 I'm very pleased to introduce Laura Fadranti. Laura Fadranti is a emeritus scientist from ECMWF. And she worked on diagnostics and evaluation of ensemble forecasts with a focus on extended and seasonal time range. Her activities include the assessment of the operational forecast and developments of products. And she is a contributor to the S2S project. Laura has had a number of seminal papers having to do with the importance of the tropics onto forecast skill over Europe. She was one of the authors first seeing the possibilities of S2S forecasts coming from soil moisture content knowledge. And most recently has written a very interesting paper about state-dependent skill. And I think this is what she's going to be talking about. Welcome, Laura. Thank you very much to the very generous introduction. And thank you for inviting me to such a prestigious school. So let's get started. And I would like to talk, yes, about the weather regimes with a specific focus on how the weather regime approach can help us to exploit the predictability at the extended range. OK, we started. Well, OK. So this is my outline. So talking a little bit about the low frequency variability, recurrence, circulation anomalies, teleconnections. Then it quickly goes through the dynamical definition how we detect the regimes. And then looking more about the predictability of occurrence of this regime, thanks to the tropical forcing. And then looking at how different applications are regimes, from diagnostic of regimes through making real focus products for user application. So let's get started and focus a moment to see what actually how these regimes, regime flow, regime types, weather types, sort of a very loose definitions. So basically what we think about this is recurrent flow patterns. So these are examples of a sequence of five dimensions in geopotential height and during winter. And you can see that these three maps, they are different, but they are also similar. So they are different in details, but they show quite similar structure. They have a high pressure system or somewhere around Greenland or Highland. And then they have a low pressure system over UK and Central Europe. And then equally you can see a reach over the West Coast of America. So generally the large scale pattern is quite common to the three maps we can see. But then what's interesting here is that when you look at the dates that this map occur, when did occur, this specific circulation patterns, they occur in three different years, in winter, but in three different years. So they were not actually see, they were not the subsequent events. They were just completely picked up from different winter, which it tells you really what gives you the meaning of this sense of recurrent flow patterns. So these are typical flow patterns that we see in winter, in fact. So they explain the low frequency variability in the esthetropics. When I talk about low frequency variability is anything between 10 to 50 days. And they tend to have some level of persistence. This in fact were a map that were average on the five days with the five days running mean. So this is the concept of recurrent flow patterns. This concept was actually very well known since the 1950 and it attracted quite a lot of interest because it helped us to understand the predictable component of the atmospheric circulation in the esthetropics. So one important way to a very innovative way to detect this recurrent pattern in mid-latitude was used by, was done by Wallace and Gatzler in 1981 doing this teleconnection pattern. So what do they use? They basically pick up one single point and you can see it in these maps as a sort of a big black dots. And then they correlate this, the value, the monthly mean value in these points, the grid point points, we do all the other values all over the northern hemisphere. And they do this for the winter using monthly means. For them, they use means level pressure. This is a redone map of the reconnection from a paper of a Nachi et al in 2017. By the way, this paper is an interesting paper for people that want to know more about weather regimes in general because it's a review paper on weather regimes. So it's nice to keep it in mind. At the end of the presentation, I put a longer list of references and this paper is included there. So here what we see, we see two, the two most relevant, most robust pattern that Wallace and Gatzler identified in 1981 which is through this teleconnection, through these correlations. And this is the North Atlantic oscillation on the left and on the right is the Pacific North American pattern. So these patterns are really very dominant and explain quite a big portion of the variability in the astrotropics. The Pacific North American pattern explain a very large portion also of the interania variability and the NEO pattern explain about 40% of the winter variability over the Atlantic sectors. Both patterns, as you can see from the structures they really modulate the position of the strength and the strength of the jet. And associated with this pattern, they are important anomaly in terms of precipitation. So these are really sort of strong modes that if we can manage to predict, we could gain quite a bit of knowledge for the future weather. So this was an example, but I mean, the concept of recurrent patterns and weather types, it's a very old concept. It's a concept that was actually known since the 1940 and the German weather service over 70 years has kept the catalog of, I think it's up to 25 weather types. So classified these maps in different, with different weather types. These are weather types are, in this case are defined in a more loose manner. And as you can see, they are regional, they are smaller. And they are basically trying to, in this case, weather pattern, we try to sort of infer from this kind of circulation the anomaly in temperature and in precipitation. So these basically are much closer to what Angel was talking about two days ago. So now going more in general, since we sort of have, so the dynamics, the low frequency variability in the esthetropics is basically dominated by these recurrent patterns. And this recurrent pattern exists because of the Rosby way and their property on the conserving the potential vorticity. So this is not, this is quite a well-accepted view, but the mechanism of how this mehanging of the Rosby way of this planetary wave actually is triggered and how it's evolved is not completely consolidated. There are several different view in that. And if you want to know more about the series, again, I can refer to this paper of a Natchi, but also there is a nice chapter on a book on sub-seasonal to seasonal prediction in which Robertson, Andrew Robertson and Frederick Vita are editors. And in that chapter, there is also a very nice explanation of the sort of nowadays different prospect, a different view about the theory and also application of the weather regimes. So to make it a sort of simpler, my view take of the sort of weather regimes are related dynamical concept, you can write it something like weather regimes are like kind of weather types that recurrent and persist for some times and it can be regional or not. Or you can refer to a flow regime. In this case, the flow regime is a more general definition and it's basically a recurrent and persistent flow path. And which is more associated with a fluid dynamical system. So you can have a flow regime also in the ocean, for example. And then there is another concept which is also a lot from this concept. A lot of sort of theory came out is the multiple equilibrium. So where you have a sort of multiple stationary solution of a non-linear dynamic system. I think I just want to give you sort of an example of this multiple equilibrium by going back and pick up one of the, I think first studies from Charney and D'Ivoire, which they use a simple idealized barotropic model to basically study the interaction of the flow with an orography. And so, and then they by looking at the simple idealized model they basically come up with two possible stationary solution. One is the same with the flow on the left side. The other solution that is associated with a blocked. So it's, and that's in fact a ridge upstream the mountains. So you see the ocean and the land. So you have the ridge upstream the land. So this multiple equilibrium approach was then followed by the many other studies which are the more complexity in model and so on. But at the end, what it was learned is basically that this kind of low frequency patterns, this multiple equilibrium exists and they are part of the internal dynamics of the mid-latitude and they stem out of interaction with orography and also from a thermal contrast of land and sea. So this is a lot of studying in the model. You have a lot of references at the bottom of this presentation if you're interested. But what I'm going to talk about if you're interested. But what about observational studies? So the first observational studies. So what I mean with observational studies trying to pick up these regimes in data in observational data. And this was done by Hansen and Sutterra in 1987 and they very simply use just a single index of the planetary waves and the look at the PDF. So they look for a bimodality of just a single index. This paper was very much criticized, of course, because you pick up a single index base on the geopotential height and define on an attitudinal band. The results was a little bit shaky, but it was actually inspire many more studies afterwards and particularly in the approach of looking and non-gaussianity of the PDF. So after many, many years, you get an enormous amount of classification methods, classification approach. And then I think in these tables which you find in the S2S book, you have a sort of a summary of how many different classification and approach you can have for to get regimes either in the full hemispheric regimes or all for the North hemisphere area or sectorial regimes over the Atlantic and over the Pacific. So here there are all different references with also categorized looking at different approaches. The two main sort of in a broad category of methodology to identify the weather regimes are basically two. One is using the cluster analysis. So trying to going in a phase space and because then we reduce some degree of freedom and then go and look into the classification, groups classification, or instead go and look at the multi-dimension PDF and look for non-gaussianity layer. So bimodality, trimodality and so on. So these are the two possible general approach and there is lots of statistical tools that have been developed and again I refer all details from this book. So for going more into sort of how look the maps, here we have an example of the regime defined as a cluster to a cluster analysis based on the, based on the pre-filter based on the phase space. Typically when we apply a cluster analysis we applied it not on a physical space but on a phase space to reduce the degree of freedom and announce the statistical significance of this kind of object, of this kind of separations. So these are an example of four regimes that typically come out from cluster analysis made with different federal algorithm over the European, Euro-Atlantic sectors. I mean, these four regimes they have a great, they have rich general consensus and many authors have end up with, by doing different analysis using a different data set they have always trying to end up with these regimes. These are quite stable regimes and define the low frequency variability of the winter in the Euro-Atlantic sectors. So in this specific ones I've been done by looking at came in cluster analysis and they are based on an interim. But I mean that if you look at error five or if you look at error 40 or if you look at any other re-analysis you end up with very similar structures. In fact, if you are looking even at simulation model different simulations, case and model, GCM model you also end up with similar structures. What is actually more variable is instead the amount of variance that this structure explains because this is much more depending on the period that we are looking at. So what are we looking here? This is the first mode you see is the Nord-Atlantic oscillation positive phase. So you have a strong indication of a very strong donor flow. Then you have a blocking structure. So you have a high pressure system over the Scandinavian peninsula. Then you have the Atlantic region with a high pressure system over the Atlantic and then you have the negative phase of the annual soil which is also called the grill and blocking. So a complete reverse of the donor flow. It's interesting that, I mean, these regimes there are also three of them. They also basically explain the preferred location of the latitudinal jet. So the preferred latitudinal location of the jet which is correspond to this PDF that you have on top. You have a three possible favorable position and which correspond to the annual positive Atlantic region and then your negative. So we can go on and say, so basically now we have said, okay, how a mid-latitude low frequency variability can be represented, described by this kind of weather regimes, this kind of flow patterns, okay? And an important additional ingredient on this is that this is a picture that is a paper that has already been mentioned and explained probably better than me by Herrick Maloni two days ago about the, when he was talking about the connection. So this is a paper from Horello Wallace which show that the similar to the connection pattern that look like a PNA is actually very much associated with the heat of the tropics associated in fact with the ENSO condition. And so the other two maps shows also the correlation at 700 hectopascal height with the index or an index integrated over the CISF-STEMCHA over the equatorial pacific. So a measure of the ENSO and the Southern Oscillation Index which is another measure of the anti-circulation. So both of them gives you the imprint again of this PNA pattern. So what they tell us here is that the PNA pattern is not only a dynamical, is not only a mode that explain lots of the low frequency variability in the estratropics and is triggered by internal dynamic in the estratropics but is also connected with the forcing in the tropics. And this has an enormous implication for the predictability because the dynamic in the tropics is more predictable. We know for example that ENSO is it has a large predictable component. And if we can predict ENSO, possibly we can also somehow have some level of predictability for the variability that ENSO is locked in the estratropics. So with these things in mind, people started to look then more and more closely to the regimes in different sectors and trying to establish whether the variability of this regime here to here was actually possible, establish the capability of the model in reproducing the here to here fluctuations of these regimes. So this is a study from Strauss et al. in 2007, which did exactly that. So you look at the Pacific sector, he identified four types or regimes. And then he went to look at the inter-internet variability of these regimes, the fluctuation of these regimes from one year to another. And he looked in both, he looked at a bigger set of long simulations. And then he looked at the re-analysis. So the re-analysis would be the verification, if you like. So the real would actually how in reality this four regimes, four patterns fluctuated from one year to another. And then you have the model. So the model is in red line. Red actually is the ensemble of integration and the green is sort of the range of the different that an ensemble gave, the uncertainty given by the ensemble, if you like. And the blue is the re-analysis. So you can see that for some modes, for example, the Pacific trough, they were quite strong in the inter-internet variability. In some years, a very, very large amplitude. And to some extent, the model was doing quite well. While instead you can see that for the haptic high, the model actually has very little variability. So this had an important implication because at least you can say, okay, with this kind of model, we have some of the mode that explain some portion of the variability in these sectors can be predicted knowing the variability of Enzo in this case. So what happened in the Atlantic? In the Atlantic, unfortunately, the effect of Enzo in the low frequency variability over the Atlantic sector has never been very clear and is not strong. But there is instead a very strong connection between the variability associated with the MGO, so at an intracisional time scale, and the NEO patterns. So the NEO, I said, is about to explain about 30% even more of the variability in winter. So having a connection with the MGO, it brings quite a big hope that we can do some good focus there. And so here, this is a paper from Kassu in nature, 2008, which show exactly this link. So it shows that during a strong convection, phase two and three, a non-convection over the Indian Ocean, which correspond to phase two and three of the MGO, you have a non-secure between 10 to 15 days later with the delay, you have an non-secure of frequency of currents of NEO positive. And then for the announced convection over the maritime continent, will instead lead to, yes, will lead 10 to 15 days later to an announced frequency of NEO negative. So this was a sort of a very important, again, an important implication for the predictability of the NEO. And I think quite recently we have another paper, which came out in 2019, which also shows that this kind of a teleconnection between MGO and NEO is actually modulated by ENSO. So in ENSO here, the strength becomes stronger. So the impact towards the NEO, it's stronger, but instead become weaker for the NEO negative and vice versa. So you can see really that how this distribution of heat, so reposition of it between ENSO and MGO affect the teleconnections. So, and I want to show you briefly also how powerful are these, that they're doing diagnostic with the weather regimes. There are lots of paper, they look at the ability of the modeling and reproduce the structure of the weather regimes and the ability in the model in producing the right frequency of the weather regimes. Because this is basically the important component that allowed a model then to be used to predict things. And this is an example from Robertson in 2020, which is actually use the weather regimes over the Pacific sector to assess the forecast performance. These are forecast 45 days forecast. So these are as to as forecast from the CFS broadcast. And basically these are forecast run every day. And here what it does, is you make a sort of a cut up the dimension of the variability in the isotropics and just saying, okay, I want to see what the forecast gives me in these four regimes, in this four possibility. So you have this diagram that is color coded, you have red, yellow, two, which is signify regime one, regime two, three and four. And you can see you have each lines is one forecast that they are all tilted because they verify that we are aligned on the same verification. So the bottom line with colors is actually the verification. And if you want to have a perfect forecast, you want to have all practical lines. And you can see that basically for me, this is what makes the full evolution of the forecast spanning all winter 2015, 2016. And you can see that there is a lot. So beyond the 20 days, late time, 20 days, there is a lot of blue, blue color, light blue color, which correspond to this regime number three, which is called the Pacific trough. So what does it tell us here? It tells us that basically this forecast beyond 20 days, it has a strong bias in overestimated the frequency of these regimes. And the paper tell us that goes through a lot of nice diagnostic that because of that, there was a big failure here in reproducing the strong anomaly of precipitation of California during this year. And this year was an year of ENSO. So ENSO was playing a strong, we had a sort of a strong ingredient from predictability. So this is just to show you the importance of how powerful are these weather regime approach. So I'm trying to cut it short now because I think the time is going, but I just want to mention quickly also that weather regimes offer also the ability to assess the flow dependence. And so we can actually create verification by stratifying the forecast at initial conditions. And because we know that some flow configuration can lead to more, can offer more less predictability. So equally like in the seasonal forecast, if we have an ENSO, we have higher predictability, if we don't have an ENSO, we don't. So this is even an exercise done in the minimum range. We actually look at how the evolution of the skill in the minimum range is a function of the flow configuration at the initial time. And we can see that for NEO positive and NEO negative, these are two flow configuration that offer much more accuracy in the forecast respect to the other two. So similar things we have done with the S2S and zones, but I'm not going to, I don't want to be too heavy with that. So it's a good diagnostic to look at the flow dependence type. I like the way some questions I remember two days ago during Angel talks about how many regimes, what is the optimal number of regimes? I want to say that there is not an optimal number of regimes, it really depends on the kind of application we want to make. And this is, for example, is two possibility of describing a low-frequency variability over the Atlantis sector using the flow, the classical flow regimes or using instead the 77 regimes. These seven regimes have been recently calculated by grams and you have the reference there. And it's actually, they have an advantage to these regimes that explain the variability all year round, because most of the regime work is really focused in a specific season, which at least for East European Atlantic sector is always happened to be winter. And so there are advantages there and actually in the ACMWF we are actually discussing whether we want to move towards these seven regimes to give a forecaster more, a better description. You see you have two flavors there of a blocking if we have the Scandinavian blocking, but you have also the European blocking, which is very important for forecasters in our area. Can I go ahead for another two minutes? Go ahead. So I just want to get on the subject of complexity, low-dimensional versus more complexity description. We have also done a study at ACMWF to try to understand how, where is the gain and where is the in having more regimes is having a higher dimension in the description of the low-frequency variability. And this is the figure basically they show you the variance is playing in a specific winter. This was the winter 2019 to 2020. If we use two EOF, simple, so a two-dimensional sort of description of the winter variability, so the red lines, or if you use the four regimes, the classical regimes, this is correspond to the green line, or if you use the seven regimes, which is the regimes I showed you before, and this is the blue line. And then you have the bench mark line, which is the looking at the variance is playing by even 20 EOF, so let's say the total, if you like, variability of the winter. So you can see here that overall, if you just make a sort of a by eye, an average of the amount of variance is playing all over without making the period, different period, picking up different period, two EOF is more than enough, it's playing what a bit of the variability. I mean, it's about 40 to 45%. But, and adding these four regimes or seven regimes doesn't add very much, but in specific period, and this is the one that I make the blue circle there, board over there, in specific period, this can be important. So again, this is emphasized the fact that depends really what we want to do with this object and how, what kind of information we want to extract. And then I think that the last few things I want to say is that when we go to two regimes, and now this is exactly the description, at the center we use two regimes, four regimes, and seven possibly we are going to consider to look at seven regimes. So we offer the focus, the full, this very simplified view, but in the more and more complex view. So by using two regimes, now we're looking at actually even, not even regimes, but UF. So we are really in an orthogonal space, very simple space. We can actually still explain quite a lot of the variants and we can actually represent the extreme years. This is, this is imagined here, we are looking at a phase space, two dimensional phase space based on the first two UF, which happened to be sort of the symmetric component of the NEO pattern and the Atlantic, and the Scandinavian blocking. And you can see that if you actually project onto this phase space, the daily values for winter 2009-10, which was a very extreme winter for NEO negative, you can see this very well reproduced equally for another winter 13, 14, it was instead characterized by a very high storminess and mild temperature associated with the NEO positive. So with this kind of things, we actually, with this kind of framework, we are actually able to looking at the extreme. So we are pushing even further. We use this kind of a simple description to use as a warning system for extreme cold temperature in winter. And this is a diagram that shows you basically all the distribution of severe winter events in a rain term and how this actually follow this project into this phase to simple two dimensional diagram. So show you that basically for extreme cold temperature in these areas of the sectors over, particularly Northern Europe, you always have a structure that look like either NEO negative or blocking. So basically, this is, we have constructing a real focus products that we are using. Focus seems to be very happy to look at this to actually show trajectory of the focus in this phase phase and to also show a PDF for up to week four of the forecast. And then I think I quickly want to show you the implementation of the probability for the four weather regimes, which is an operational products at the moment. And this is the latest forecast. So this is the forecast from Monday and which tells you so this is again, it's a color coded kind of map. So here it tells you that this 100 means that we have an ensemble of 50 members, 51 members. So all 51 members gives you, so you have 100% of probability to being in a blocking for this period of time. And then the block, the probability of blocking goes down a little bit but it's quite mundane. So we expect that for the next two, at least two weeks we have a strong blocking conditions over our area. And then with that, I think I'll give you on the summary and I'll leave you to read to you but what really I would like that you take home is that the weather regimes are an important tool to describe the low-frequency variability in mid-latitude. And because of their nature to be sensitive to tropical heat anomaly and also anomaly in the stratosphere, they are an effective way to exploit the standard range of stability. Thank you. Thank you very much, Laura.