 Next speaker is going to be Matt Newman. Matt is a senior research scientist and he's part of the atmosphere ocean processes team and he will be talking about was the February 2021 cold air outbreak over the central united states a sub-seasonal forecast of opportunity. Okay is that uh is that showing? Yeah it's perfect. It's not yet full screen I think. I see a bar on the right but it's big and readable. That's weird yeah I don't know why it seems to be full screen here. Oh yeah now it is. All right uh so this is work that I've been doing uh with John Albers excuse me and Sam Willow here uh and uh this is related to a couple of questions that we've been particularly interested in uh people remember my lecture the there were things I was focused on there too uh first can we identify high school uh S2S forecasts ahead of time given that on average the scale is very low it's really probably too low on average to be used in many circumstances but clearly the case to case events can be skillful. If we can do that can we in particular identify the dynamical processes responsible for these high school forecasts so that we have some confidence in where that uh prediction of high school is coming from and the example I'll use here is for NAO and finally to to uh focus on a single event was the recent cold air outbreak in central us one of these potentially high-skill forecasts so the way we do this is with something called the linear inverse model or limb where we are basically representing the system in a fairly simple way a linearly predictable portion and a stochastic unpredictable part and we're able to separate variability into these two components under our coarse grain assumption where we're basically observing and assuming that the non-linearities are fast in the system so that they're unpredictable compared to the linear predictable dynamics which are typically on a slower timescale and and that's particularly a good uh approximation for S2S timescales because what we're doing is we're not predicting individual weather events which are unpredictable beyond about two weeks but rather the aggregates of those events in a system like this anomalies can still grow and evolve through non-orthogonal eigenmode destructive to constructive interference even though all the individual eigenmodes of this linear operator here are stable and we can get this empirically that's kind of the main idea here although one could in principle do this uh in a forward sense from first principle so in this system uh forecasts are pretty simple you just solve this equation the ensemble mean uh forecast is written down simply uh then your probabilistic forecast or categorical forecast come about because the ensemble mean is undergoing some mean shift so basically the skill is entirely coming about from this predictable component and the pdf forecast are likewise entirely uh from that just shifted left or right depending on the mean signal so that immediately implies that we can use a forecast signal and noise ratio in a system like this to identify the forecast that we expect ahead of time to have high uh scale we in other words were calculating at the time of forecast it's still uh state dependent but it's not a non-linear state dependence it's an entirely linear process and uh it's obviously going to be dependent upon the forecast lead time so these are the two hind casts and forecast data sets that I'm going to be going through uh we have a limb that was trained over this period of time and we're looking at hind casts for winter time 97 2016 we're using seven-day running mean jra data listed here on the right uh and to make the forecast skill uh quasi independent we use that tenfold cross validation and we're comparing it to the eci ifs operational in 2017 which we obtained from the s2s data set and that was mean bias corrected that skill comparison for the globe has been published earlier but today we're just going to look at the nao and then we'll also look at real time forecast for the cold air outbreak event in this case we're going to be using a real time limb that's currently being transitioned to cpc it's it's running there currently which is basically the same as this limb or this limb here except we're also including north american two meter air temperature because that's what we're trying to predict and that's been running since about december of last year and then we're comparing that to a more recent version of the ifs uh so that we can get the real time uh forecasts for this period from that as well okay so first just looking at the nao uh here is uh a way of of identifying high versus low skill forecasts ahead of time we use the limb signal noise ratio and we stratify both the limb scale the limb forecasts and the nao forecasts by whether we expect them to be high skill or low skill so we're taking the top 15 percent of expected high skill forecasts and that shown is the solid line we're showing the skill of those forecasts and the dotted line shows the skill the remaining forecasts and we can see that in both these cases the limb is picking out the weeks three four five and six a high skill of the ifs and of itself it's able to identify that pretty cleanly and separate it from the lower skill of forecasts which we don't expect to be as skillful so again this is kind of immediately suggesting that at least in this case the extent to which the limb is not just predicting its own skill but also predicting the ifs skill uh suggests that that the skill is coming uh even in the ifs is coming primarily from shifts of the mean uh the ensemble mean not so much from changes in spread and skill in fact we've checked out a little bit uh for the pacific in particular and there's no obvious spread skill relationship in the ifs or obviously in the limb now we want to do is we want to diagnose where this high skill is coming from so we dig a little deeper into the dynamics of the limb we can do an eigen analysis of that limb forecast operator and look at the different eigen modes that essentially represent how different aspects of dynamics evolve uh over time and this uh plot here is just showing all the eigen values of all these modes so there's basically as one can see kind of two separate fairly nicely separate categories and we use that to do some diagnosis here we have a group of modes in blue which have typically long e-folding times so these eigen modes tend to decay on time scales longer than about a month and they typically are low frequency or even stationary modes all these modes it turns out have a large contribution from sst and stratospheric component of the limb state vector they have the other aspects as well but but they're notable because sst and stratosphere is more important in these modes whereas the remaining modes do not enlarge they have short e-folding times they have no sst component uh interestingly the mjo is in here as well which has been a common common thread in a lot of work in the past a lot of limb analysis in the past and i should notice there's also and i'll bring this up there's one there is one eigen mode which interestingly is purely stratospheric it has no sst component so what do these look like what is this stratosphere sst subspace the slower uh subspace look like this is a bit of an illustration we take a composite uh and uh of the NAM index at 10 millibars and then we look at what that composite looks like here's the typical cross section there's kind of Baldwin and Dunkerton sort of kind of quasi-dripping paint plot and one sees in fact something which is is almost entirely that downward propagating stratospheric eigen mode so that that process the that descent from the stratosphere the troposphere can be is in fact represented by just a single eigen mode at the surface it has a predominantly atlantic sea level pressure signature and like i said before there's no sst associated with that on the other hand if we do the same thing but do a composite lower down at 300 millibars we find a structure which is much more of a blend although there's some of this downward propagating component it's it's not so important as other modes which represent an sst signal more of a a projection on kind of the nonical canonical non canonical and so more of a central pacific anomaly and the nao structure is much more uh annular like and in fact what we find is that the the week three six high scale forecasts are almost entirely within this joint stratosphere sst subspace again remind you the black line is the ifs high expected scale and the orange line is the limb high expected scale so we repeated the analysis by only using the initial conditions in the stratosphere sst subspace as opposed to the remainder and almost all this scale is coming about because of that subspace so that's essentially the predictable part of the system and that means that the more that an initial condition tends to project in this stratosphere sst joint subspace a set of eigen modes the more the larger a predictable signal it'll have and therefore potentially higher scale so let's look at a particular case then we'll look at the at this february 2021 cold air outbreak this is the two week temperature anomaly it was really impressive obviously a lot of records were set particularly in northern texas had a very large societal impact and they're still fighting over it in texas i understand because the power outages and so the question we have basically is is how well did the the limb expect this could be predictable and what might have contributed to that potential forecast scale so this is what the cpc official weeks three four forecast was they do a forecast just two category they're looking for probability above or below the median temperature they weren't particularly confident for their forecast in general 55 is is pretty low although their typical probabilities are not a lot higher but clearly they were going for warmth in a broad part of the us and that was in a unreasonable forecast that's basically what all the the numerical models were showing here's the the ifs for that period very strong warming throughout most of the eastern two-thirds of the country for this period of time and in fact the cfs and the jma which are two other models cpc looks at a lot they basically were pretty similar the limb had something pretty different it was going for pretty pronounced cooling in this region and in fact had very high probabilities particularly for week four so we were getting up to 75 probability and a week later the week three probabilities we were we were in the 80s which was very high very confident for the limb and I should point out that the limb is is a reliable forecast system so that 80% basically means 80% all right so where is the limb uh getting its forecast from primarily it's getting it from from this sst stratosphere subspace and it turns out without getting into a lot of the other details this is basically from linemia uh that was occurring at this time and we had obviously very pronounced linemia and so it's picking out this very strong cooling there's a small weak mjo component and a a piece of in the stratospheric mode remember there was a sudden warming early in january and so we were still in february more at the at the tail end of that event notice by the way that these amplitudes here are double this so these are even weaker relative to this than just the colors make it look internal space obviously there's not much again we're not really expecting there to be much predictability on week three and four in the internal subspace but of course there can be a large amplitude just because we can't it's we can't predict it doesn't mean it's not there and in fact we saw that but importantly in terms of the verification we also picked up this very strong uh uh topically forced linemia signal linemia sst stratosphere subspace signal um there was a bit stronger mjo than we had predicted and pretty close uh in terms of the stratospheric mode again remember this is these amplitudes here are half of that okay so just to conclude then uh the limb can predict at the time of forecast which forecast will be skillful so it's able to identify about the the top 15 percent of high scale uh nao forecast in other words uh forecast skill that one might think would be actually usable on these weeks three and four time scales both of the limb and in the i f s and then we we can use the limb to decompose uh all anomalies into these two independent but importantly non-orthogonal uh eigenspaces uh subspaces which we can use to understand where the forecast of opportunity are coming from there's an internal subspace which dominates most of the variability again it's important to remember that most variability a weeks three and four time scale is not predictable uh on these uh time scales it's a it's this smaller subspace contained within this set of eigen modes which we've labeled this joint stratosphere sst subspace which basically consists of this downward propagating stratospheric eigen mode which has more of an Atlantic surface signature and then a group of eigen modes with joint stratosphere and sst components essentially a lot of this stratospheric component is what you might expect if you're getting wave propagation coming out of the tropics obviously as you as you're when you're 300 millibars in in the high latitudes you're you're in stratosphere so in the context of of the uh the definition that counts as a stratosphere component and then finally uh the north american uh cold air outbreak of february 2020 was clearly predictable well in advance on s2s time scale so predicting it four weeks ahead was uh was clearly clearly possible coming primarily uh from this la niña uh signal and i'll just conclude there thank you very much for the nice talk i'm always amazed um how skillful these limbs are if met designs them um the first question goes to uh arum hey thanks man for the talk and nice analysis uh maybe maybe this is a strange question so you showed that uh the limb skill is uh about the same as ifs one of the slides or for the for the nao yeah it's uh yeah yeah this one so given the these plots and all the models were predicting about normal anomalies what would make a forecaster discount the normal base forecast and go with the length uh are you mean in this case yeah yeah well they didn't in fact they went with no they did not but they should have but what what argument they have to follow i think i think uh you know we're we're trying to this has been a really uh interesting question for us trying to get a sense of what are the best uh guidance tools that we can give the forecasters right now it's one thing to just to just do this for working with cpc which is what we've been doing over the last year has taught us a lot about how people make the forecast and and one of the things that's become clear is precisely that we want to do more of this sort of diagnosis so that they have this in real time and we can say to them look the reason why we have uh strong cooling is coming from this la niña signal you know and we can show i mean potentially you can show the whole evolution of that that would be a bit much in real time but i think with time as they gain uh experience in using the tool and in a way use is the only way that a forecaster right right in the forecast that i have access to 10 different tools and five six of them which are marble based are predicting warm it is very hard for them to go out on the limb and take the something which is not not confirming with the model based forecast so anyway you know the problem yeah yeah no i agree completely whether so the week after this we were we were going cold even more strongly i mean i i there's very high probabilities and the models were going more along the same lines so what we were able to do was essentially to say to the forecaster at the time you can be more confident so they the forecaster was going cold for essentially a week three forecast but not going as strong as as the limb was saying and so we said well you can be more confident and he did take it into account which was nice that was kind of the high point for us so far i mean like i said it's a learning experience for us trying to see how how these tools are used in in real time as opposed to looking at hind casts and you know and and kind of working out diagnostics right thank you thanks so much i i have a comment and a question i i'm always what i really like about limbs is that you can decompose that in these different modes and i think you've shown a beautiful example for this year um you might have said this but i haven't fully understood it yet is there a way to decompose the ssd stratosphere modes into two modes i know it's there's a sad i it's you know after a while it gets overwhelming right i mean i'm going to sit here and show you every mode it just becomes a bit much and again these are non-orthogonal so a lot of times what's happening is you're having a couple modes that may all be kicked by noise in a particular configuration and they're evolving differently and it's the the sub the entire space that's evolving that matters um but yeah in principle we could have focused on you know any other other modes if we wanted to do that thank you what where was going is is it possible to decouple the ssd influence from the stratospheric influence in the coupled mode yeah uh i mean we've done that things like that in other contexts we haven't done that here yet but in principle it is yeah how much anish has a question yeah thanks matt yeah this is really interesting and there are lots to think about in terms of um predicting predictability and how users can use it and so my question is related to predicting predictability or predicting prediction scale from each of these modes like do we know if like from like climatology or historical forecast which modes picked up by limb like contribute more to skill and so the users can trust it more when that signal is coming up like when you decompose it into different components right that if the and so the lani near signal is strong in the limb then if that is a mode that is historically a mode that contributes to high skill in this framework and the users can trust it more whereas if it's if it's other modes then well i mean to some extent that's what this is here right basically we're saying is if the initial condition had a very high projection on this and almost no projection on that then we would say that uh we don't expect the forecast to be skillful right probably won't produce a large amplitude anyway but but uh you know the temptation would be to look at the model and say well maybe if a model had a higher amplitude that was because the ensemble was enlarged enough it didn't have enough to kind of average out to something closer to zero right or the model could happen if the limb doesn't have but in the context of the limb that's that's the difference i i get nervous about i mean i i think it's really interesting when you get one eigen mode that really looks physical because it says to me it says that that that really is a modal structure you know mode gets tossed around in our field you know all the time to mean a lot of different things and it's not really very rigorous there aren't very many modes of the system in a physical dynamical sense but it really to me it really does seem like this is in eigen mode of the system there's something physical about it you know you hit the system in a certain way you can just you're ringing a bell and you you get this eigen mode propagated there's the kind of a four-yearish and so eigen mode is is another one that you see like that there's an mjo eigen mode that comes out of a limb that seems to be robust but then other than that you know everything else is these other modes that are that are non-orthogonal because they're non-orthogonal they can cover up you know those kind of ringing modes those real eigen modes in different ways and you can get different evolution as a result and it's hard to just look at a particular eigen mode and say okay well that eigen mode is going to give me something because what really matters is how it combines with all these other eigen modes and again that's kind of that's the fundamental aspect of these non-normal systems is you can't you can't partition variability you can't partition predictability in terms of these kind of individual modes as well. Marty is there a signal of noise that's basically a function of the amplitude predicted amplitude right? Yeah yeah and and in the limb it's it's all signal noise now you know you can get more sophisticated you could in principle have a linear state dependence of the noise that would still give you linear predictability that's kind of another long story but that's hard to extract out of data you need a lot more data now you have to look at the at higher moments in order to pull that out and you can get some non-gasian behavior but it's still everything's linearly predictable but now there there can be some variation of the noise but we were kind of struck when we looked at least at the IFS and compared it to the limb in our 2019 paper that yeah it was very hard you know there's you could see a little bit of a signal spread scale relationship but it was really weak and it was really just at the extremes. Thanks. Thanks very much Matt so this concludes today's workshop thanks so much for staying around sorry we ran a little over and we're looking forward to tomorrow we're among some fantastic lectures we will hear from the students so thank you very much everyone and have a good afternoon. Thank you.