 Tukaj, Then the other ones will actually be more on fact flow regimes and how they relate to the concept of multiple equilibrium, which is the main topic of this school. So this is the outline of the first lecture. I will give some introduction about some dynamical concepts, and some overview of essential literature. Some of you may have already maybe seen some of these slides so maybe familiar with these, In v štih koncu se vsezato je veliko zelo, da sem treba pred uko? Zelo, z bolj, na primeriske leko, posledaj spesifikanje in detalje in oče. So informacijli, če bo veči vsezat v posledaj srogov in vsakvala v importovati in vzela, da bi se izgledati, interišljali, nekih vsezat in na zdrav, In zelo sem izgleda izgleda klaster analizu, kako je zelo izgleda za regime. Specično je izgleda, da je tukaj atlantik. To je tukaj, da sem izgleda in izgleda. Zelo sem izgleda, da sem izgleda izgleda izgleda izgleda izgleda predigitabilitva in kako je zelo izgleda izgleda tukaj in alternativna forma da bi prijevajte prišljevanie z semstvenih vrste. Prvo, prijevajte površtje, da se dojeme socija, da se niči glasbej tukaj s nekaj površtje. Tako, da smo tukaj bahali o multiplejkibri, in z vsevrednjo nililinerih sistem, in smo videli izgledovati v demedijanje simulacije, simulacije vsedu v nekaj planet, in vsedu konfiguracije vsedu planet. Zelo nekaj nekaj, kot početno prorabimo, da so priježim tudi zelo vsedu početno vsedu na vsedu vsedu na vsedu. I to je početno nekaj koncept, ki so prišelij, načo se početno vsedu vsedu In je to vzlušnjena v odkričenju, je to vzlušnjena v konek od splorov, vzlušnjakih, glasbo, interglasbo periodov, je to vzlušnja v konek v splorov, vzlušnijenju, splorov, počelju. Vzlušnja koncept je nečestnik delov. Vzlušnja gena je pravosti, tudi do vzlušnja vzlušnja, v njim, geofizičkih, vzlušnjenj napotrženje.een Scrivable Rio are usually, think about some stable points, but in reality The atmospheric sustained system is continuously moving, so basically What you may have are? Stationary states, which are not stable, but they are weakly unstable and then you can have orbit around this stationary states, and so somehow you can have you know the flow Tako bilo konfigurable, ki so komponente za vsem, pa je vse zelo trenutnega, zame zelo, da je izvah na nekaj konfiguracij. A zelo v vsej v grade, kaj bi pa tako razpratili zvršenje zočnimi, zato vzelo, tako. In izgledaj, kaj ti je zelo zapečnimo genutnik do vede, kako je so povedali, kaj ti se povedali, zato na vede geni je vse geni, v nekaj vodnih vodnih vodnih način, je tudi všakulja konfiguracija v pizde, kaj je karakteristika vzeličenje vzeličenje. In kaj je, da težko se všakulja s vstupnem vodnih vodnih njevrednih vodnih vodnih vodnih zanim, tudi, da je zelo veliko populirala in ga je učinjala, da je vzela v dva, in in palmer in in the nineties is the analogy with the Lawrence Convection Model published in 1963. That was the first example of a chaotic attractor. And the this system is just a system of three equations with nonlinear terms. You see here the let's see when we have a pointer somewhere here. Does it work? No, well it doesn't. You see here this minus xz and xy terms. So this provides some nonlinearities in the system. And basically this is a very simplified system of so-called Rayleigh-Benard Convection, which is the convection which occurs between two plates, which are kept at different temperatures with the bottom one being warmer than the upper one. So the system gains heat from the bottom and loses heat at the top and this heat is transported by convective cells. So physically this system has a chaotic attractor in a certain range of parameters. And this attractor is basically shaped by the existence of three stationary solutions. One of them corresponds to no motion and is strongly unstable. So we never actually see the state in the attractor. The other two are only weakly unstable and basically they are at the center of the two wings of the attractor. So somehow the system is time evolving, but it has two sort of preferred regions in phase space where the state vector resides and these basically are regions around two unstable stationary solutions. So we can think about the two wings of the attractor as representing these flow regimes around the two unstable equilibrium. Now if we now move to the atmosphere, then basically this concept was usually applied again, mainly in late 70s and 80s, early 90s, to atmospheric models and usually people use rather simple atmospheric models, either a simple barotropic vorticity equation or some quasi-geostrophic system with maybe two or three layers. And in this case you can sort of summarize the dynamics of the system by an equation for either barotropic or quasi-geostrophic potential vorticity, so potential vorticity is q. And so the time derivative is given by the erevection of potential vorticity and then on the right hand side you have this d term, which is basically a relaxation towards some equilibrium, which is determined by a forcing term q star. So when we look for multiple equilibria, we look for stationary states of the equation at the top. So we look for values of q, and from quasi-geostrophic theory you probably know that basically from potential vorticity you can derive this function, and therefore once you know the potential vorticity the whole flow is determined. So when we look for multiple equilibria, we look basically for stationary solutions of this particular equation at a specific instantaneous time. The concept of weather regime is not about what happens in one particular instance, but rather what happens in a certain, in a period, which is longer than the typical time scale of weather system. So if the weather cleaning has a time scale of maybe three days, then a weather regime may have a typical time scale of ten or fifteen days or longer. Sko what we can do is actually to average this equation in time, in in a similar way in which you can do a composition between the zonal and the flow as Simone showed yesterday, you can average the top equation in time. And because of this linearity, you have just the terms in the equation where you replace the s ločitkem potenčnoj potenčnih potenčnjih z tajimi vzdušnačenih. Da sem tudi tudi tudi vzdušnji, kako je tudi včutk, od zeločenih mode in začavati prihvetnih, sem vzdušnji izboženih, ko sem pripobstavila. Vzdušnji je tudi vzdušnji z vzdušnjih z plavantarii, ta je, če je to, kot pa je tudi vzdušnji. So basically it tells you that the high frequency variability gives a feedback on to the last scale flow, and this maintains the flow in some sort of statistical equilibrium. Now, there been a lot of papers written on multiple equilibria and flow regimes in the atmosphere, so we just remind you of some very well known papers that somehow were some sort of, -, zelo izbtubneS, the study, and probably the one about multiple equilibria in atmospheric flow was the one by Czarny and the World published in 1979, actually Axel Wiennilz publish in the same year, a very similar paper that somehow got much less known. So in this model is a simple barotropic model kaj je stvari in však. V vsem schvarnje je tografij, kaj je zelo, in stvari je pozivno všeč, ko so zač할 je rešna zelo in pri toga vača zemenja, kaj je tudi nekaj saj blizu. Savoje se tako stabilne štari, One has stronger zonal flow, and the ridges are in phase with the topography. The other one has a weaker zonal flow, the ridges are positioned on the valleys, and the wave amplitude is larger. This paper was very influential at the time, and then actually in a Chinese school developed a number of his postdocs who developed a more sophisticated model. For example, David Strauss developed a two-level baroclinic version of the system. Shu Klein Moore, again, with Charny, investigated again a barotropic model, but with very many degrees of freedom. But actually, the term weather regime was actually introduced by a paper by Reinal and Pierre Hamburg in 1982, and what they did, they took the two-level quasi-geostrophic model that was developed by Charny and Strauss. This actually had, if I remember correctly, five stationary states. But then they added, that model was only a model for, again, the zonal flow and the planetary waves. They added many more degrees of freedom, so they would allow the system to develop baroclinically unstable waves. And what they showed was that, in fact, the baroclinic waves were destabilizing some of this equilibrium, some cases more strongly, some cases more weakly. And then what the attractor of the system would do would basically switch between the neighborhood of two of these weakly unstable states, and they referred these two as the ridge regime and the trough regime, again, because in these two regimes the waves had a different phase with respect to the topography. So in one case there was a ridge over the topography, in another case there was a trough over the topography. There were other unstable states, but somehow the system was not spending a lot of time with this. So somehow this was the paper that actually bridge somehow the gap between the multiple-equilibria studies that discussed the equilibria and the more sort of common knowledge of mid-latitude weather which is dominated by baroclinic disturbances. However, the concept that the eddies were actually interacting with the last-scale flow and they could maintain the last-scale flow in a stationary state was not actually new and was actually probably, this may be popular by the work of John Green in this school and John was working with John Green at Imperial College at the time. So basically the Imperial College School is on the impact of high frequency eddies with blocking highs. And you probably know what the blocking is. It is basically a ridge, an area of high pressure which is located at the high latitudes and it is called blocking because it basically blocks the flow of baroclinic transients along the storm track is usually divided into branches. One goes to the north and one goes to the south. So although blocking is more frequent during the winter season there are summer blocks. At the moment there is a summer block over the UK and they are actually having much higher temperatures than we have here. So Green actually focused on what happened during July 1976. There is a strong block that caused the drought over the UK and Green showed that this actually block was maintained by the flow of potential vorticity brought by high frequency transients. So this concept was developed in a number of subsequent papers. These are just a few ones. And the ones that John did in 1987 with Kit Hines actually showed how a modern structure again is a stationary solution of the flow can be seen as a prototype of a blocking dipole and again it can be maintained against dissipation by the vorticity flow by baroclinic transients. Another paper that developed this concept was the one by Votare and Legrand. They again looked at two level quasi-geostrophic model in a channel in many degrees of freedom and they found regimes. But the difference between this paper and the previous ones is that in the other papers the regimes were formed around multiple equilibria. So you had a system, the system had multiple stationary states for the instantaneous flow. Some of them were strongly unstable so the system went easily away from those states. Others were only weakly unstable and the reactor was somehow shaped by this. The difference of the paper by Votare and Legrand was that in their model there were no multiple equilibria of the instantaneous flow. So what they did, they actually forced a jet through a thermal forcing in the left-hand side of the channel and what they showed is that because of the eddy feedback the jet could actually have flows that were more zonal like this one or flow where the jet was actually split and there was some hint of a dipole in the middle and they called it a blocking state. So what they were arguing was that somehow you could have weather regimes even without having multiple equilibria whether this is the case or not is still debatable. Is there a thing that somehow... One is zonal flow, one is blocking time. So why didn't you say that? Well, in the sense that these are... I think it's better to call these flow regimes. So if you take the time average flow then you have these states which are relatively persistent but if you analytically solve the equation and look for stationary states... Well, I didn't know what I did and I claim that there was only one stationary states for this instantaneous flow. So the alternation of regimes only came because of the fact that the bioclinic transients could actually support different configurations of the flow. So in this case there was no need for the large scale forcing to actually allow for multiple equilibria of the system. Do you assume that they also left a biolimensional sort of invariant map for all this? I don't remember honestly. I don't think they made an analysis like that if I remember correctly. So they only talked about the fact that there was only one equilibrium but definitely the equilibrium must have been unstable otherwise they couldn't have had multiple regimes. So the other thing I want to say about this paper is that it actually refocused the attention from the hemispheric flow and the large scale planetary waves to what happens in one particular sector. So basically what they were saying is that their model was an analog for the regimes in the North Atlantic. There were many talking about analog for Atlantic blocking where you could apply this as well to the North Pacific but somehow if this idea is true it means that you can actually have regimes independently downstream of a jet so you don't need somehow planetary wave dynamics to have regimes and you can study the regimes independently perhaps in the North Atlantic and the North Pacific. Now okay, you have these theories of planetary waves then you have to find a way of detecting them in observational data or in model data and one of the first attempts was done by Alfonso Suterre I just happened that during my first year at TCMDRF I was a visitor and he was a visitor as well. He was actually his permanent position was at Yale with Barry Saltzman and he was doing some of the in fact the multiple equilibria and stochastic resonance studies that David Ferreira talked about in his talk. So he was very much in this idea of multiple equilibria he was now interested in finding some observational evidence for these theories of multiple equilibria in the planetary waves and while he was at TCMDRF he basically found that in the TCMDRF analysis for the winters that he had available at the time there were only four years in the ECMDRF analysis he could find by modality if he combined the amplitude of zonal wave numbers two, three and four from geopotential height data of course four years were not a lot so it was hard to prove the statistical significance in such a short record so when he went back to Yale he was with Tony Hansen and they looked at the record of geopotential height in the NSEP well at the time it was the NMC reanalysis and they had 16 years so they published this paper when they showed that the probability density function for this planetary wave index had two modes one corresponding to weaker planetary wave amplitude and one corresponding to larger planetary wave amplitude and if you take the composite of all the fields in this mode and then all the fields in this other mode and you take the difference what you see on the right hand side is the plot of the geopotential height difference so the high state had actually ridges over the North Pacific and the North Atlantic after in the position where they are blocking so somehow this related to the general concept at the time that where there were no more for blocking however this work was much criticized mainly because people found out that the results were very sensitive to the exact bend in which they were computing this Fourier decomposition of the planetary waves it depended also on the method that they used to compute the probability density function and yeah with 16 years even with 16 years was not easy to demonstrate the statistical significance for that. I think recent studies that have been published more recently that have revisited this have actually shown that the indexes indeed by model in a longer record however this was the first attempt and this somehow used the simplest method to try to multiple regimes or to condense everything into one single index and if there are multiple regimes the idea is that the probability density function of this index should have peaks in correspondence to these different regimes and the minimum in between however when you condense everything in one single number of course you have to make a lot of assumptions you discard a lot of degrees of freedom and so soon after that people started to think about well can we have something can we look for regimes in a way where we can actually see more structure in the patterns related to these regimes so the simple extension you can go from one to two degrees of freedom and what people have done for example already Kimoto and Gil for example they did two papers with this technique Susanna Korti Tim Palmer and myself did one in 1999 you can do a principle component analysis of the geopotential height field you only retain the dominant principle components the simplest thing is that you retain the first two and then you can compute again with suitable statistical techniques a probability density function in a plane instead of just in one dimension so you have now two dimensions and when we did that with Susanna and Tim we found a probability density function that had three peaks and if we actually composited the geopotential height anomalies around these three regions these were the anomalies in geopotential height that we found so this was done using monthly means from again the end separate analysis this time we had about 50 years but again because we used monthly means again in the size of our sample was not too large and again we were criticized that the statistical significance was not maybe as large as people would have liked but anyway it was an attempt somehow to to put a bit more structure into the patterns of these regimes and not allow just a variation along one simple index and somehow what the reason why perhaps this two-dimensional picture was easier to digest is that you could see here structures similar to the linear interconnection patterns that have been studied by many people Wallace and Gussler and many others like you have here the North Atlantic oscillation here in this positive phase in the other regime on this negative phase and then you are something like Pacific North American patterns so somehow you could see these hemisphere scale regimes as particularly stable combinations of these interconnection patterns and this was somehow more easy to to sell to the meteorological community than just the simple one-dimensional index of Hansen and Sutela but of course you can go to even more dimensions and if you do that it's hard at this point to just compute the probability density function even if you use data with higher frequency the daily data you don't even in the longest cycle you don't have enough points to really estimate the PDF in many dimensions with techniques like the Kermer technique that is often used in one or two dimensions so people reserve two techniques called cluster analysis cluster analysis is a multivari statistical techniques and basically what it does is that you represent your data through a set of coordinates can be any number again often people do a principal component analysis and use the principal components as coordinates and then basically cluster analysis we look at the distance between these points and we form groups clusters of points that are close to each other so basically we partition your whole record of data into separate groups now the the objection that can be done to cluster analysis is that it will always find groups it's designed to find groups so you cannot say because you find clusters that this means that there are dynamical regimes in fact if you think about a multivariate system probability density distribution is just a multivariate Gaussian distribution so you only have one maximum if you apply the cluster analysis it will give you clusters so what you have to do when you do cluster analysis is to do again a test of statistical significance and this is often done in this way so you take a reference data set that you know only one maximum in the pdf usually you take multivariate normal distribution you apply the cluster analysis and somehow you can quantify how well the data are actually clustered by basically measuring the ratio of the variance so you can look at the variance which is explained by the mean of these clusters and then you can look at the variance of the deviations from the means and if this ratio is large so if the centroids explain the large proportional variance then somehow it means that the clusters are more robust and vice versa so you can have this number this ratio, this sort of signal to noise ratio you can compute it from the real data and then you can repeat the calculation many times on data that you construct but from for example a multinormal distribution so that will give you a range of values for this ratio that may just happen by chance so this is what basically the cluster analysis would do even if there were actually no regimes so you can look at the distribution of these random values and you may say that the clusters from the real world are significant only if this ratio is larger that say 95% of the values which are obtained by chance so Michelangeli Votarin Legrapp did such an analysis in 1995 it was applied to the North Atlantic sector and when they used this in a cluster analysis technique which is usually called K-means it's a rather simple analysis that basically looks for assigns each point to the closest centroids and it does it iteratively until it finds an optimal partition of variance and then they computed the significance for different number of clusters and they came out with four clusters that were actually already found by Robert Votarin in an earlier study and basically these Atlantic clusters are not totally symmetric so you have two clusters that actually correspond to opposite phases of the North Atlantic oscillation which I think are the ones at the top you either have a high or a low over Greenland and in one case you have an enhanced zonal flow and in the other case you have a weakened zonal flow shifted to the south on the North Atlantic and then you have two states which are the ones at the bottom with enhanced regions so you may have either a ridge here over the North Sea Scandinavia and this often gives rise to a blocking or you can have a ridge here in the middle of the Atlantic and so this regime is usually called the Atlantic Ridge and this is called blocking so this paper again was quite successful and mainly people then adopted this four regime classification for the North Atlantic and this is of subsequent research so let's make an assumption that you believe that there are flow regimes and somehow you have found a suitable method to detect them now if you work in a weather forecasting center as I do at the moment you would like to use this concept to make predictions now you don't need weather regimes to predict the weather up to three days because the weather up to three days would be determined by baroclinic weather systems but if you are going into the medium range say the second week of your forecast or if you are doing sub-seasonal forecast or seasonal forecast then you, it's very hard and after let's say ten and fifteen days it's getting impossible to tell what happens at one specific time and what you want to do is to give probabilities for certain flow configurations and so flow regimes become quite handy so what you hope is that there is some predictability in the frequency of occurrence of these regimes so you can say in the next month let's say this particular regime would become more frequent and the regime would become less likely now we have seen that regimes exist in non-linear chaotic system so at first side you would say well there is not a lot of hope for that the system is chaotic you will have transitions which are driven by baroclinic eddies we know that baroclinic eddies we can only focus them for a few days so what can you do the answer is that actually the atmosphere doesn't have always exactly the same forcing or at least if we concentrate on one region let's think about the North Atlantic region so the flow is forced by for example in the topography the flow is forced by LNC contrast and these are always there but some of the forcing actually comes from the law of rosby ways that are located in the tropics and this vary because the location of tropical convection varies so basically the hope of finding predictability in flow regimes mainly comes from the concept that the forcing from the slow part of the climate system so it could be the tropical ocean but people are now studying the impact of the ice variation or snow cover over Eurasia so this sort of slow component of the climate system modify the forcing for the large-scale flow in a region and therefore they can modify the properties of these flow regimes and coming back to the analogy with the Lorentz system you can simulate that by adding one additional term for example this white star on the right hand side of the second equation and since in the Lorentz system the y variable is basically a measure of the horizontal variation of temperature having a forcing for y it means that instead of having a constant a uniform heat flux at the bottom you may actually have stronger heat flux in other points so what this will do is that it will break the symmetry of the system in the Lorentz system the two regimes are simply determined by a change in the rotation of the convective cells so energetically they are equivalent so if you start putting a bit more heat in certain points of the bottom plate then the flow will preferably have ascent where you have more heat so somehow this would be a sort of physical analogy for this at this white term so if you do that now so when you modify the forcing parameters in a nonlinear system you basically have two scenarios one is that the one that is usually illustrated by the analogy with the Lorentz model and that is when the variation in the forcing is relatively small compared to the overall forcing of the system and in that case so if the regimes are quite well defined putting a weak anomaly in the forcing does not change number and therefore the special patterns of regimes they remain roughly the same the frequency of occurrence is changed and in the Lorentz system this happens because it makes one of the two stationary solutions less unstable and one is made more unstable so then the system stays preferentially around the stationary solution which is more stable so when the forcing parameter is weak you only modify the stability of the equilibrium and therefore the frequency of occurrence but if the forcing anomaly is strong then as it has been mentioned earlier in the week you can go to bifurcation points so bifurcation points it means that you can go from a situation where you only have for example one steady state to two steady states then the steady states may become they can change from stable to unstable and so the shape of the attractor changes substantially so there are situations where the weak forcing anomaly is appropriate but there are also situations where it is not and you may have more dramatic changes as we have seen for example in the aqua planet simulation and the interaction with the eyes so what are the real sources of this forcing variation in the real world as I mentioned the first thing that comes to the mind is the variation in heating in the tropics and of course one of these the main sources of variability for the for the forcing of planetary ways is the variability associated with the linear and the sudden oscillation I assume you are more or less familiar otherwise I could spend the rest of the morning describing these particular slides which I think is one of the most frequently seen slides in presentations about long range predictability but the important thing to notice is that the effect of the linear phenomena is basically to change the position of the main convective heating in the tropical pacific the heat source is changed the rosby wave source is changed so the rosby waves propagate into the mid latitudes are changed and so this basically translates into a different forcing for the northern hemisphere planetary waves at least in the pacific and then we know from linear in this case we don't need no linear studies from a lot of observational and linear modeling studies if you modify the heat source in the tropics then you generate teleconnections through rosby waves that will propagate into the mid latitudes and a very famous paper in this was the one by Horrell and Walder published in 1981 when they related variability in the tropical pacific with the variability of the pacific North American pattern so you can exploit this so we need something like that with David Strauss and again Susana Corti in 2007 we used a large ensemble of simulation forced by observed SSDs that were run at the center for ocean land atmosphere studies where David is working so this was a set of ensemble with 55 membri so pretty large ensembles for about 20 years so we did a cluster analysis of geopotential height over a sector covering the North Pacific North America and the Western Atlantic we used the same technique that we used in Michelangeli et al this came in cluster structure we came out with four clusters for regimes basically the top two were called Alaska region pacific draft because basically you have either a region or a draft over the Aleutian islands or Alaska and then the bottom two were more sort of zonally symmetric and so we call them Arctic low high and this amount connect some higher latitudes in a more sort of symmetric pattern SSD was prescribed SSD was prescribed and I think observed SSD for this 18 winters so we did this for the model and we did this for the analysis and there was a reasonably good correspondence between the clusters in the analysis and the clusters of regimes so we could look at the frequency of these four clusters in the analysis and in these ensembles and we did plot like this where the blue curve is the frequency of each cluster in the analysis the green band gives the spread of frequency between the 55 ensemble members so we compute the frequency for each season and the red curve is the ensemble mean so if you put all the what you get if you compute the frequency putting all the 55 members together and you can see that not all the regimes are equally predictable certainly it turned out that this specific graph was the most predictable one you can see that there is quite a good correspondence between the peaks in the red curve and the blue curve and if you actually look at the years that you cannot probably see this actually corresponds to the aninio year and this is why this is because this particular cluster projects strongly onto the mean response by and so if you look at other clusters like for example this Arctic high you hardly see any predictability so it's not that every cluster is equally predictable every regime is equally predictable and in the pacific somehow the fact that the pacific is so much influenced by and so so it makes it easy to predict those regimes which have patterns which somehow are most strongly related with the answer response so this is an example when you use basically the weak force in paradigm so you just assume that the clusters are the same and what you change from one season to the other is only the frequency and then you can basically you try to predict the frequency but actually since for each of these years we actually had the 55 members in enough data to do also cluster analysis in each individual year and so I mentioned before that you can actually measure the strength of this cluster by the signal to noise ratio which is the very ratio of variance explained by the centroid divided by the variance the internal variance of the clusters so we did this analysis with David in 2004 actually before the other paper and what you see here is this variance ratio for clusters in the Pacific the domain was likely different so in the end we found that the tree cluster partition was the most robust but we plotted this signal to noise ratio as a function of the linear tree SST index and what you can see is the very strong relationship so basically it turns out a lot of variance where you are in a linear state but gradually when the linear forcing increases then you end up in these two points where 1982-83 and 1996-97 sorry 1997-98 so the two biggest in linear before the most recent one in 2015-16 and actually when you come to such a strong forcing it actually turns out that these ratios are not statistically significant so basically when there is a strong El Nino the forcing is so strong that basically forces the system just to stay in one single equilibrium with just linear oscillation around this so you can see this as an analog of a bifurcation so basically when the forcing the linear forcing is very strong then you only have one equilibrium and gradually when you move towards a linear state then you start having multiple regimes and perhaps a simple explanation of this is that usually these regimes are associated with zonal asymmetries and so during an El Nino state especially in the very strong the temperature across the tropical pacific becomes more uniform and so the convection is distributed in a more uniform way between the west and the central pacific when you have an El Nino state instead the convection is strongly concentrated in the west and therefore the asymmetry the zonal asymmetry in the forcing is stronger so on the one hand you say oh no so it's nice to study things in the pacific because there is this clear examples of the forcing on the other hand this tells you that the influence of El Nino on the structure of the pacific regimes is actually very strong and so it may explain why people who have done for example cluster analysis over the pacific region often find result which are a bit different depending on the particular sample they take the particular technique or the domain while people who have done the analysis on the Atlantic they seem to agree about these four main clusters that I have shown before so perhaps the Atlantic unfortunately less predictable for people who are in Europe and would like to know something about these regimes frequency but it might be it might give an easier job to the theoretician to explain them because you don't have this continuous very strong variation in the forcing that occurs in the pacific because of the El Nino phenomenon so it's a bit of a double edge word so signal is larger so the overall variability is larger in El Nino years but most of this variability actually comes from the separation between these different regimes so the predictability of the El Nino may be less predictable El Nino will be less predictable on the seasonal time scale because the fluctuation between these regimes of course generates some often unpredictable signal on the seasonal mean well this tells you that there are more regimes here whether these regimes are more or less predictable it may depend on whether you can say something about the relative frequency of regimes now this is not an index of the predictability of the index itself so the El Nino 3 may be equally predictable in positive values and negative values but if you now want to make a prediction of what will happen in the extra tropics as a result of El Nino it may be easier to focus what happens in an El Nino state because the system is strongly forced towards one single regime when you are in El Nino the system may for example develop blocking over the North Pacific that usually are not developed as frequency what is your experience of focus so La Nina is less predictable the the extra tropical flow I would I think the studies that were done by for example by Tim Palmer in the 80s they found that during the La Nina years that often had negative PNA states the flow was less predictable the time for example Tim Palmer interpreted this in terms of probability but you can also interpret that in the sense that El Nino state would give you different regimes and so you may have switch between very different regimes during the season in La Nina and so this may give you less predictability ok so we are coming to the end but before that I want to mention that recently so say on the seasonal time scale perhaps the Pacific is an easier problem to deal with at least in certain situations because of the El Nino forcing and it seems that on the seasonal time scale you cannot say too much about the Atlantic but recently it was actually pointed out that if you move to the sub-seasonal time scale then you may have predictability for the North Atlantic regimes and again this comes from tropical forcing but in this case not the seasonal mean forcing associated with the SSD variation but just the variation in the position of convection associated with the modern and Julian oscillation the modern and Julian oscillation is a mode of intracesional variability of the tropical atmosphere you usually start with convection developing in the western Indian ocean then propagating towards the east and as long as you move this main area of convection on the maritime continent then the west Pacific and then usually the convection dies when it moves over the colder water in the east then again the Rosby wave source is changed and then you propagate the signal in the extra topics now usually the phases of the MJO are now quantified through this diagram which is was designed by Wither and Handon in 2004 now it has become very popular they did a combined principal component analysis of zonal wind and DOLR and basically if you use the first two principal component you define a plane you can divide it in eight sectors that correspond to the different regions where convection is located so for example phases two and three correspond to the phases where convection is over the Indian ocean six and seven is where convection is over the western Pacific so the system moves in an anticlockwise sense if the point is within the circle close to the origin we say that basically there is no active MJO and this corresponds to basically one standard deviation of these principal components so this is now a tool that we use, especially of course there's a big sub-seasonal program going on sponsored by WCRP and WWRP and so these particular tools are now used in many forecasting centers and you can see predictions of the modern and junior oscillation where basically the predictions are displayed using this wheeler and Handon diagram now Kassu in 2008 so that if you actually do a cluster analysis over the Atlantic and again you find the same for clusters so that's nice and you look at the frequency of these clusters as a function of basically the phase of the MJO basically from the same time to 15 days before you see a relationship and you basically see that in particular positive NEO states which are these ones here tend to occur about 10 days after the phases where the convection is over the Indian Ocean and vice versa the negative NEO phase tend to occur 10 to 15 days after the MJO phases where you have convection over the West Pacific so this again has become a very popular and influential paper so again, number of centers including ECMWF are now sort of exploiting these connections and we have for example displaying frequency of these four clusters together with the MJO statistics and it works sometimes you can really see that if there's a big MJO you can expect a phase of the NEO and it really happens so it's not just a statistical construct so in the rest of in the other talks I will actually mainly focus on the North Atlantic from a theoretical point of view as I said is somehow perhaps an easier problem to deal with and so we can maybe have five minute breaks break and if you have any questions here Fred. So why is it that on a seasonal timescale and so in the Pacific strong forcing there is so little signal in Europe whereas on intra-seasonal times the same situation forcing is in the Indo-Pacific region maybe slightly different but basically forcing is in the region but there is a strong signal in Europe. I think it's just a problem of persistence my idea at the moment I will develop in the next lecture is that in fact what happens is that you don't have a direct forcing by the SST in the same way that you have for an union so really stationary forcing what you have is that the SST probably change the phases of the MJO if you have warm SST over the Indian Ocean then phase 2 and phase 3 maybe stronger with stronger convection but the convection moves so in fact David Strauss has shown that if this movement is lower then the three connections are stronger and you can actually imagine it that if you have just a forcing that stays in with the same sign for a very short time and then this reaches to the opposite sign then it will be hard to make a very persistent to get a very persistent response so I think the fact that probably a seasonal mean is not the best period to look for in the North Atlantic the typical time scale is perhaps the one more associated with the MJO if you think about the time scale of one MJO cycle which is about two months and say well in this particular cycle maybe one phase will be stronger one phase will be weaker so you will have a sort of net forcing in one particular direction in fact if you look at the if you do for example an auto correlation function for an MJO index maybe one month a bit more than one month but there are only very few winters for example when it stays of the same sign throughout the winter in fact the strong anomaly that we had in the NAO in 2009-2010 was not because every individual day was particularly strong but it just happened that there were so many days of negative NAO then the seasonal mean turned out to be four standard negative but not because the individual events because it was one of these very rare cases where the system was actually persistent for the whole season usually if you look in shorter periods then you can see something better something better predictability in the tropics because the atmosphere has to be driven more by the ocean with the shuklaz who can have long range predictability just with SST basically in the Pacific you see that and we were discussing with Brian this morning you can still interpret this in a linear framework you say you modified the SST you modified the heat source you have a rosby wave in anomaly I think in the case of a linear it works perfectly well somehow you don't really see you don't really need regimes perhaps to explain the forcing by and so although when you are in a linear case then the fact that you have much more variability you perhaps you may need a concept of change in different regimes for the Atlantic I think SST is one factor but the substantial intracisional variability in this MJO so the source may still be an anomaly in tropical heating but it may not be necessarily associated with a strong SST anomaly it may happen simply because one particular MJO episode may happen to be particularly strong this is still a question of debate so how much the MJO is constrained by SST ok few minutes of freedom