratospheric pv is wrapping downwards and inwards around and along a where you're taking low pv air that's this part of the tongue wrapping upward and inwards so essentially what you're looking at here these are modeling results from wave breaking you're seeing the wrapping up of this filament that's vertically deep and it impinges upon the triple pause and that's where a lot of this mixing is coming in it's not always just the low frequencies though here this is a different warming in 1999 again we see organization nice beautiful organization from the low frequency but in this case if we look at the snoptic scales and I've connected the wave train we see this nice beautiful effect from the snoptic waves so this certainly certainly contribute during some of these events well what does this mean what's our currency as I mentioned at the beginning I said it's where you have divergence and it's the basic state that goes on so what I've done here is I've taken the divergence climatology and then I've and it's not showing up very beautifully I've taken the divergence anomalies from climatology or sudden warmings and again where I was showing those PV plots and I showed you the two centers of action we also get divergence anomalies over the Pacific that essentially projects onto what's already there when I showed you that picture from George Pilates that was a regression of climatology right so those wave of breaking they're all the time during sudden warmings you just get that response just gets amplified so it just projects onto what's already there however over the Indian sector to kind of far eastern Europe that is very different from climatology it's totally different sign on top of that if we look at the wind pattern we see that during sudden warmings when you warp that PV right I talked about the invertibility of PV you can recover the winds from that we also get strong deformations in what the wind looks like so the two ingredients that I talked about that are important for tropospheric teleconnections the basic state and the divergence patterns both of those are altered so that's kind of my takeaway from that and do we have like 30 seconds? no yeah okay very good I just wanted to make the point here that it's important that vertical how vertically deep the sudden warming event is what I've shown here are two pictures one is for a February 2010 major sudden stratospheric warming so it met the definition and this is PV on 850 and you can see this is instead of a split event this is just a wave number one displacement so this is when you just push the vortex up and if you recall from my previous talk I said that split sudden warmings are very very very very very very deep and displacements have a first bare clinic structure which means that the largest amplitude of the perturbation is high in the stratosphere and it decays as you go down January 2012 was a minor warming doesn't show up in any of the data records it's certainly it's hard to argue that it looks any different than in the major sudden warming so what does it mean in terms of what's going on down on the tropopause if we look at the low frequency stream function for the major sudden stratospheric warming event this is the low frequency stream function if I showed you climatology you wouldn't be able to tell the difference because it's identical the synoptic scale stream function you'll notice that these the way breaking that I showed before extends down to say 10 way deeply here this is synoptic scale way breaking and it's more kind of climatological because there's no low frequency variability to warp the PD however if we look at the minor warming we see now there's this strong imprint on the low frequency variability and with that we see this nice these PD events are reaching down all the way to the equator and again it's a function of both the low frequency and the warped synoptic scale variability so the important part here is is that I know a lot of studies and a lot of these nudging studies and things like that they try to correlate the warming itself and they look at like 10 hectopascals but that's pretty far up in the stratosphere the point is is you somehow need to get an anomaly that's down in the lowermost stratosphere to imprint something on the tropopause and that PV invertibility principle that I showed you when you invert that to get the wind in the geopotential and I said it's an elliptic operator that's non-local changes in geopotential drop-off at I think 1 over r and changes in wind I think are 1 over r squared from the distance from the maximum of that PV anomaly so that means if you have a big PV anomaly high in the stratosphere but nothing down at the tropopause you don't have enough to really have a PV anomaly to imprint anything on the tropopause and you're not going to get or it's unlikely that you're going to get a strong effect in the troposphere so when people are going out there don't necessarily think that you should just grab the time periods when there's sudden warming it's the vortex variability and how vertically deep that is so with that I'll just throw my summary slide up there and you guys can read that and I'll take any questions