 Would this be very complicated stuff? Good morning, everyone. I would like to thank the organizers for organizing this nice workshop and also for their support. Today I'm going to talk about telecollections and link to regional scare precipitation from a statistical perspective. I would like to thank my colleagues and some co-workers, Leon Shafik, Faisal Siyad and Mohamed Latif, Nikolay Tandevilov and Igor Zviriav and those team warnings from different parts. So I'll talk about, I'll give you a background on atmospheric flow, large-scale features and the relation of telecollections to precipitation and then briefly on comment on teleconnection and extremes. So as I start, I thought maybe I'll give you just a very brief background on where we come from. So that's a nice winter view of MISU. The department was established back in 1947 by Gustavo Rosbi when he came back from MIT and we do quite extensive research program in different parts, in different topics. We also offer bachelor master and PhD programs and I must say that MISU actually pioneered the application of the open IFS in teaching that was encouraged by Ireland, thanks for that. Unfortunately the last two years no students actually registered for the numerical prediction. Are we looking for PhD students? We offer PhD. Yeah, we have some positions advertised but not at the moment. So when you talk about teleconnections you can't really forget, you cannot overcome the dichotomy between weather and climate and also Rosbi waves. So I chose here to show you two pictures of difference between weather and climate. So the weather basically is the state of the atmosphere at a given place whereas the climate can be defined as the collection of long-term statistics of weather as was put by Edward Lawrence in 1970. But I also thought about something else which is the memory we keep about the weather aggregation and that's not really taken into account. Of course I'm not going to develop this. So large-scale flow and Rosbi waves when we talk about Rosbi waves we basically look at propagation of small perturbations. Ivana also talked about this before. A simple framework to study the Rosbi waves is to use simply the linearized beta plane vorticity equation. And this can explain actually a number of responses atmospheric responses to various forces such as diabetic heating or topography. And this is an example taken from Huskens and Karoli where you have propagation of response to a thermal forcing here. The response normally follows great circles and that's also shown early on by Ivana from Horan Wallace. Now what is the problem in teleconnection? What is it? If you take for example here I've taken the monthly sea level sea surface temperature over the Indian oceans. If you take a base point which is given by the blue cross and you correlate that point with every other point normally what you get you get one at the base point and then the correlation decreases outward. Normally monotonically if you have an autocorrelated noise but this is not a generic situation. If you take for example the sea level pressure what you get you get a kind of tipping point where you have positive correlation in the south and then negative correlation in the north and that's what we know the North Atlantic constellation. So a bit of history here. The question of teleconnection that seems to go back to Hill Benson in 1897 and also Lockyer in 1906 where they saw some sort of see-saw between southeast Australia and southern America. But it was in 1935 that Angstrom in this paper Angstrom was not actually by the way was not an atmospheric scientist. So he noticed that the weather at a given place is not an isolated phenomenon but intimately connected with the weather at adjacent places. And also we cannot forget Gilbert Walker. Gilbert Walker actually mentioned that the relationship between weather over Earth are so complex so that it seems useless to try to derive them from theoretical considerations. By the way Gilbert Walker was sent to study the Indian Mansoon but he ended up discovering the North Atlantic oscillation and the southern oscillation. Some of the main teleconnections this is also a background material, the ENSO which is known, ENSO is a Capricenome in the ocean and the atmosphere in the tropical Pacific and also this is the southern oscillation. So this is a point correlation where the base point is here. So you get a higher correlation for a plus one and then decreasing outward and then you get a flipping or a change of sign of the correlation. So that's the time series of the El Niño and that's the Darwin sea level pressure so you see the anti-correlation between both. This also shows the worldwide effect of El Niño that was also shown by Ivana early on. So these are also famous northern hemisphere teleconnections where we recognize the polar Eurasian pattern, NEO Scandinavian pattern, PNA East Atlantic pattern and also the East Atlantic West Russian pattern. So I should say that these patterns are derived from a linear perspective using EOS and rotated EOS. So the North Atlantic Oscillation, one of the main modes of variability in the northern hemisphere, basically measures the CISO of the atmospheric mass between the subtropics and Iceland. The northern annular mode, which is a hemispheric version of the NEO so that's a time series of the NEO plus the spaghetti plots for seismic prediction. That's what we are supposed to do in this workshop. The dichotomy between NEO and the AEO can be seen just by M-bomb. He can tell you more about it. So why are we interested in teleconnection patterns? So as we have seen in the previous talks, they link obviously remote locations on the Earth and they also have a large impact on surface weather and climate and they also describe large amounts of atmospheric variability because that's how they have been defined. They have been defined based on EOS which means maximizing variability. They can use it for different purposes such as extended range seasonal prediction and also downscaling. So how to obtain these teleconnections? There is no unique way to obtain them. As you should know from the outset, there are different ways. For example, state linear analysis based on regression, point correlation, particular orthogonal functions, nonlinear EOS, teleconnections, cluster analysis, and also composite analysis. And the norm we tend to give slightly different results. So I will comment here on one of the mostly widely used methods for orthogonal and particular orthogonal EOS. So EOS basically looks at solving a linear eigenvalue problem. C u equal lambda u, c is the covariance matrix. And this means that you end up with orthogonal pattern and uncorrelated pieces and that's one of the weaknesses of EOS. So this shows, if you have, for example, a nice distribution like multi-normal, that's the EOS one and this EOS two. So this is an application of to sea level pressure from and set and car. So the leading EOS comes out as Arctic Oscillation or any EOS, a bit mixed. This is also one drawback of EOS. We tend to mix physical patterns. Whereas the second one is known as the Pacific pattern. And then you get the EOS three with nine percent explained values as the Scandinavian pattern. And these are the different explained values of the different EOS. There's also paper that I published last year on giving an alternative to EOS. And this is a regularized EOS and actually what it does is it simply overcomes the pitfall of this geometrical constraint. And it does instead a generalized eigenvalue problem where mu here mu is the smoothing parameter. And the nice thing about this is that you can see here by just plotting the Lagrangian there is an optimum value of the smoothing parameter. So for mu equals zero you get the standard EOS. So there is a standard base price here. This is an example of showing the difference between EUF1 and smooth or regularized EUF1. So the EUF1, this smooth EUF1 comes out clearly more as an Arctic oscillation rather than a mixed pattern. So other tools like cluster analysis can also define clusters using either K-means or Gaussian mixture models. And I also mentioned that yesterday for example we've seen with Barbarasi talked about other tools like networks. So this is also, Ivana also mentioned teleconnection link to jet streams. So the jet stream is a belt of high wind speed around the Earth because it's not continuous with a picture of the jet stream. Jet stream also has two components the polar jet stream or the edge driven jet stream to hide the subtropical jet stream. And the distinction between them is not really as clear perhaps only over the North Atlantic. It also depends on the end-of-phase as mentioned by Ivana early on. So link for example, so now you can see the link between the jet and some of the teleconnections and most variability. So this is a work by Wollings et al. in 2010 when he showed that the NO essentially describes variation of the latitude and the position of the jet. Of course much of the extra tropical weather and climate is associated with the jet. And this can be used for different purposes such as climate change and large scale flow. So here I'm going to talk about the sum of the work I have been doing with colleagues on precipitation and teleconnection. And the first thing is, the first one is a work by Igor Zelia from Moscow where we looked at the link between the Mediterranean Evaporation and Teleconnection. So these two show the EUF 1 and 2 of the Mediterranean Evaporation which comes from the Woods Hole Ocean Institution and also group precipitation in year 40. That's the PC 1 and PC 2. So you can see the PC 1 and PC 2, the PCs of the most variability of Mediterranean Evaporation has got internal annual and also inter-decadal variability. So if you compose for example, following PC 1 positive, so they take the positive phase which corresponds to a positive anomaly of the evaporation, you get a large positive SST anomaly in the eastern Mediterranean and vice versa if you take the opposite of this. So now look at the link between the evaporation and sea level pressure. So that's a large scale. So here I show you two, one for the winter and one for the summer. So for the winter, the correlation between the PC 1 which shows overall excess or reduction of evaporation of the Mediterranean, you get what we know, that's precisely the East Atlantic pattern. And if you look at now the composite with respect to the PC 1 positive, so you get the effect of the negative, the positive phase of the East Atlantic pattern where you have dry wind from the northern. From the northern Mediterranean. And that enhances the evaporation. The negative phase now leads to a decrease of the evaporation of the Mediterranean. Notice also that in the summer time you get some sort of tropical origin of the effect of the Mediterranean evaporation. So you have two sources depending on the season. We also looked at the water budget and by looking at the moisture transport and the conclusion was that during the positive phase of EUF 1 which is global excess of evaporation the moisture convergence is obtained over the minor Asia whereas during the other phase the main moisture convergence is over the western and central Mediterranean. Another nice example is also the link to the Asian monsoon, so this is some sort of work in progress. So you can see a nice dipole structure, that's the correlation between the Mediterranean evaporation and all Indian rainfall. All Indian rainfall is a nice index of precipitation for the monsoon. I mean despite the shortness of the record you get a very nice enhancement of evaporation in the eastern Mediterranean and vice-versa. Some of the work also relates to the rainfall trends over the Indo-Pac summer monsoon. So here I'll show you here the trend of the precipitation of the summer monsoon over the Indian subcontinent. So you can see here there is a negative trend of precipitation over central India but there is an increasing trend over northern Pakistan. This is by Latish who is a PhD student in Islamabad. And so he tried to link this to the moisture transport so that's the vertically integrated meridional moisture transport. So there is a positive trend here on the negative trend of the Bay of Bengal so that links the decreasing trend of central India to the Bay of Bengal whereas the increasing trend over Pakistan is linked to the Arabian Sea moisture transport. There is also a link of the Pakistan precipitation to large scale and that's a picture showing the circum-global teleconnection pattern more than the Indian precipitation. There is also some work progress on the monsoon moisture transport and global SST. So Faisal is working on this and he's looking at the two boxes one of the Bay of Bengal and the other one is of the Arabian Sea and he looked at the correlation of PC1, the vertically integrated meridional moisture transport and sea surface temperature. So it seems that Elinio is forcing the moisture transport of the Arabian Sea monsoon brush. Whereas the Indian Ocean Dipole forces more moisture transport over the Bay of Bengal. There is also work on the now de-trended. This one I showed the trend but now they have been de-trended. So this is now the correlation of PC1 of vertically integrated meridional moisture transport with oil and the rainfall. So what you can see here is that the south Indian precipitation is forced by Elinio whereas the northern Indian Pakistan is more forced by the opposite phase. This is my last example which shows a different part this is the northern tip of Africa. So that's Tunisia and I looked here at two stations Vizert which is in the north part and then Siljana which is in the foothill of the Atlas chain and I looked at the lagged correlation between Vizert and October precipitation and September sea level pressure. So these are monthly precipitation. So we get significant correlation over the SO region so that's associated with the positive phase of the Enso so that's Elinio. So that's the northern part I mean there are simply a few hundred kilometers away but yet if you look at this southern foothill of the Atlas chain you get an any correlation any signal which is a bit surprising. So three words on teleconnection and extremes so as I said these EOFs they are based on a linear analysis so you take the EOFs which are directions they are not actual positions in the state space and it has some serious drawbacks and in particular they don't treat extremes in any special way. So here we propose a different alternative by myself and Nikolai from Open University on archetypal analysis. So what archetypal analysis does it basically identifies the convex hull of the data and try to identify typical patterns on this convex hull. So this is a picture of the convex hull so this is my data this is the convex hull this is the convex envelope and then you try to identify a number of typical or pure types, archetypes on this convex hull. So the objective to minimize is this is the cost function that we minimize and A and B actually are probability matrices like those used in Markov chains. So if I'm applying this to the sea surface temperature you get really three robust quite robust patterns and they come out as El Nino extreme phase and Glaninia extreme phase notes the asymmetry between El Nino and Glaninia now these are no directions they are actual positions in the state space and the other one is which surprised me is what we labeled here the western boundary current and that's the time series associated with the western boundary current so it seems that the western boundary currents are increasing not much work I looked at this in the literature but there's not really much work done on this so it seems that the western boundary currents are increasing sorry so this is also an application to the sea level pressure from 1948 to 2015 and I also get some four robust archetypes so the first one is the Nino comes out really robustly the other one is not is not really a positive Nino it's more of a mixture between Eurasia and Mediterranean so these are the extreme phases of Nino and this pattern but there's also the polar Eurasian archetype extreme phase and there's also a pattern here that links the Atlantic to the Pacific the northern Pacific to Scandinavia and this is my summary which basically contains what I have been saying and some references if you are interested in more references