 Sorry for the problem, but anyway, I will talk to you about the weather type It's a work we have done with other people including Andy who is here So I will talk about weather type, which is a tool to diagnose the viability and we will see that it can be used to to progress in the S2S problem So just first general statement So the first one is very important. Of course, that is the atmosphere is chaotic. So We cannot find true analogues because it does not exist by definition The second point is that the B or multimodality of atmosphere is taken It's not yet fully demonstrated Even when we truncate the circulation So we will consider the classification into weather type In an attempt, very modest attempt, to aggregate instantaneous or daily mean atmospheric state into a few clusters And we will use its centroid as some empirical estimate of this cluster So usually the weather type are used using a specially consistent variable which are sea level pressure geopotential 8 in the extra topics and of course it filter out the small scale variability They are usually computed at regional scale But also at zonal scale at least on the extra topics where the weather type approach have been used since a lot of years We can also consider the fact that usually the minimal cycle is filtered out which is nice to enhance the medium scale Variability, but the problem is that it could be an issue especially in the tropics because it could be analyzing between the timescale So first of all it was used in extra typical extra tropical zone So it was used basically as an intermediate scale between the synoptic scale that is the low the traveling transient low pressure system and The annual cycle and we consider the annual cycle will work on the speed of westerly and location intensity of associated barometric center of action So in particular weather type help to define an intermediate timescale Which is associated for example with storm tracks that is the direction and the The moving of low pressure system. So the first attempt was made more than 40 years ago It was called a gross vector lagoon and it was Think of the supervised classification of atmospheric pattern which use the flow of a country so the first try was about the British Isles and The sense of the flow over this small region. So basically It's lead to a lot of different weather type But it alone of course oppresses a regionalization of surface small-scale temperature or rainfall anomaly Then as a weather type have been used as a unsupply supervised technique and there are a lot of technique I will show you an example with camins clustering But basically this classification lead usually to few atmospheric pattern Except for self-organizing map which lead to more weather type Basically for example for north Atlantic we consider that they are four to five weather type in winter In tropical zones the the trying the preliminary work are more recent But we can consider that the first work in the 60s about the flow In the current equatorial latitude is very close to a supervised weather type classification So trying to see if the flow is Cyclonic or trans-equatorial at the equator. It's very close to a weather type classification Of course in the tropics we need to reconsider the choice of the variable because it does not make really sense to take The surface means level pressure of the geopotential eight But we can use either or end the tropospheric wind or divergence and outgoing long-wave radiation or vertical velocity as a proxy of deep convection As in extra topics the weather type filter out the faster and smaller smaller scale Of course because these scales are too scarce to be identified as a single weather type so Any transient and not repotensible pattern will be filtered out by the weather type approach So it could be viewed as different but but a complementary approach of the atmospheric Circulation with a space-time analysis that when we filtered A priori the bandwidth we want to analyze So I will show you a simple very simple toy example To show the links between the statistical cluster and the eventually dynamical attractor and Then I will show you a case study about the Caribbean basin. So it's very preliminary work We will look at the mean property of weather type and we will see that it is a consistent modulation of daily rainfall and Then I will show you two example to see What we can infer from from the vete the weather type occurrence and the sequence of weather type That is perhaps we have more information in the sequence turning the single and stentaneus occurrence Then I will show you an exercise about the potential predictability of weather type occurrence from SST and then I conclude So a very simple example is here. So I create a three variable x y and z during mill unit time thousand time temporal units So I just create a Two basic states that is one or minus one and just I add a certain amount of noise. So you have The system here So basically there are eight possible three dimension attractors so three dimension is defined by the number of variable In the whole phase space here I have just six case Because I did did not define in my sample minus minus plus and plus plus minus case That is I have only I sampled only six attractor in my example So we can try to clusterize these observations is the 1000 observation I have in the in three dimension So I use the k-means dynamical clustering. So it is an iterative technique So we choose randomly seeds then we cluster the observation to these seeds The centroid are Recomputed after after this step and this centroid are considered as seeds for the next step So this is repeated till a convergent criterion about the biasing of the intra cluster distance to the centroid is reached so here I just compute a classifiability index to find the optimal number of cluster So it is the blue line for the observation in my toy example and in black line I have Monte Carlo test with red noise So we can see that there are two peaks which are not really defined for the second one But the first peak it is at two cluster and it is quite Expected because we create a b-model Distribution and then we have another peak at six cluster And it's quite close to what it is expected because I create six attractor in my sample So if I look with the weather type Clustering so here you have the color. It is the six different weather type which are sampled in my example And here it is a definition in the three-dimension space So we can see that the weather type or the cluster are Isolated cluster and they are visible of course, but in that example, of course, we can also consider that we Does not really need Statistical analysis to find the six cluster So you see that there is noise and the noise made the fact that We have some spread around the cluster centroid and if noise is zero, of course You have no noise and the attractor are fixed point in the three-dimension space So if we return to the true atmosphere or the true climate There are some problem to find or to define the attractor at least for three different reasons The first reason is that we have no three-dimension, but we have a huge number of different dimensions the second reason is that the climate system is not forced by Just a be stable a system. It is forced by continuous values forcing which is to continuum of time scale And of course the climate system is chaotic So in chaotic systems attractor are not fixed points. It is more a strange attractor Which have non-integra dimension in the in the case of the Lorentz system, you know, perhaps three three differential equation it is 2.7 We should remind also with three variable model and two discrete states. We have eight possible attractor But if we turn to a more complex system with four variable and three discrete states We have 81 possible attractor So it's very difficult to define the attractor if any in the climate system and clustering is a more modest approach To see the recurrent pattern, but it is perhaps very difficult to find the true attractor if any so I Will show you a case study about the Caribbean basin. So here you have the mean OLR outgoing long wave radiation in the color and Vector as wind in low level in 925 hectopascal and The number here are the wind speed so you can see that we are in a trade regime With a constant trade over the Caribbean and we have the ITCZ At least in summer over the northern bond of South America and also the monsoon in Central America I will show you here the temporal Viability of this grid point which is basically in the trade regime. So it is a wavelet Structure the wavelet transform of the daily outgoing long wave radiation at this point So we can see that there is a continuum of time scale, but there are some peaks Which are more important where the variance is concentrated Basically, it is annual cycle. It is not a big surprise because I didn't filter out the annual cycle And then you have some peaks in the Intrasonal timescale and in shorter timescale here and here you have longer timescale which can be Associated with and so but other process in the Atlantic We focus on the three first year. We can see that of course the main Signal is the annual cycle but then now we can see that there is a strong modulation of the Faster timescale which is more present in summer and you have intermediate timescale between 16 and 30 days mostly at the beginning and the end of the summer So it means that the intracisional timescale is perhaps more important at the beginning and the end of the summer than during the season where the faster timescale which can be associated with Easterly way for example in the core of the rainy season So the previous two slides considered just one point and one variable So of course if you consider the complete atmospheric variability we will have a far larger a number of dimensions, but We have some physical rules that decrease the degree of freedom in the tropics the first rule Which is very important is a well-known relationship between the convergence the vertical Sundance as you see surface temperature So we know that the warmer statistic or respond to low-level convergence and vertical deep convection So it is a process at at least regional scale So it organize the convection and intend to reduce the number degree of freedom so it leads to a very very strong relationship between the thermal deregulation which could be Adelaide cell or Walker cell or Monsoon or Enso and It it works at very large scale larger than one million square kilometer We can also reduce the degree of freedom with some statistical analysis like uf to retain the largest Special scale of atmospheric motion. So I just show you the the wavelet transforms the first leading uf Computer across the Caribbean basin, so we still find of course the very strong influence of the annual cycle And we still find it's very difficult because we have 35 years here, but we still find the modulation of the inter-seasonal Variants very strong at the beginning and at the end and the strong fast variation during the core of the season of course if you look at the 3-dimensional for the three first pcs the three-dimension joint Frequency it's very hard to find Visually at least some concentration, but the weather type will we try to cluster in that amount of data Try to cluster the concentration of points So it it is a classifiability index for my area of Caribbean basin So you can see that a good choice could be a cluster, but I just Indicate here that other people find other other number and I think it's not a real issue because What matter it's really the interpretation of the weather type It is not the number if we accept or if we assume that we are not trying to find The real dimension of the atmospheric variation since I think it's very difficult with the data we have at least So it's a mean annual cycle of the a cluster During the year, so it is just the mean frequency and you can see that on that area The main difference is between winter and summer It's not a big surprise because we know that the annual cycle is the main Forcing of the atmospheric circulation in the tropics or even in the extra topic So it's not a big surprise that when we use unfiltered data. We we found basically the B modality if any between summer and winter and we we have already done this as a size of Indonesia, I will say few words tomorrow in my lecture and We found also the same thing that is the transition between winter and summer is very abrupt and Very well well defined with with with a type So we have three with a type in summer four five six and the other one occur during the winter season That is from late October to late April. So we have a very abrupt Increase of the summer time with a type in early May We can see also that in summer you have a very it's the most exclusive The weather type four which occurred during the mid-summer drought. So we see that we found also the B modality of the rainfall season in the Caribbean that is the first annual peak in May June then a second annual peak in August to October When we look at rainfall indeed we find some some of these Relationship so here it is one thousand a grid point of one degree by one degree from the gpcp rainfall data set So here in in black you have every grid point. It is a mean the means is an al cycle So it's it's quite noisy when when you you look at the median and the upper and Lower, excuse me and upper quartile You can see that for example you you find really a sudden increase of rainfall across all the basin which corresponds to the transition between The winter to the summer with a type and we can see that the Transition from summer to winter with a type is more gradual We can see also some some some decrease relative decrease during the mid-summer drought But of course it is not well defined because we we consider also grid point in the eastern Pacific where there is no mid-summer drought So here are the the weather types and trade So we can see that the the winter with a type so one two three then seven and eight They are mostly differentiated by the axis of the trough we can find on the northern edge of the domain But it can also describe some long-lasting feature as a cold surge in with a type seven In summer basically you have a differentiation between these weather types with a type 4 Which is an increased subsidence very fast Caribbean low level just level jet in the southern of the Caribbean sea So this is basically the normal weather type that is it exists the most of the time in summer and the two weather type 5 and 6 Describe cyclonic feature which can be associated with phase of easterly wave that if you have a Cyclonic phase here on the western Caribbean in weather type 5 and on eastern Caribbean in weather type 6 so with weather type even if it's not really Done for that you can find of course traveling wave, but more you can't you you will take with a type of course more you will Define different snapshot of a traveling wave But even with three weather type in summer we are able to to define some phase of a wave So it is just expressed I anomaly versus the annual cycle before it was a raw data so we can see that Basically the negative anomaly of OLA correspond to Suswark flow when we look in the winter, so it's it's quite expected of course and in summer We can see that the the weather type 4 which is the Anticyclonic with a type with fast Caribbean low level jet We have just an increase of convention here winward on the Panama and Nicaragua with basically an aerographic forcing So the two other weather type 5 and 6 you have a low pressure anomaly here on Western Caribbean and then it is displaced on eastern Caribbean area So if we look at the rainfall fields for this weather type So here it is a raw value in millimeter per day and here it is anomaly daily anomaly in millimeter per day So basically it's a very close association of course between rainfall and OLA anomaly and for example we see in the weather type 4 that the rainfall are Anomalously low over all the Caribbean, but it is Mitigated over the the Florida but also over the island because we we can expect that during these weather types The weather the journal cycle is quite quite strong over the northern part of the Caribbean island But we have an increase of rainfall of course till their winward of the Panama and Nicaragua Well, it is well known for the other weather type We can see the the positive anomaly related with the with the cyclonic parts of the wave I said before a story with a story where wave it could be other wave but it seems that if we if we look at the the combination between the weather type and the the time scale the More important time scale during the summer it could be a story wave One issue with the weather type is that we know that it filters in a data Adaptative way some scale of motion But what is interesting is that we filter also smaller or faster scale as soon as they are Synchronized by the weather type So here I just present you the case of the summer with a type So it is the weather type 4 5 and 6 and the dots are simply the center of the low pressure system So I just compute the low pressure system So you have the number here of low pressure system over the whole period and you can see that for VT the weather type 4 You have almost never Low pressure system in the Caribbean, but then they are mostly Concentrated on the Pacific ITCZ and then on Texas for the V the weather type 5 you have More Relatively more low pressure system because you have more day in weather type 4 that in weather type 5 and you see that They are concentrated on the western part and for weather type 6 You see that you find almost all low pressure system which occur east of 180 80 degrees west you find also some low pressure on the on the east on the west Sorry, but here you have more low pressure system than in the east of the Caribbean area If you turn into the anticyclonic Center Basically, you have also some modulation. It is perhaps more subtle, but you have still some modulation for weather type 4 you have a concentration on a very small area of the Anticyclone the center of the anticyclone and you have more anticyclone than just expected by chance So we can see that the weather type by filtering some special scale and temporal scale allow to Find the recurrent pattern, but of course they help also to synchronize and to to to look at the synchronization of smaller or faster events One important Deal also with weather type is that? About the interpretation so I will present one example about the the transition between summer Winter to summer condition and then to from summer to winter condition because then after I will look at the predictability of these events So here I just compute an onset Which is not based on the onset from rainfall It's just based on the occurrence of the summer weather type versus the weather the winter weather type So I just defined the first day of a five-day spell of either one of the summer weather type without any of them in in five consecutive day in the Following 30 days, so I just you know Define a false onset if you have just a spell and then you have more winter with a weather type I found the mean date on a May 9 and the internal variability is very low It is just eight days So here you have the situation the composite situation before the onset with OLR and wind It's after the onset and here you have the difference and the color in the difference are significant and here you have the same with the rainfall We can see that the onset is basically a V-ring of trades Which takes a sous-soit component of a Caribbean basin You can see here the Anomaly in the wind so you have a decrease of trade and a varying Northward and you have also a very large scale increase of rainfall So it could help to understand that the vetted the weather type transition from winter to summer It is also a sudden transition between Quite dry or relatively drier condition to wetter condition in summer If we look at the the end of the summer So it is the same principle the same rules to define but it is just Reversed but it is the same rules. We can see the difference before the withdrawal 10 days from the withdrawal and here the difference. So here It's not symmetric. It's not a symmetric event Here you have mostly an increase of Anticyclonic condition over the Caribbean basin and we can see that the rainfall decreased But for example for the island the region regional scale withdrawal is not perhaps a good tool to Diagnose the local scale over the island at least and you can see that of course the rainfall increased over the windward side of Panama Nicaragua, which is a specific area in the Caribbean basin when we look at the modulation of weather types, so I I switched to longer time scale So I saw the faster time scale, but then I switched to the predictability issue and the longer time scale So here you have the modulation in frequency of the eight weather type across the year by the and so condition So in red you have the warm and so in blue you have the cold and so event So I define the and so as the anomaly during the boreal winter when usually the and so peaks And then you can see for example in winter the main modulation is between weather type 2 and with the type 8 and it is very close to the association We know before from before from previous analysis between the positive and our Phase during cold and so from January to negative in a warm and so from January in summer we can see that the impact is very large during the ongoing Developing and so we have more with a type 4 during warm and so event and less With a type 5 and with a type 6 so it corroborates the fact that with a type 5 and with a type 6 are perhaps the same phenomena That is they are linked from a physical point of view and they are out of phase with with a type 4 When we zoom on the ongoing summer we can see that during the onset So I just take the mean date of the onset from the regional scale transition We can see that there is no predictability of the onset. So It is an issue of course for the predictability But it says that we can have a quite a large-scale phenomena, but it is not necessarily Predictable that is a spatial coherence is a perquisite for the predictability, but it is not sufficient rule to get predictability We can see that for the law the transition in In winter then The weight of events so is still quite low But then the predictability from and so at least but we will see what that when we use also local SST we have basically the same feature is Peek during the second annual peak of rent for so in that season we can expect quite large predictability and then as before we can see that With a type 5 and with a type 6 act together and they are out of phase with with a type 4 So then we can we can try to look at the predictability of with a type occurrence from SST So I just use a local SST and also the eastern tropical Pacific And I use an index for the equatorial Nino 3.4 in green here. So here you have the mineral cycle of this index So we see that the Caribbean sea is quite warm in means so because we are above 27 degrees in mean But we can see also that the annual silk cycle is very important for example during the summer the north of the bison is warmer than the south and We see also that very close to the onset regional scale onset the eastern Pacific begin to calm to cool down and then it becomes cooler than the Caribbean sea and the Gulf of Mexico so we can Synthetize that by using a logistic regression So it is the same as linear regression except that we are trying to predict Multinomial categories, which are the weather type Instead of continuous value. So here I just present an example where I use these four index to predict the occurrence of the weather type during a running 31 days After okay, so for example, I took the SST from March the end of March end of April And I tried to predict the the weather type occurrence from May 1 to May 31 So it is a real exercise of prediction Here's the skill just for the summer weather type So from the beginning of the mid of April to the mid November where this weather type could occur and Here the color referred to the three summer time weather type So we can see that around the onset the skill basically is close to zero So it's not a big surprise because we saw that any new does not force This season and we can see also that there are two peak two different peak of skill one in July and then a larger one From mid-August to late September so it corresponds basically to the transition between the first annual peak to the mid-summer drought then to the second annual peak of rainfall and we see that at the end So I remind you that the end of the season is is basically in late October you have A slightly better skill than at the beginning, but it's still lower than in summer So what what how can we interpret? this change in the light of the weather type sequence So I show you the example of the onset and the second part of the season so here I show you the map of the local scale onset. So here it is the onset Sound with the daily time scale the rainfall daily time scale So basically I take the first sequence above a certain threshold. It's not very important not followed by dry spell So we can see that the mean is very close in most of the basin Than the mean weather type transition between winter and summer So basically the local scale rainfall onset is tightly fast locked with the transition between winter and summer weather type It is not it is not trivial because we find here We didn't use the local scale rainfall in the definition of the weather type but it is not it is not predictable at least from SST so We can we can make an hypothesis that this spatial coherence is due to an atmospheric process And in fact when we look at the relationship between the monthly SST anomaly and wind speed so I correlate for each grid point here the wind speed with the SST anomaly Okay Here it is the correlation field so blue is negative red is positive and black It is zero correlation So we can see that basically the correlation is better is stronger where when the wind speed leads the SST So in me it means it should mean that during that period the end so is in a very neutral state and The local SST mostly Responds to atmosphere but not force the atmosphere so we can understand why the transition is not Predictable so from where comes the predictability From which time scale and from which process and hypothesis very preliminary because I find I Have done this analysis yesterday, so it's really I need to check but anyway I Look at the at the variance and I do an MSSA That is a space-time analysis to find the oscillation in a field and I found a pair Which is very strong in the boreal spring and which described an oscillation near 15 to 20 days And here you have a composite of this wave So you see that basically it is a traveling wave It's wave-like pattern. It's probably a rosby waves and we have an association between negative OLA anomaly and a sous-souvoir very large scale Susurly excuse me a sous-sourly anomaly over the Caribbean and it seems I compute the conditional probability of the regional scale on set with this phase and you have a 22 case out of 35 in this this and this and it never occur in this one and this one so it means that well it is possible but My hypothesis is that the Regional scale on set that is a transition to summer Will be basically forced by two forcing that is the annual solar forcing which is quite reproducible So it does not lead to a very large internal variability So the annual solar forcing will force a slow warming of the inertia and it's very important We are we are close to a very warm SST So we know that it's very important for the convection and It force also the northward shift of the ITCZ till the north northern Sus America and eastern tropical Pacific so in May the ITCZ shift over tropical Eastern Pacific here so we think that it is a Main contributor that explain why the onset is not very variable On at internal time scale But it needs a trigger and we think that the trigger come from this wave Which is which is of course an intracisional signal, but it is not MGO If we are right, it's not we need to check But if we are right, it is an intracisional signal which come from the middle latitude and This trigger will trigger the increase of Sus early winds and then with a lot of moisture and we are close to a threshold For the convection it will help to trigger the local scale onset But of course in that case the predictability is not does not come from SST So it is not a seasonal predictability. It should be an intracisional predictability When we look at the second part of the season as we saw before we saw that the predictability is better for the weather type. That is we can quite accurately forecast and it's very simple. I took a monthly time scale very very basic But we saw that we we have we have a lot of skill during the second part of the season So I extract here the same Correlation for August So you see that here in August you have almost the same intensity correlation when the wind leaves and when the SST leaves so basically it indicates that It is a season where the earthy coupling at least locally work That is when we increase the winds we cool down the sea here Because you have a stronger wind speed So you have more heat flux from the sea and you have a stronger Upholding here along the North-South America coast but also also when you are you cool or you warm you but if you cool the sea you increase the northward Sea surface temperature gradient and you increase the zonal sea surface temperature gradient with the eastern Pacific so basically As soon as the summer is on especially during the second part you gain some Predictability from SST, but it is not trivial that is it is not always The beginning basically you have no predictability from the sea and you need to to find source in the atmosphere But then after you can use at least if you use of course Ocean plus atmosphere you you will increase the skill we can expect that but at least you have some seasonal predictability at the end of the of the summer So there are a lot of work to do still but The next step is to to use the occurrence between the weather type 5 and 6 which are the cyclonic weather type with the the easterly wave because of course when you look In the MSSA in summer you have a major oscillation Which could be linked with the easterly wave. So it is just to show you that weather type. It is not just a tool fixed on a specific bandwidth It is a very flexible tool to find a Lot of things and to find a lot of source of predictability in the atmospheric motion So just to to conclude so basically We are not trying to find the dynamical attractor. I think that Some other work on that but I think that to find dynamical attractor. We need a lot more than The year we have available perhaps it is possible in a reduced system or in Simulation but I think personally but it's personal view that it's very difficult with just observation So it is more modest when we we try to look at weather type It is just to emphasize a larger scale So we can use a preprocessing US, but it's not needed It's just for computation issue, but it does not change if you preprocess or not It does not change the result and you will reduce a transient and a principle feature So it's very complementary to the to the usual Approach of the inter-seasonal variability or subsseasonal variability that when we we we filter up Priory a bandwidth and we analyze this bandwidth. So it's quite complementary to this approach So basically as I said the the sole parameter which is important is not important That is when we are trying to look at the optimal number I think that there is no optimal number. It is just a matter of Interpretation but not a real problem because we are not looking Really at dynamical attractor. We are just trying to simplify the complex variability and other people here Found in a very recent studies so on the same area. It was quite funny because we publish almost at the same time and I didn't know them and Basically, they analyze other variable And they found other number, but basically the interpretation are the same as us So I think that the problem we can discuss a lot about this issue as Usually about a statistical test and so on But I think it's not a real issue because the problem is to interpret and to see what is going on but not to to try to find an hypothetical dimension which We make no sense from my point of view at this scale and with the data we have The second point is that the weather type are very efficient because they didn't really Filter In a user Adaptative way the scale it is a data Adaptative filter, so I think it's better and even the shorter time scale Are found with this approach as we saw about the cyclonic and anti-cyclonic pole We find it with the weather type. We find the recurrent synchronization of this Faster feature than with a type So it's a Caribbean basin the main station is between winter time and summer time and we found the same result of Indonesia the work with with Andy But other as we will see tomorrow in the lecture about the local scale prediction I will use the example of Indonesia. We'll see that for Indonesia. The onset is Basically the most important and the most predictable component of the season but in the Caribbean It is not the same so winter weather type basically the axis of traveling trough on the extra typical edge So if you fight if you take more cluster, of course, you will cut More efficiently the wave, but basically it is waves we found also long-lasting a cold search that is a longer event of For example with a type 7 The summer with a type it is mostly an opposition between a trade regime with a with a type 4 with fast Caribbean low-level jet regional scale subsidence of the whole Caribbean basin and strong and sometimes over the eastern Pacific ITCZ and two cyclonic regime which basically are different snapshot of wave and basically it seems to be really Connected to Asteroid wave The weather type 4 is a small exclusive during the Midsummer drought so we found one day Is a sample where it's always With a type 4 it is the 29 of July So it means that during that period the Caribbean should be in an almost stable mode that is and we can think that it is mainly forced by the annual solar forcing and The the weather type 5 and 6 basically it is a perturbation of these of this mode So the predictability is very weak on the early stage of summer condition it increase to our design with a transient decrease it remains to understand why we have these double peak of predictability from sST The onset it seems that we have the combination of two Different forcing the analysis of solar radiation and stochastic forcing associated with the wave and Basically, this wave is mostly of extra-topical origin not it is not the MGO Origin so we understand we can understand that in that case whether The onset is quite a large-scale phenomena, but it is not predictable from sST that is We should be limited to a Medium-scale predictability from the atmosphere During the second season the predictability seems to peak so we could Enphasize one hypothesis, but of course perhaps there are many features which are combined, but Basically, we we make the hypothesis that the ocean atmosphere coupling locally Is is triggered by the fact that you have a local scale In the sous-saint Caribbean sea a local scale positive feedback between the wind speed and the The the temperature of the sea that is if you increase the speed The sST anomaly become cooler and a cool sST anomaly leads to a stronger Caribbean low-level jet and of course during the late part of the summer and so could be both More important than at the beginning of the season because it increased in power during this period. So basically This case today we studied the ability of weather type to to encapsulate different phenomena, which are not filtered a priori, but which are filtered in fact by the weather type themselves but also by the sequence of weather type that it is not just a matter of occurrence But it is also a matter of sequence of weather type and it leads to to the idea that perhaps we can gain some Information not only by using fixed time period, but also scenario between different pattern of circulation and I will use also this this approach tomorrow in my talk about Indonesia So here are the few paper you can you can look at if you if you want More details Thank you