 I want to just present the results of some older and some newer experiments in understanding the extra tropical response to the MJO. OK, and I wanted to acknowledge, if you can hear me, one of my students, Priyanka Yadave, and postdoc Eric Swenson, some of these experiments. So as you know, just to introduce it again, the MJO is the largest element of intracesional, here I mean by 30 to 90 day variability in the tropical atmosphere. And discovered by Roland Madden and Paul Julian in 1971, it involves a large scale coupling between the atmospheric circulation and tropical deep convection. The atmospheric circulation actually goes all the way around the globe. Tropical deep convection is more limited to the Indian Ocean and Pacific Ocean. So I want to emphasize that it's not, we'll see what MJO actually looks like in the real data, but the abstraction of it in our mind, the paradigm we think of it, is a traveling envelope of enhanced and suppressed convection, the proper case eastward, OK? So these are results. What I've shown here is actually just a paper trying to distinguish fast and slow MJO episodes, but that's not the point of the slide. What we see are two hovmuller plots. So time goes up, longitude goes across, and what you're seeing is the OLR just averaged over tropical regions, I think 15 south to 15 north. And so when you get these values of low OLR, here are these dash curves means the outgoing longwave radiation is coming from very high clouds. So it's assumed to be convection. And we've drawn arrows to indicate what we consider to be episodes of the MJO, which have various, some of them are faster, the green ones are slower. Just keep in mind that this is kind of our imposition on the data of how we organize the way we think of it, that we think of a blob here and a blob here as part of an eastward propagating oscillation, again here. So blob here, and then the convection appears here, and then later on it appears here. So this is what the actual data looks like, because what we do then to analyze this, and this is a point I wanted to make early on, is we take some kind of complicated EOF of the tropical circulation, so we reduce the data, in effect. And reduce it to a model of something that propagates around the globe where you can get an amplitude in a phase. And so you do lose some of the detail of the real data in doing that. This is another example of the velocity potential. This is actually taken straight from the climate prediction centers website. This is the velocity potential. Negative means tropical convection. Now time goes down. And this is just the five-day running mean, some smoothing. And you can see again these episodes, sort of blobs moving. When you do this EOF reduction, it's a standard RMM1 and RMM2 indices. Even though in the real data, you see their periods where there's a blob moving here to here, but right in here there's not, right in this point, there's not that much convection. This has been reduced in a sense, something much lower dimensional to an oscillation that has an amplitude in a phase, these standard RMM indices. One of these is the forecast. And one of these, in this particular paper, and one of these is the actual observations. But for our purposes, it doesn't matter. So the idea here is, if it's in this phase one, the convection somewhere in the Western Hemisphere in Africa, and as it moves through phase three, the convection is in the ocean. And so in this particular case, you can see there's a regular progression. But in fact, in either forecasts or observations, you can get periods where this particular model of the MJ is clearly crazy because the amplitude decreases and it starts propagating the other way. This is kind of a result of the way we reduce the data to the simple two dimensional. So just keep that in the back of your mind. So when the amplitude's small and the propagation goes the other way, it's not clear this really has anything to do with the real data. So this is another standard example of what the phases look like. And this is from a casu paper, which I'll return to. Whenever that standard two dimensional representation is in a certain phase, you just average all the OLR in this case. So negative means right convection. That says the convection in the Indian Ocean in phase three. And we'll be seeing a lot even next week about teleconnections between the Indian Ocean and the Atlantic. In phase four and five, it moves across the maritime continent. And by phase seven, it's already in the Western Pacific. It goes between phase one and phase eight. And the contour is sort of just the average stream function. So let me just already make a point that it makes sense to average the OLR at different phases because that's how we know where the forcing is, OK? Because we're supposedly talking about tropical forcing. It's not clear once you get to remote regions from the forcing that it makes sense to average the stream function or the high field at the same time at the same phase without a lag because there has to be some time for the propagation to be the influence to be felt in the latitudes. And that's kind of the subject of my talk. So as I said, the simple measures of simple regressions are composites of upper level field based on different phases of the MJO. Clearly, the middle altitude fields, if we want to try to analyze or estimate the remote effect, they should lag the MJO heating by how much? Do we have any guidance at all by that? And OK, the other thing that we could try to look at is see how the teleconnection patterns change. So this is just a paper by Haile Lin. So this is simply showing the response of 500 millivar height to phase three with one pentad lag five days and 10 days. And they're different. And you can definitely see that by 10 days, you get this strong. This is what Andy was referring to as the teleconnections. You can see a strong signal of what looks like an MAO plus the Atlantic here, positive here and negative there. You also get something at phase seven where it looks like it's a negative MAO. This is sort of a standard way of looking at it and it evolves after some time. Another way that people have looked at the effect of this is this is going to take a little explanation. So we have these indices, NAO, PNA, and they're symmetric in the sense that every day there's an NAO index. You just sort of project that on a single pattern. It may be positive, it may be negative. But there's a, it may be very close to zero in which case you don't, I guess there's not much projection. You can't really say what the MAO is doing. There's sort of another world view of how we organize a mid-latitude circulations. And that is to try to come up with, it's not the mathematical term, it's cluster analysis. To try to come up with a set of preferred, a set of states such that any single map and any day can be classified as belonging to one of the, one of a set of regimes or clusters. And this is statistically justified by the fact that the distribution, the probability distribution, and I won't go into the mathematics, but the probability distribution is not really just a multi-dimensional Gaussian distribution. There are regions which are slightly more preferred in, there are states which are more preferred than other states and states which are less preferred. This allows you to make a classification not completely unique, but useful classification, which people have used for a long time, particularly in Europe of these regimes and a standard winter, memorial winter, 500 millibar height set of regimes would look like this. So there is something we call the NAO, minus in the NAO plus, they're not just the opposite of each other, okay? So that's a non-trivial point. Also there's something called the Atlantic Ridge and the Scandinavian Blocking Regime, very high here. So any, again, any state in the state of, that was in the period this was used, which was, I don't know, some 30-something years, any state can be classified by being closer to one of these four than the other. So the question then is, so those are the regimes, and these are the same NAO composites that I showed you before, actually just going through eight phases. Why do we put these on the same, Kassu actually did this, why do you do these on the same page? Well, the idea is to see with a certain time lag whether these states become more, any of these states become more preferred after a certain lag. So here it is, this takes, I realize, I've looked at this so often, it's very familiar, but it is a little bit confusing when you first see it. The rows are simply the phases of the MTO, so just think of this as Indian Ocean Convection, okay? What this shows is, and there's a, the columns refer to the frequency of occurrence of the regimes and the data. So again, 10 days comes out, just like in high-lens paper, 10 days comes out somehow from the data as being reasonable. So this is the time lag. So basically what you see is when the convection is in the Indian Ocean and you wait about, this is 10 days here, okay? This is the probability of occurrence of the NaO plus goes up by 40, 50, 60 percent, okay? And these sort of increases as the lag goes for phase three, and of course phase, this whole thing moves down this way, phase four, because phase four follows phase three, so when the lag is less, you should be getting a similar increase in the probability of NaO plus, whereas you get a corresponding increase with lag of the probability of an NaO minus occurring, about 10 days, almost up to 60 percent, more likely to get an NaO minus than normal, about 10 days after phase seven and eight. And again, phase eight occurs after phase seven, so this thing should just be moved to the left. So just to remind you, we're talking especially about the NaO plus and NaO minus, which seem to have a strong relationship to the MGL. Okay, so this is sort of a, we talked yesterday about interpreting this in terms of a quasi-stationary response. So the idea here is that the Rosby wave source, which you talked about yesterday, is created in the Indian and Western Pacific Oceans as the MGL convection propagates eastward, and there's quasi-stationary wave frames. Turns out they lead to the retraction of the Pacific jet and changes the associated flexes of momentum and possibly implications for Rosby wave breaking in the eastern oceans, eastern Pacific. Another way of thinking of it is the index of, well, the wave index of refraction, similar to what we saw yesterday in the stratosphere, is relevant to response. And so there's gonna be some sensitive to changes in the basic state, which means that if models have biases, they may have trouble. Bias isn't just the basic states of the winds. Of course, that geographic theory, that would lead to changes in the sort of index of refraction for the waves. The propagation of the MGL influence into the North Atlantic, because this is all, you can sort of all see this happening in the Pacific with forcing in Indian Ocean, but how come the signal is so clear in the Atlantic? I think that's not as well understood. I think that's one of the big challenges in the physical understanding of the response, is why the response is so clear in the Atlantic compared to the Pacific. So okay, so this is just to review yesterday. Remember, this is what we're gonna, these two terms are what we're gonna call the Rossby wave source, because I'm going to actually show you that later. Okay, so let's still think about stationary wave theory. I wanna review briefly two papers, okay, which use the idea of stationary waves and then review, then go over some experiments I've done, which have a kind of a different approach. So this is this paper by Matthews at all in 2004. Andy, were you, I don't know, were you a co-author around Matthews? No, okay, it's, but Brian was. This was, the basic method here was very interesting. It's to use a model, okay, a full non-linear model, but a dry model, completely dry, all right, and you start about a climatological basic state, three-dimensional meaning that it has variations in pressure level and latitude and longitude, okay, and you have a constant forcing term, which is concocted to try to keep the model close to that basic state, and what you do is you, so if you just let the model evolve, it should evolve very slowly, there's a certain way of doing this, of massaging the model, so you add a heating, okay, but now since the model is completely dry, you can add the heating arbitrarily as a source, and you integrate for the first 25, what happens is after you add the heating and you compare it to some control simulations, you can see a difference, and you can see it directly related to the heating, and you're saying, well, what about all the baroclinic, all the baroclinic instabilities, all the mid-latitude storms that form all our weather? It turns out they actually don't show up until about 25 days of integrating, so this is a very sort of model with high damper, okay, so the basic idea is you can estimate a direct response to tropical heating from this, if you, I think they look at day 19 of each integration, like with the heating in different places, and look at day 19 and they can estimate, estimate the direct tropical response because the model is fairly damp and it's fairly low resolution. So what they do is they put tropical heating anomalies corresponding to a 48-day regular MJO cycle and they prescribe the vertical structure and they basically start, all their experiments have tropical heating in one of these 48-day positions, so they basically put heating over Africa and then the next experiment, they put a little bit further east and a little bit further east, okay, each one of those positions is a separate experiment, and they pick a forecast time, which is 19 days, in each run, so the response to heating is well-developed but it's not overrun by baroclinic transients, and you get this picture, which takes a little bit of explaining. What you get is, for example here, this is the 200 millibar U-wind again, okay, this is an anomaly correlation average over the entire extra tropics between the model-wind at this particular day 19 of the forecast and the observed winds. So here, what this lag means is that the model integration which started, this lag is about 10 days, right, where the, this is sort of the initiation of the western-most position of the MJO in this scheme of things, so the heating is probably over Africa and 10 days, so the model integration was started 10 days previous to this time of the MJO cycle, okay. So the model integration was actually started, probably, this is a repeated cycle is the MJO cycle, the model was started back here and you're comparing it to the U-wind at day zero and you get a correlation with about a 10-day lag but for the MJO cycle, comparing to the middle of the MJO cycle where I guess this is probably the maritime continent, you only need a two-day lag. So the model integration started two days previous to the time equals 24 in the MJO cycle, has a high correlation, very high correlation with the observed, observed U at day 24 in the MJO cycle. Okay, so the only, the point I wanted to make is you can interpret from this, from these model experiments, the lag, we don't understand the time lag, but it's two days or 10 days and there's issues of model bias here, but at least there's some ability to say that no, I can formulate a stationary wave problem and 10 days later compare it to the response to a particular phase of the MJO. So in this world view, okay, the response to the MJO, to each phase of the MJO is completely separate, right? They don't influence each other in a way, right? You wanna understand the response to the MJO in a certain phase, put that, just think of it as the stationary response that would occur if you just kept the forcing fixed, okay, with a certain lag and we don't quite know what the lag is. The other hand, this is the picture I'm gonna show you the picture that I showed you yesterday from Grant Bransett's paper, but I'm going to explain it a little bit more carefully. We're gonna have heating events that only last two days in this model, again a dry model. So basically, the idea here is that you do a whole bunch of forecasts with a full nonlinear model, you repeat them, a whole bunch of initial conditions, then you do 100 forecasts, then you repeat the forecast by putting a pulse of heating in a certain position for two days, turn it off and look at the differences, okay? And this is what I showed you last time. So this is the result of day three, day six and day nine. And the idea here, well, what I emphasized yesterday was the fact that okay, this actually looks like the same, similar to the field in this case, 300 millibar original wind, the same field that you'd get if you just kept the heating fixed there, okay? But think about this for a minute. Sorry, think about this. So this is a nice picture. This is actually very relative to the MTO, right? So you put the heating, that's what, phase four, I think of the MTO with the heating, right? Just put it over the maritime continent. And so it's over the maritime continent for five days or three days, whatever, this wave training starts to develop, all right? But now if I want to look at the downstream response anywhere, five or 10 days later, this yellow circle is further east and stays there. So to get, right? And it starts developing its own wave trains, especially going to the Northern Hemisphere. And then 10 days later, it might be in the Central Pacific and it keeps developing wave trains. So if I'm downstream anywhere, particularly over the US or in the Atlantic, I have a complicated problem, right? Because I'm getting wave trains that come from this, from the heating several phases earlier of the MGO that have finally reached me and I'm getting wave trains that are, that started later than that, right? Which are starting to reach me because they started closer, right? So if I'm, you know, in three days it goes this distance, in nine days it goes this distance, if I'm sitting here, I'm gonna be getting kind of a sum of all these wave trains from these moving, think of these yellow dots as moving. It's not clear, yeah, it's not clear. I think the wave train, it seems that the wave train probably gets faster than the source, okay? But the point is that, so to think of it, that's kind of the right question to be asking about because at a certain spot, you're kind of getting like a superposition of signals, right? Some of the older signals came from further away. So basically there's a way of doing this in physics. In physics this is just the remote response. This is standard physics. The remote response at any point in space and time will depend on this to a source which depends, which has this complicated space and time dependence will depend on this mean function which connects both the source time and the response time and the source position and the response position. So from this point of view it seems kind of hopeless. So, and on top of which I'm gonna actually skip over this. We talked about this yesterday, the role in the latitude and stabilities. On top of all of, this is just the direct response that we're worried about here. On top of that, of course, we have the response to the verifold of instability, which is a different issue. But I wanna get back to this idea of how can we begin to have a methodology which responds to the full cycle of MJO experiments. So, MJO heating is not just stationary heating. We might be tempted to model it as that. In fact, it's a cycle of heating. And one other point I wanna go back up to which has not been, still hasn't been talked about much. Even today, pardon me while I move back, is please notice that there's not just heating here. There's also cooling, anomalous cooling. Okay, and it's never, very often it's not clear in experiments whether people are really just targeting the heating in the phase three in the Indian Ocean or the heating and the associated cooling. Because extra more convection in the, in this region may mean less convection in that region. And it's actually well known from very old studies that models on a seasonal timescale can be also sensitive to cooling in certain areas or the lack of heating. So, the way we want it to approach this is, look ahead, is to use, to do intervention experiments which are very different. So the first thing is you use the full, the first important thing is you use the full ocean atmosphere couple model, sophisticated convection, parameterizations, parameterizations for boundary layer, turbulence, okay, everything sort of, in this case it's the CESM, a climate model from National Center for Amnesty Research which supposedly simulates the climate very well and tries to take into account a lot of different feedbacks. And don't, so you don't force, there's no way to force the model with specific heating because the model generates its own heating. Okay, heating due to, to fluxes from the surface, heating due to latent heat release, radiative heating. What you simply do is you add something to it. You add a specified evolution of heating in X, Y in pressure and time. And what you're gonna add is somehow supposed to represent an MJO cycle. Okay, in this particular experiment we actually made it too complicated. We tried to take a typical MJO cycle for a whole season from real data. What you do is you add the identical evolution of heating to each member of a large ensemble. Okay, so you have, you do seasonal forecasts from either initial conditions from a long run or from, which in this case it was, or you could even do real initial conditions. And you repeat those by adding the identical heating to each of the ensemble members. And this then allows you, so there's something in common among all the forecaster or seasonal experiments that you've done because they've all had the same heating added to that. And this allows you to use a statistical technique called predictable component analysis to pull out what is in common and what is in common among all these ensemble members in terms of their evolution. And that's the response to the MJO. So you leave all the internal feedbacks in the model untouched. So before I even show you what the add heating is, what that means is if I add heating somewhere in the model, okay, the heating will increase the vertical velocity in the tropics like we discussed yesterday. Guess what? That vertical velocity which you're adding to the model is gonna cause increased latent heat release in the model. It's gonna cause more convergence, okay? And the model will take that added vertical velocity and maybe magnify it, right? And leading to more clouds than were there before and then you'll get more radiative cooling because they're more upper level clouds. So all of these complicated radiative effects are left intact. I haven't touched them. I've just added something. So let me, enough word here. This is, in these experiments, don't ask me why these look so blocky. Okay, they're not continuous. That was a technical issue which we've since overcome with a different model, but never mind. This is an example of what we added to the temperature tendency equation, right? The models have an equation for thermodynamics where they update the winds and they update the surface pressure, they update the temperature. All we've done is added this heating to that tendency equation. So this is, it's confined to the tropics. I'm showing you the tropical average at three different longitudes. And these are 180 day time periods starting from October 1st where all the forecast started from. And so this is, I'll show you another picture of it. That makes more, may make more sense. The point is as the MJO, there are three cycles and as the MJO evolves, it's really, it gets, the heating gets deeper and deeper. This is pressure level. The units here are degrees per day. So it never gets really much above a degree per day. I mean, a degree Kelvin per day in terms of how much temperature tendency I'm adding. And this was, Caroline Le Pen actually designed this to be representative of the heating from a typical MJO, having three MJO cycles originally derived from trim data, from satellite data. So this is the plot that gets misinterpreted by a lot of people. So I better really be careful here. Forget about the colors, okay? Ignore the colors. I hope you can see these blocky lines here, okay? Can you see these, these lines here, 0.5, and then this is 1.5, 0.5 is here and this is the 1.5 here. These are the three MJO cycles. Okay, so this goes from, so this is longitude now, all right, from 60 degrees, all right, to Indian Ocean to the Eastern Pacific and this is time, this goes actually up to 180 days from October for six months. This is what we added, just these, and again, the fact that they're very discontinuous was a technical issue, having to deal with the model. This is what we added, we added three MJO cycles. If we don't add this, and we just look at the same run, the run that was started from the same initial conditions, this is the heating that the model will produce. This is the NCAR model, the CESM and I think the contour interval is two degrees per day, so it's very hard to see here but when it gets up to this high red, it's 10, 12 degrees per day. So the model produces on its own without any help from us, it produces quite a bit of tropical heating but since time goes up this way, you see some eastward propagation occasionally, but you don't see something that really jumps out at you as the MJO, because the MJO should be, well, here's something, but then the heating seems to be going westward but this time goes up. So again, maximum magnitude 10 degrees per day. I add this blocky heating, just constant, add it to the temperature tendency equation, the total heating started from the same initial condition is what's given in color here. And when we started these experiments, this was totally not known what would happen. We first of all worried the model would blow up which it didn't. Secondly, we were worried that the model would do something crazy but what happened was actually quite interesting. The model, what happened this heating here which has a lot of variability in it but nothing too obvious compared to the MJO was simply reorganized by this added heating. So this is still extremely noisy heating in here but sort of the envelope of it is organized by the relatively small heating we've added. So we basically made the model have an MJO and if you average over all 50 experiments or whatever, something like 50 experiments, that same plot, the same evolution and this isn't another important feature. Here you can see the added heating in black and the response to the heating. I don't even have the contour, sorry, but it's the ensemble mean response. Follows the black heating. So normally, just back off for a second, normally if you don't add any heating and you look at the day by day response, the day by day tropical heating in the model and then you average it over many, many runs, you expect to get, all the details should get washed out. So all you would expect to see is something like the mean heating which is what you do here. The fact that we get this surviving in the ensemble mean is a further indication that we have something in common among every single member of the ensemble. So then there's a statistical technique called signal to noise optimizing EOFs or predictable component analysis in which I'm gonna try to make this as simple as possible. It's like EOF analysis, right? In EOF analysis or principle component analysis, you get a series of patterns, each one with a time series also, sometimes called the variates, right? And the patterns are fixed and the time series change in time. It's exactly the same thing here. You get a series of fixed patterns with time series. In EOF analysis, the leading mode, which is the leading pattern and the leading time series maximizes the amount of variance. In this case, it maximizes the signal to noise. So EOF analysis, you're gonna apply to just one ensemble member. This predictable component analysis, you need to apply to a whole, in order to define a signal and noise, you need to have an ensemble. As the signal is what's in common in the ensemble and the noise is what's not in common. And so these modes can be defined on a daily basis trying to pick out those modes which evolved, which are most in common among all ensemble members. And what you end up with is the leading two modes actually form some kind of an oscillation. So look at just the black curve, actually, look at the black curve, okay? So this is just the lag correlation between the leading two modes. So mode one meets mode two, you get a correlation of 0.6 and you get a higher correlation of 0.8 when mode two leads. So this turns out to be the signature of an oscillation, okay? So you're gonna apply this to any aspect of the model output, including the Rossby wave source, which is what we defined before, if you remember, the advection by the divergent flow of the vorticity. And that actually turns out this is, of course, the Rossby wave source is the most closely related to the heating and that is the highest correlation to 0.8 and minus 0.8 with lags of about 12 days. So the leading two modes do describe an oscillation and you can apply the same principle component analysis to the heating, which is insightful because the ensemble mean heating day by day. Now just look at the colors here and forgive me, now we have a longitude going up from 0 to 180 and time going this way just to confuse things further. And you can see the Easter propagation, but even in the ensemble mean there's still some noise, okay? I think you saw that earlier on. Even in the ensemble mean here, there's still a lot of noise, but the predictable component analysis pulls out the contours here, which are this smooth representation. This is in watts per meter square, this is vertically integrated heating, the smooth representation of that of the most, the leading two most predictable modes of diabetic heating. So now you can try to relate them, so you can relate many features of the simulation okay through the predictable component analysis to the MJO cycle. And another point that somebody made to us, the importance, I think Highland made this yesterday, the importance of the feedback of the baroclinic transients on the flow as an important dynamical modulator when you look at the response. And so what we did in this experiment was actually fairly simple. What you can do is you can write, okay, just this here is just the conversions of the, that's the horizontal of the wind, and these are the primings transients with fewer than 10 days or less. You can see the convergence of artisan flux, this term here is corresponds to a change in vorticity. And you just take the inverse del squared operator to make it a change in stream function and multiply by f over g to get a change in height. So approximately in a barocropic sense, the tendency in height is related, can just be obtained this way from the convergence of vorticity flux due to the transunities, okay? And so this encompasses both the extraction of kinetic energy from the mean flow and actually, if the momentum of fluxes are also involved here, so this could, you can relate this to somebody who has to be way breaking. So for example, okay, so the way to understanding these modes is actually a little bit tricky because there are two phases, just like the barocropic instability modes. There are two phases and it oscillates between them, okay? So just looking at one phase or the other is not as insightful as you might imagine. So what I want to show you is, first of all, this picture, okay? This picture is trying to give you a cartoon of what actually happens. Again, this is the time going from October to six months and this is longitude. And the colors are the vertically integrated heating, those same leading optimal modes, the two of them together that I showed you before, okay? So exactly the same picture I showed you before, except it was on its side. And if not, so we can add, we can control what the added heating is. We can't control the way the model responds to it. So even with this optimal mode filter, you still get a rather complicated evolution of the heating, but you do get cooling, heating, cooling, heating, and there's some heating here. You do get several cycles, okay? And the Rossby wave source at 32 degrees north, which is just exactly where I showed you in that picture of the Sardis Mucan Huskens paper where the Rossby wave source starts to get pulled out of the deep tropics is shown as a function of longitude here, okay? And you can see it's quite coherent in some way, some way, the cooling is followed by, it's positive and the heating's followed by negative, okay? And what we see, what about further downstream? Again, what I showed you, sorry, which one, he'll actually show you the storm tracks, okay? So this is the high-pass kinetic energy, so it's basically related to the storm tracks. And it's interesting that the storm tracks appear, you can see the storm track responds in eastern Pacific, again, somewhat consistent, all positive, negative, positive, negative, positive. And finally, to verify that what we were doing actually makes sense in terms of what people observe in the Atlantic is we did something completely independent of this predictable component analysis in the Atlantic. We took all the data from all the runs, okay? And did this cluster analysis that I showed you in terms of getting, so each day belongs either to the MAO plus the MAO minus the Scandinavian block of the Atlantic Ridge, no filtering of the data, usually in cluster analysis you do some kind of filtering of the data to try to remove the beryclinic transients, okay? But the whole point of this experiment is to follow things day by day. So absolutely no filtering of the data, which is normally not done, okay? And so every single day, okay, every single day, what you can do is you can look at all the experiments for that day and just find out how many of, how often the MAO plus was present and how often the MAO minus was present. Present, how often the MAO plus was present is given in this magenta or purple curve and how often the MAO minus was present is given in the green part. So you can see already in these experiments, okay? So sometime after the heating passes the, actually, sometimes after the heating propagates out of the ocean, you're given a region where the MAO plus is much more like frequency MAO minus. And of, there are periods, the cooling, this cooling certainly is followed, you don't actually see the opposite by much in these experiments. You see more of the domination of DNA plus over DNA minus. Of course, this is extremely noisy because I've done absolutely no filtering. So there are many other, this I'm not gonna go into in great detail, but the modes that I looked at for the high field and for the vorticity flux forcing, which is the transient forcing, were completely hemispheric modes. And it turns out that if you stare at these correlation curves, and they're very confusing, they just show though very clearly that the leading mode of the vorticity flux convergence leads the leading mode of the height response by my phase, okay? So the transients actually have a very important effect here. The leading, the Rossby wave source, the leading mode of the Rossby wave source leads the leading mode of the height field by about the same amount of the correlation of the O1, okay? So piecing these, and then it turns out that the leading, the second mode of the vorticity flux also leads the second mode of the height field, which then leads back into the forcing of the first mode. So it's definitely a cycle, okay? And it is extremely, it's a little bit hard to disentangle everything that you want from these experiments and we're still working on it. We're working on actually different versions of these experiments. So trying to summarize at what we've learned from these experiments that strongly propagating nature of the pure predictable components, we really get cycles, we don't, okay? Shows that the cycles of MJO heating and cooling, the cooling could be just as important as the heating, okay, leads to propagating and not stationary response. And all the elements of stationary wave theory are in play. The Rossby wave source, the tight coupling of the dark limit vorticity flux convergence to the height field. These results can be interrogated further in terms of understanding the interaction with the storm tracks, the role of veritropitin stability in the Rossby wave rating. And we're still assuming relatively uniform phase beats to the MJO. So the one thing I want to close with is current work that we're doing in which we went back to observations and we said, wait a second, there's another problem. The MJO, remember if these blobs that move, that seem to move, but they don't always move uniformly. So this is an example of a recent paper, okay, where you see on these, again, these famous foreign MMM pictures, you see various MJO cycles taking from data. So here's an MJO cycle, okay. Here's one where, you know, in this particular example, this particular example, they move fairly quickly through different phases, but here's one where it tends to stay in one phase for a long time, okay, before propagating out, okay. And you can see that, again, they're more, well, the amount of time it spends in any of these orbits spends in any one phase is quite variable, all right. This is just to indicate cases where it's, there are more dots in one phase here than there are perhaps in another phase where it may not stay as long. So we try to quantify this over 35 years of era interim re-analysis, and this is what Piyanka Yaday did, and so we looked at the time that it takes to propagate from the Western Pacific into, sorry, the Indian Ocean into the Western Pacific, something like a phase three to phase six for each MJO episode and just, we try to discriminate between things that look really like an MJO episode, and this is the propagation time from phase three to phase six in days, and this is the histogram, and there are a bunch of fairly quickly oscillating modes and there's kind of a minimum, and then there's some longer modes, okay. So the question was, was there a distinction between the shorter modes and the modes that take, the oscillations that take longer to reach? So we did this typical lag composite, for example, for one case of phase, phase four, and we actually found a day zero very different than what people normally find, but what we did find was that the strongest MAO response occurred actually a little bit later, not from phase 10 days after phase three, but 10 days after phase four, and this is sort of an MAO, strong MAO plus response, and it occurred, it's actually much stronger here than it would be in the more rapidly growing modes. So the forecast pictures that Andy showed, showing the middle attitude response, okay, from forecasts, I think it may be dominated by the episodes that take longer, and the last thing I'm gonna show you is there's a hint that there's also a change in storm tracks. So these are the slow cases, okay, and we start from day phase three at various lags. What I'm showing is the heat flux, the meridional heat flux with oberclinic transients, okay. The anomalies are given in shaded and the contours are a climatology, so you get a specific storm track and an Atlantic storm track, and there's definitely storm track, there's definitely shifts in the Atlantic storm tracks, okay, of further south, okay, that occur as part of this response, okay. Remember, this was, would day phase three or phase four, this is part of the response to the element that leads to the positive MAO response, and this change in the storm tracks have been speculated to play a role in the Atlantic response, okay, and I'm just showing that we have some evidence that that actually occurs here. We haven't quite disentangled all of what it really means yet. So the current work is actually, what we're doing is intervention experiments. We actually have finished them and are analyzing them, not from the NOAA model, the weather forecast model used by NOAA, but we're actually real forecasts from real initial conditions, okay, and we've added fast and slow MTO cycles, but we've learned our lesson, we've added much smoother cycles as we try to get them we did before, and we're trying to determine if we can see some of the stronger MAO response maybe a little bit later for the slow episodes compared to the fast episodes, what is the, we're trying to look at what is the role of the baritopic instability, and the real sort of hey, the really important practical point is to answer the following question, Andy showed how the improvement in MTO prediction is, there is an improvement in MTO prediction now. So to what extent would a really good prediction of the MTO tropical convection two to four weeks in advance be associated with dramatically improved extra tropical predictions? That's kind of the goal that we're leading to, okay. We're interested in the extra tropical response to MTO, not just because we're interested in response and intellectually why it occurs, but what is it worth spending a ton of money and a lot of observation systems and a lot of modeling work to get a better forecast of the MTO, okay. Will that really give us forecast up a windows of opportunity to forecast things that are going on even as far in the Atlantic in beyond three weeks. All right, thank you, I'll be happy to take questions.