 the tropics and some things that will be very useful for your project that you do for your lab part. So it's mostly some diagnostics for the tropics, the intracisional variability of the tropics. So the outline of my talk includes the Madden-Julian Oscillation, a brief overview, and some MJO diagnosis, diagnostics or MJO diagnosis, and the Boreal Summer Intracisional Oscillation, which is another component of the intracisional variability of the tropics. And then for this part, the intracisional variability of the midlatitudes, I will present some of the very new results from my current work and then some conclusions. So when we look at the tropics, we can categorize the major modes of tropical precipitation variability, for example, as consisting of this annual cycle, then we have the ENSO cycle, then we have the intracisional oscillations, and then the cloud clusters. And here these arrows try to give us an idea on the interactions between these components of the tropical variability. I took this diagram from a paper by Rasmussen and our team. So what I'm going to focus today will be this circle here with the intracisional oscillations. And as we heard in the previous talks, they can modify the annual cycle, but they are also controlled by the outer circle, the annual cycle and the ENSO cycle. So this is something that we want to keep in mind. And this is the reason that we said that the interactions between the tropics and the midlatitudes are influenced by the mean state because, as we can see, there are other outer circles that play a role in this variability. So now let's take a look at the variability in this window, the intracisional window, which is defined as 22 100-day variability. And here I am showing on the left the variance as the ratio between the color, the shading here represents the ratio between the variability in this 2100-day window and total variability for the wind. The top left, OLR, top bottom, and the left column corresponds to the winter, boreal winter. It's an extended boreal winter defined between November and April. And then the right column corresponds to the boreal summer, again an extended boreal summer that covers March, October. So we see that a large fraction of the total variability of the tropics, because we are looking between 30 south and 30 north, up to 50%, is explained by this variability by the intracisional variability. And it's much stronger in the winds than in the anomalies. Another thing to notice is the location, the regions where this variability dominates. For example, we see some seasonal variability, seasonal variability when we compare the two seasons in both fields in the wind and also in the precipitation. And of course, in the boreal summer, we recognize the largest variability in the Indian Ocean, which we know is associated with the summer Indian monsoon. And we do, we see in the precipitation the intracisional variability that we know it's associated with the MGO. So what we have in this, so this is the total variability, but can we go farther and parse this variability in, as in certain band frequencies or wavelength. And we have seen this diagram many times during the talks, during this week, is the Wheeler-Kilades diagram or the wave number frequency spectra. And since I'm not sure how many people are familiar with how these diagrams are computed, I decided to throw here just a little bit of information. And the way that we calculate these diagrams, the diagrams are based on the OLR. So we, at each grid point, we divide the OLR into a symmetric component and an so-called asymmetric component. And what we mean by a symmetric component is defined as the average between the OLR at that particular latitude and the OLR in the other hemisphere. And then the anti-symmetric component is defined as the OLR at that particular latitude from which we subtract the OLR at the equivalent latitude in the southern hemisphere. So if we add these two, we actually get the total field. And after we do this, we do frequencies on our wave number power spectrum. And what we see here in these two diagram is actually that component of the power spectrum that's above the power spectrum of the basic state. So it's the ratio between the actual power spectrum and the spectrum of the basic state. Because we are interested in what, not in the power spectrum of the mean state, but what the noise basically, the variability that stands above the mean state. So that's how we end up with these diagrams. And on the horizontal line, we have the zonal wave number. And on the vertical, we have the frequency. So now if we look at frequencies between the 200 and 20 and 100 days are the frequencies that actually start here, we have the 30 days and go down. So this is the region of interest for our intracisional variability study. And as we can see here, we have this big blob that you was shown in the previous day that corresponds to the Madden-Julian isolation. We don't have too much into the anti-symmetric component. And in the westward portion of the spectrum, we have a little bit of the power associated with the equatorial-Rosby waves. So now let's talk about the MGO. This spectrum, both of them, this spectrum are computed using the whole year. So we don't compute this power spectrum by applying them to a season. You can do that. I don't have that figure here, but let's start talking just a little bit about the MGO. And I don't know how many of you know that Roland Madden and Paul Julian. I have them in this figure. This is Roland Madden and Paul Julian. And if you think this is the only oscillation that you can shake hands with Mr. Madden and Mr. Julian, none of the other oscillations are associated with a person. And currently, they are both retired. So just a very quick overview. What is the MGO? And this diagram was actually published by Madden and Julian in 1972, where described what is the MGO. And at that time, they had observations at two stations. And this diagram was based just using observations at two stations. And the observations were surface pressure, winds, and precipitation. So a few landmarks on this diagram. Here we have Africa, Indonesia, and South America. The regions highlighted with red represent regions with negative pressure anomaly. And the regions highlighted with blue represent regions with positive pressure anomalies. Here we have the data line. And the green arrow just give us the local circulation. So they describe the MGO, at that time it was not MGO, it was just an oscillation in which convection builds up in the first in the Indian Ocean, where we can see this region with low pressure. And the convection, it's sliding to the east of this region of low pressure. And then the circulation associated with this build up of convection. We have two cells on the west of the convective activity. We have a cell circulation with a westerlies at the surface and easterlies above. And to the east of the convection, we have a cell with a reverse circulation with easterlies at the surface and westerlies above. So about four days later, the convection intensifies. The region with low pressure system extends and the region with high pressure system disappear. And as a result, the cell located to the east of the convection expands all the way to the deadline. Then again, four days later, the convection moves eastward. And then the both cells expand and they notice that the circulation to the west has a stronger upper tropospheric westerlies. Then again, four days later, the low pressure anomaly in the Indian Ocean propagates very rapidly eastward, which therefore the circulation extends farther eastward. And there is a slight displacement of convection. Another thing that happens around this day is that the circulation to the east and west of the convection, they become symmetric. Four days later, the convection has moved. Now it's in the western Pacific. And the region of high pressure starts to build up to the west of convective activity. Twenty days later, the convection is in the central Pacific. And at this point, we still have this pattern of convection and the circulation that the circulation becomes decoupled from the convection. By day 24, the convection dissipates. And then finally, about day 28, the high pressure area with high pressure, it was the station where they had measurement. They had measurement of the Canton station and Nairobi station in Africa. So the high pressure system starts to build up and the cycle repeats. And this diagram that they published in 1972, it's still valid. This is still our understanding of the Madden-Julian isolation. And nothing has changed regarding this diagram. So this diagram is very nice. But what do we do to actually identify the MJO in observation if we take precipitation or pressure or winds? So we have a few methods available. And depending on what your goal is, you can choose any of these. So I already presented you the Willer-Killardis diagram. So I'm not introducing it here. But with the Willer-Killardis diagram, it's very limited if, for example, you want to identify a particular event, you cannot say anything about that. So the simplest method of identifying the Madden-Julian isolation, which was actually used by Madden and Julian, it's just the temporal filtering of the OLR anomalies or the winds. Then we can look at the space-time filtering. We can do an EOF analysis of a single variable. Or we can do a multivariate EOF analysis. And here are just a few examples. When we do a time filtering of the OLR anomalies, we end up with a half molar diagram. In this diagram, the time starts at the top. So as we go down in time, we see these regions with the negative OLR anomalies, which we can associate them with an MGO event. So this method has the advantages that it captures the special and temporal scale of the oscillations. But it's hard to identify in this diagram is where an event starts and where it ends. It's very hard to say if this is an independent event or there is some relationship between some of the events. And in this diagram, we look only at the OLR anomaly, whereas in that description that I presented, we have a coupling between the convection and the circulation. So the other method that we have available, it's the EOF analysis using one variable. And here we have an example of the EOF analysis applied to the OLR anomalies, wind at 850 millibars anomalies and winds at 200 millibars anomalies. The anomalies have to be bandpass filtered. We first remove the annual cycle, the seasonal cycle, and then we bandpass filter the data to retain only the 20 and 100-day variability. So here in this, we see the patterns in the first three EOFs, one, two, three, in the three variables. And then we can look at the lag correlation between these variables. So for example, here, the lag correlation between the OLR and zonal wind at 850 shows a lead lag relationship of about five, six days in EOF 1 and probably eight days in EOF 2. This lead lag relationship between the variables changes a little bit when, for example, the lead lag relationship between the OLR and winds at 200 millibars is about eight days. So again, this method gives us, because it's based on the only one variable, even though we look at all of them, has some disadvantages. And for that reason, one of the most used method is the multivariate EOF analysis, which John mentioned yesterday that probably it's not the best one because tends to be dominated by the winds. But what we do in this method, we take the filtered anomaly of OLR and winds at the low level and upper level. We normalize each variable by its standard deviation. And then we do an EOF analysis of these variables, average between 15 south and 15 north. The first two combine EOF, describe the propagation structure of the MJO. And the first two PCs are used to calculate the RMMM index, like it's shown here. And here is an example of how these MJO EOF patterns look like. So this is the first mode. And in this mode, this mode explains about 22% of the variability. Then if you look at the variance explained by the individual components, the OLR and the winds, you do see that the variance explained by the winds, it is larger than the variance explained by the OLR. And the arrows here show the direction of the winds at the surface and upper level for the regions in the Indian Ocean and Western Pacific. And we can see that these patterns corresponds to the circulation cells that we saw in the diagram of Madden and Julian. Similar thing with the second mode. And now when we look at the correlation between the two EOFs, we see that the lead-lack correlation, it's about 10 days. With the, since now we can actually look at the phases of the oscillation, which we are interested to evaluate, we can plot the two principal components, PC2 versus PC1. And this will give us the phases of the oscillations with the phase one when the convection is located over the Western Hemisphere. Then we have the Indian Ocean, maritime continent, Western Pacific, and so on. And here is an example of, we have seen this diagram. So the MJO is initiated in this point here, in sometimes in December. And then the amplitude grows. And it moves eastward. And then it switches to the, we are in January. It goes all the way around. It's maintaining its strength. And then in February, it starts to decay. And it comes back in this circle, which represents the weak MJO. One of the advantages of this method is that we can identify the MJO initiation. We can distinguish between events. It's based on multiple variables. But one of the disadvantages is that the wind dominates the signal. And therefore, sometimes it can give force MJO events. And here, if we look at the phase evolution of the precipitation here, and we are using the multivariate EOF analysis, we can actually match with the diagram of Madden and Julian. So I think here, phase one is down here, which corresponds to this panel F here. So we have the left panel corresponds to November, March, which is Boreal winter, and then May, September, Boreal summer. So this is actually the precipitation. So positive values corresponds to active convection precipitation. So we do have in the Indian Ocean positive precipitation anomaly. And then here we have phase two, the precipitation anomalies goes and it moves eastward. We see even though the MJO, it is weaker during the Boreal summer, we do see a similar life cycle during this. Yeah? True. The first question regarding this diagram, the left panel for winter always causes all south of the point. Yes. And yet, it seems a little bit odd. Well, if you look here, it's a little bit symmetric. And I think this is the strongest signal. So probably that component is dominated by the strongest phase. I guess what I'm saying is that the space is not completely symmetric. Yes, the oscillation is not completely symmetric. That's true. But if you do look at the asymmetric component, there is something here. It's very weak and not well defined. I mean, if you look at this, you do see a little bit of similarity. But yeah. And another reason is that this is based on the annual values. So if we look during the summer, convection is located north of the equator. Yes, there is a lot of details. And a clobber, the fact that the precipitation is located north and south of the equator for different seasons. Winter. But now, is it also a good summer? Yes. Of course, let me move. So with this, if you don't, anyone else has other questions about the MJO? Because I'm going to move to the Boreal Summer Intraccisional Isolation. No? OK. So in the Boreal Summer, things are a little bit more complicated than during the winter. And we do have the, like you already have seen in the previous diagram, that we have intracisional variability. And for the summer, the most common name is Boreal Summer Intraccisional Isolation. And it's still a debate about this relationship between the MJO and the northward propagation intracisional oscillation. So during the summer, in addition to this eastward propagation that we already saw in the previous diagram, there is a strong northward propagation. And people refer to this oscillation that propagates northward as the northward propagation intracisional oscillation. And various papers find various degrees of relationship between the MJO and the northward propagation ISO. And some people claim that 50% of these NPISO are actually related to MJO. Other people go all the way to 85%. So the jury, it's still out for debate. Yeah, well, so for example, one explanation is that once, so you have eastward propagating convection during the summer, and then this convection is dying out. And when it dies out, it generates these raspy waves that propagate northwest. And that's what generates the northward propagation ISOs. So the question is, is it an independent ISO or is it related to this eastward propagation? So we saw yesterday the talk where Hailean was talking about the mechanisms explaining the MJO. Well, for this boreal summer intracisional oscillation, we have way more mechanisms proposed to explain the oscillations. And the relative importance is still not sorted out. So the northward propagation oscillations have also two components. One is the 3060 day component. And it's a pure northward propagation oscillation. And then there is another oscillation with the period. It can be pure 30 days, or somewhere between 10 and 30 days that propagates northwestward. And to give you an example of these NPISO events, here are three examples. One is corresponds to an event in 2008. And we see this robust northward propagation from the equator all the way to 20 north. Here in this example, we see events that propagate both northward and southward. So it's a mixture. And then in this event, we see some oscillations that are initiated in the equatorial region, but just stay here and don't manage to propagate. So how we identify these oscillations? We have way more methods than we have available for the MJO. But relatively, well, now it's not recent. Five years ago, Lee, at all, has actually shown that the same multivariate analysis that has been used for the MJO can be applied for identifying the northward propagation oscillations. The only thing you have to do is you change the domain where you apply the UIF analysis. And they found out that the first two UIFs describe the 3060 day oscillations. And UIF 3 and 4 describe the 10 to 30 day oscillations. And here is an example from their paper. Another difference is that they actually don't recommend doing any filtering of the data. You remove the annual cycle and the seasonal cycle and do the UIF analysis. So when you do this, you end up with this is UIF 1 and UIF 2 of the northward propagating component. And if you look at the lead lag relationship between the two PCs, you see a relationship between about 12 days. And they did filter the data after they did a similar analysis where they filtered the data. And the relationship seems to be about the same. Then these are the patterns of UIF 3 and UIF 4 for that northwest propagating component. And the lead lag relationship, it is much shorter, about two, three days. Yes. Oh, UIF 2. From the pattern, you can say yes. And with these ones, you can also do the Wheeler-Hendon diagrams and look at the evolution of these oscillations. OK, so any questions about the tropical variability? Because I'm going to move to the, yes. Is your opinion, is it just the fashion of the MJO? And then you see kind of the tilted rospy tire. Something is tilted and something moves. That's what we. The direction of the normal propagation. That's what we claim in our paper in 2014. Yes. But then we looked at other mechanisms in a, and it's very hard to say which one dominates. So there are, see, this Borneo summer intracisional isolation, it's more complicated in the sense that it happens on the limited region. So you have northward propagation associated with the summer Indian Mansun, with the over the western Pacific. But you have other Mansuns regions where you don't have intracisional oscillations, right? So I think right now people are trying to show that there is some ISO associated with the West African Mansun. And you can correct me if I am wrong. So with the MJO, it's easy. You just apply the UF analysis from zero through 60, right? With the Mansuns, with the intracisional oscillation, this Borneo summer depends where you do your analysis. There are regions where, for example, the SSD is important, regions where the SSD is not so important, it's more complicated and it's not a clear answer. Yeah, yeah. Well, we remove the seasonal cycle when we do these analysis. Yeah, so I think the right answer is you need another workshop on this topic. It's a topic on its own, very, very broad. And you can bring the best experts. I am not. So now I want to move on into this mid-latitude variability. And the results I'm going to show here are a collaboration with my colleagues and other collaborators from NOAA CPC. So I was very interested. And I'm not actually the first one who asked these questions. People have looked before. If there is any intracisional variability or any mid-latitudes. So to try to answer that question, I asked my colleague, V. Krishnamurti, who has used before this data adaptive method, the multi-channel singular spectrum analysis, to look at the variability of the mid-latitudes. And this method is a more sophisticated US analysis. And it was introduced. I don't know if it was introduced by Gil, but Gil seems to be the one who promoted this method. And actually, Andy has used this method also. So there are a few studies based on this method. And you can actually download the code from UCLA. And there is a commercial company that actually sells the code for this analysis. So I won't go into the details of the analysis. I just want to present the results. So when we applied this MSSA to the 500 hectopascal geopotential high daily anomalies, we extracted three oscillations. So when we did the pore spectrum of these oscillations, we found that one oscillation with a period of 120 days, one with a period, this is a mean value of 45 days and another one with a period of 25 days. So when you look at the standard deviation of each of these oscillations, you see that each of them explains about between 10%, 12%, so when you combine them, these oscillations explain about 30% of the daily variability of the mid-latitudes. And I labeled them as the, since the first one has a period of about 120 days, it's not an intracisional oscillation, so I call it the mid-latitude seasonal oscillation. And then the next two, I call them the mid-latitude intracisional oscillation one and mid-latitude intracisional oscillation two. So how does the patterns of the life cycle of these oscillations look like? So here I'm looking at the mid-latitude seasonal oscillation cycle, and I have only the first half of the cycle, the second half it's similar, but with the reverse signs. So in phase one, we see this negative geopotential height anomalies over Iceland, and we see this positive geopotential height anomalies over the North Atlantic region, extends a little bit over Scandinavia, and another pattern of positive anomalies over the Pacific. So in phase two, which corresponds about 15 days later, we see that the negative height anomaly retreats forward, and this positive anomaly almost encircles the whole globe. Phase three, this positive and negative anomalies you have two vortex cores that circle around each other. And then in phase four, this negative anomaly that was located here over Iceland disappeared, and it's replaced by this positive anomaly is moving northward compared to phase three. And the positive anomaly that we have over the North Pacific is replaced by this negative anomaly. So I have done analysis to see what's the relationship between NaO and this oscillation, and there are similarities, but you cannot say that this is the NaO. But not in all phases. So yes, there are phases when there is high correlation, but there are phases when the correlation is zero. I don't have here, but I will show you the results. So I talked to a lot of people. Some people said it looks like Arctic Oscillation. I looked at the relationship between the Arctic Oscillation, and yeah, I know that there is a high correlation between the time series of NaO and NaO. I cannot find the same high correlation between the time series of this oscillation and the NaO, and also the patterns, phase by phase, do not correlate. So my initial reaction was that, well, this is some sub-saisonal variability of the NaO, but it's not. So let's move to the next one, the mid-latitude intracisional oscillation one. And here again, I am showing this just the half cycle. And the first reaction was this is PNA. Well, it turns out that it's not PNA. So it looks more like the PNA over this region, but you also, for example, looks like you have the opposite sign of PNA over this region. Well, like I said, I mean, maybe. But it turns out it's not PNA. So I'm not going to explain all of these patterns. And then this is the second intracisional oscillation that it looks like this. So phase one has a strong positive center over the Alaskan region and part of Greenland here. And then this strong negative center over Eurasia. And these centers move around. So to look at the. That one. Yeah. Well, yeah, I have not done this one in 25 days. OK, I have not done that comparison. I will do that. So here are some propagation characteristics of these oscillations. So the first one is the 120 days, the middle one, the 45 days, and then the bottom one, the 25 days. And here we average between 16-word and 17-word, although this is outside of our mid-latitude domain. And here we have an average between 40-word and 15-word. And the idea here is to look at the horizontal propagation of these oscillations. So for example, we see on the vertical axis, it's the phase. And unfortunately, it's just 0 to pi. But here this one represents 120 days, the middle one, 45 days, and the bottom one, it's the 25 days. So we do see they have both strong westward component, westward propagating components, but also not so strong, I would say, in the mid-latitude. This 120 day, but we do see some propagation in the 45-day oscillation, and not so much. It's more of a standing oscillation on the 45 days. We also plotted here, we averaged in the zonal direction. So to be able to look at the meridional propagation characteristics, and this is between 40 and 30 west, and this is between 190 west. So the 120-day oscillation shows a strong northward propagation in this region, not so much over this region. The 45-day oscillation shows some southward propagation over this region, and some weak northward propagation over this region. So they both showed eastward and, I mean, zonal and meridional propagation. And I did have calculated phase speed, but I don't have here, and I don't want to be wrong. So we look at the dynamical consistency of various fields based on these oscillations. And here, I'm just showing phase two, just one phase. I mean, if you get the dynamical consistency in one phase, you will get the same thing for the other phases. And we have the surface pressure and surface temperature here, and here the horizontal wind at 850 hectopascals. So we do see that, for example, if we have in this region negative surface pressure anomaly associated with the, it's not exactly the same location, but a warm surface temperature. And for example, if we look at the winds, we do see some cyclonic and anti-cyclonic circulations in that you can match them with the pressure. Yeah, they are. They are equivalent barotope, yeah. Yes, I thought that the temperature of the wind is quite easy if you look at the temperature distribution in Europe, it's consistent with having more of an effective kind of regularity for winds. OK, so we still have to sort out a lot about these oscillations. But the question we started to look at is, do these oscillations have any impact on the forecast scale at week 3-4? I mean, if they are real oscillations, you expect that they will help you with improving the forecast scale in this time scale. So we took the linear regression model that NCEP is using to issue the week 3-4 outlook. And that model has the RMMM indices for the MJO, the two-week mean NINEO 3.5 for ENSO, and then a daily index for a linear long-term trend. And this model predicts the two-meter temperature anomalies and precipitation anomalies. And to give you an idea on the scale of this model, here is the purple line. It's the statistical model that I am describing here. And then the other lines corresponds to the CFS, for example, the red line, ECMWF, the blue line. So you can see that this model has comparable skill with the dynamical models. This is the, here is the height key skill score for two-meter temperature week 3-4. Week 3-4, yeah. So we added both the 45-day index and the 120-day index. But I only show you results with the 120-day index. So this is a little bit, it's a complicated figure. So what it shows here is the impact on the two-meter temperature for the week 3-4 outlook. So each grid box here represents the area average of the United States. How I'm doing in time? I think I have a lot of questions. OK, right. And here, the distinction is made on all ANSO phases, El Nino phases, neutral phases, and La Nina phases. And the vertical axis has the MJO phases, 1 through 8. And then the last row here corresponds to week or no MJO phases. And then on the horizontal, we have the month for which the forecast was made from January to December. So what I am showing here is the high-key skill score difference between the model with four predictors, the one that has the 120-day oscillation, and the model with three predictors that doesn't have the 120-day oscillation. So warm colors means an improvement in the forecast skill. And we see a lot of blue colors here, especially for the winter, I'm sorry, warm colors, especially for the winter months, not so much for the summer. And this plot here shows the statistical significance of this difference, because you can get the difference, but I mean, you can get something that's different, but it may not be statistical significant. So we do see that months and MJO phases for which this new index, new predictor, makes an impact are actually statistical significant. And we are looking here at the correlation between the observed and the predicted 2-meter temperatures. And we do see, so this area here inside the black line is the area where the correlation is statistical significant. So during DJF, we do see a strong impact of this index on the forecast skill, not so much for the winter, the summer and so on. So one more thing that we did, we look at the variance explained after we added this predictor. And this is the variance explained by the forecasted temperature without the 120-day oscillation. And this is the variance explained after we added the 120-day oscillations. And this is for all n-sophases and MJO phase 6. These are for all n-sophases and MJO phase 7. And this is October, November, December, a slightly different season. So there is a lot of improvement by adding this in the prediction scale of week 3, 4 after adding this new predictor. Well, it does show some MJO phase dependency. I mean, if you look here, so the vertical corresponds to the MJO phases. You do see some phases where the impact is stronger, like 1, 4, 5, 8, 6, depending if you throw in El Nino or not. But if we don't, well, my whole conclusion was that it's actually independent of n-sophase. So that was a very encouraging result because right now they make very good predictions when you have a strong n-sauce signal. If you don't have n-sauce, then their prediction scale goes way down. So when we looked at the neutral phases of n-sauce, we do see a comparable impact with the presence of n-sauce. So that was something that, for people doing prediction, was a very encouraging result. So to summarize this, I'm going to give you some results. We can say that the mid-latitude also is characterized by some sub-seasonal to seasonal variability. The 120-day oscillation predictor demonstrated forecast of opportunity during the winter. And this 120-day predictor increases the variance in the correlation by about 25%. Unfortunately, the results are only for United States because this model is the operational model that NOAA is using for the week 3-4 outlook. But if you have similar models for other regions, I will be happy to see if it has any impact on other regions because it looks like these oscillations have a global structure, not only over the, like, NOAA has only, the main centers are located only over the Euro-Atlantic sector. In particular, your oscillation here is actually a very strong sequence of the NOAA-Atlantic European. Yes, it does have, but it also has signals in other regions. So it will be worth exploring that. You cannot use the same model and retune it and apply the Euro-Atlantic? I think you can, yeah, but you need to know what's the, you know, has to be calibrated, I think, for that particular region. So you actually have a model that you apply for Pakistan. So that might be another option. OK, so I'm done, so I'm happy to answer other questions.