 ..mwneud i'r hanfodd.. ..fyddiw'r hanfodd.. ..eg ydym yn.. ..a chyfodd.. ..ynghyd o'r byd. Mae'n gwneud hynny, mae'n gwneud. Mae ddod. Mae'r postig ar y ddechrau ysgol. Mae'n meddwl i'r Martin.. ..y'r ben Havi.. ..y'r interacio'r trawg ysgol. Mae'n gwneud ar gael nifer. sydd ydy'r cyffredin niwedodd cychwyn cymgylcheddol ar y sgwrnum, y odd yn hynny mae unig gael yng nghylch gyflwyno yn gyllewyr. Mae'r ffairfyniol. Felly rydym yn cymryd hynny yma. Mae hynny'n mi'n galwion yn ynghylch beth oedd hynny oherwydd gweithio. Mae ydych yn cyffredin ni'n ei fawr o holl yn ymdavol. Yn mynd i'r cyffredin ni'n bysgr siw, Felly, y ffordd yma ymlaen i'r ffordd y ffwrdd ar gyfer y bwysig yw'r ffordd ystod yw'r ffordd ac yw'r ffordd yw'r ffordd a'r ffordd yw'r ffordd yw'r ffordd yw'r ffordd. Mae un ffordd yw'r ffordd yn ychydigol. Felly, yn y ffordd, y ffordd yw'r ffordd, yw'r marwau, yw'r ffordd, yn ysgrifwyd â'r cydnall, a'r cydnall a'r cydnall. Mae gynhyrch yn ennill yn ei ddweud. Felly mae'r plod yna o'r Laman etal, pethau i'r ffordd mlynedd yma yn y ffodol 5 Cymru yn ychydig genedlach. so how strong our storms are. And in the black contours is the climatology and the shading, the cold shading is the response in the future. And what you can see from this plot is that the storm tracks on average are supposed to shift forward and also in longitude, for example, the North Atlantic is predicted to be more extended over Europe. Yn y ffordd, mae'r ffordd yn ddod o'r moddol yn ychydigol, a'r ddod o'r ffordd yn ddod o'r moddol, ddod o'r moddol yn ddod o'r moddol yn ychydigol, rydyn ni'n gweithio'r ffair hwnnw. Mae'r unrhyw ffordd yn ymddiad o'r ffordd yn ddod o'r ddod o'r ddod o'r ddod o'r ddod o'r dynamos. Yn nghymru sy'n ddod o'r ddod o'r ffordd yn ychydigol, drwy'n gweithio'r ddod o'r ddod o'r ddod o'r gweithio rydyn ni, miliwn ddod o'r ffordd yn gweithio'r ddod o'r ddod o'r ddod o'r ffordd yn ddod, yna gallu cydcast. Yn y ffordd, mae'n rhaid o'n gwleidio'n cyfnodd y byddai'n gweithio i ychydigol yn y stryd o'r ddod o'r ddod o'r ddod o'r ddod o'r hwyl tyfnol. So we chose a non-linear oscillator model that Martin presented this morning. Which basically describes the interaction between the storms within the storm truck and the large-scale flow. I won't go into the details of the model since Martin described it quite nicely this morning. But basically this model is a two dimensional model, so we have S is the large scale flow of thermal wind, baroconicity, whatever you like to call it. And that's forced by say thermal forcing and decreased by some eddy activity. And then we have another equation that describes the eddy activity change and that's forced by this interaction between the growth rate times the heat flux and it's dumped linearly in this case. So this system has two types of forcing if you like. There's the forcing of the baroconicity which provides the energy into the system and there's the dissipation of the energy which is via the eddies. And this is an oscillator as we saw this morning and just to remind you that you can plot this in a kind of phase space for a different amplitude of these oscillations. And if you were to look at time series of the North Atlantic and average them in this phase space then you get a nice agreement with the model. So great, so we've got a simple model that describes the very basic dynamics involved within storm tracks and we managed to recover this behaviour, at least on average, in the observed data. And this actually works in idealised models and in the Pacific. So this circulation seems to be a general property of the system. And so okay, so we've got this hypothesis that in the time, so we can use this model to look at the time mean behaviour of the storm tracks, as Martin mentioned this morning. And this model predicts that the eddies will respond to the forcing of the mean flow, not the forcing of the eddies. And the mean flow, the baroconicity will respond to the forcing of the eddies, not the forcing of the baroconicity. So this may seem to be quite intuitive because, like I said, if you imagine our system you've got a forcing of the mean flow, of the large scale flow, sorry. And this interaction with the baroconic eddies and you force this bit and you don't get a response in this bit, you get a response in this bit and vice versa. So okay, it's actually not a surprise that this side of the mechanism is the case, or is predicted to be the case, because in the atmosphere it has been observed in models and also to some excellent observations. And this is a process called baroconic adjustment and it's based on this idea where if you try to force your storm tracks or the baroconicity, so if you try to increase the temperature gradients, then yes, instantaneously the baroconicity may respond, but that then gives rise to activity in the eddies which will then start eroding the temperature gradients and so the baroconicity will be maintained at some critical level by the eddies. So no matter how much you try to force the baroconicity, the eddies are the ones that respond. And there's this idea of eddie saturation which is pretty much the same idea, but it's, that's a term used in oceanography. And so there's this other side of the predictions which is about friction, so if you dissipate eddies you should be changing the growth rate of eddies, so the baroconicity rather than the actual eddies themselves. So this relationship is difficult to test in observations because you have a limited time series and diagnosing the response to friction and thermal forcing may not give you very robust signal. And so we decided to look at this mechanism using a hierarchy of models. And so usually when people talk about hierarchy of models, they think about the numerical complexity of models. So you might have, for example, the difference between speedy and the open IFS. Speedy has eight vertical levels, it has some simple parameterizations, and the open IFS has more sophisticated parameterizations, more vertical levels. So people usually think about if you were to set these models in the most realistic setting as you can, how realistic is the output. But in fact you could use these complex models in a simplified setting as well. So there's two types of complexity and we are using these types of complexity to develop an understanding of this, of this relationship within the storm tracks. And hopefully you'll agree with me that this is quite an efficient way of doing it because what you could do is to take speedy and just run it as an aqua planet model with no storm tracks, nothing, and see what it looks like. Then add a rectangular force heating like Paola was presenting, then add continents, and then look at the output. And then you could move to the next complexity of models, so say the open IFS, and do the same thing. But this takes a lot of time and a lot of computing power and storage. And so it's actually quite useful to move along this line, so if you go from the very, very simple models at, then when you move to a more complex model such as, let's actually do this, such as a Heldense or S, I don't know if you know this. Well, let's just say speedy because you're familiar with speedy. So if you move to speedy, then you're not only increasing the complexity of the model but also the complexity of your setup. And then if that doesn't work, then you can go back to your simpler model and move in this direction. But there's no point in moving in this direction and increasing the setup to the very, very complex setting and then, you know, filling out the matrix one by one. So, yes, so we're using this hierarchy of models and we're using, we have our simple non-linear oscillate model, which I'm calling the AN model. I don't know it. And so we've been testing this relationship in a model that's based on thermal relaxation and Rayleigh friction. And this just means that your forcings are very, well, very, very simple and there is no moisture. And so, yeah, so that's the next step. The next step will be speedy, which has, for example, moisture and is more, for example, has the radiative scheme and convective scheme. And then the open IFS, which is even more complex. And then we can have a look at the same five models later. So today I will talk to you about, so this is still work in progress. So first of all, let's have a look at the PIMA work. So we have a model that's, oops, it's quite a cost resolution. So PIMA is a dry dynamical core of the reading IGCM, or it's based on that. And it's forcing, it's diabetic forcing. It's parameterised in quite a simple way. It's about relaxation of the temperature, linear relaxation of the temperature towards some kind of a field that you define relaxation field. And then there's some hyper diffusion, which you don't have to worry about for now. And then there's the friction. This is divergence and vorticity. So they're both dumped linearly as well. And the time scale by which you dump these two variables, you can divide into the mean and eddie. And because we want to test the dissipation of eddies, which is what's the simple model is predicting that the baroclinicity should be dependent on. Then we're only changing the time scale of the eddies. So we're leaving the friction of the mean flow as it is. And so as you might imagine, if you apply these, so if you apply these forcings globally, then this relationship absolutely does not work. So, and the reason for that is that in the tropics, you get a response in the static stability. And so this is just an example. So if you increase the eddie friction by a factor of two, then you get this tripolar structure in the static stability. And similarly, if you increase the polar equator gradient in the, well, if you try to force the polar equator gradient, then you will get an increase in the static stability in the tropical region. So this, and this is the reason why the Hadley cell is the most dominant response of our model. So this is showing the stream function, meridino stream function, and the anomaly is in the colours. So the Hadley cell strengthens as you increase the eddie friction and also as you increase the thermal forcing. And this is not really what we want because if we go back to our very, very simple model, then that doesn't care about Hadley cells or any spatial variations. And so what you have to do is to try to separate the, by having this hierarchy, you get a perspective of what you need to change in your model. So you need to isolate the forcing of Puma only to the extra tropics. So we did this by applying a weighting function for both the thermal and frictional forcing so that only the extra tropical regions were affected. And what that did in terms of the friction. So this is again the example where you increase the friction by a factor of two. So the colours are the response. So the isolation of the forcing to the extra tropics only, you will get this tropical response in static stability is gone. So that's good. And that's associated with a very different response in the Hadley cell, which doesn't seem to respond at all anymore. And the main response is in the storm track regions in the mid-latitudes. That's good. And in terms of the thermal forcing, if you again isolate this thermal forcing to the extra tropics and the polar regions, then the static stability response seems to just, and the tropics seems to disappear, which is quite good. And again, that's associated with a very different response in the global circulation. So the Hadley cell is again unaffected. And that's great. You've seen this plot this morning, because having isolated the forcing to the mechanisms that you are interested in, has now made a very, very simple model, has justified a simple model in the GCM. So the model predictions have been true, at least in this simplified setting. So great. So really, as you increase the Hadley dissipation, it's the baroclinicity that responds, and not the Haddys, whereas as you increase the thermal forcing, which is supposed to force the baroclinicity, it's not the baroclinicity that responds, it's the Haddys. And okay. So by having this hierarchy of models, we were able to kind of revise our experiment and go back and improve it so that we could test this mechanism in a more reasonable way. And so the next step is to look at speedy, which the setup was introduced by Paolo this morning. So it's basically a heating triangle in the mid-latitudes, which produces a localized storm track. You can look at the storm track in terms of the heat fluxes. So the reason why we chose this setup, actually, is because it produces a really nice tilt in the jet, and these models, these aqua-planet models, are quite known to produce very zonal storm tracks. So having a tilt was quite special. And so, yeah, here you can see the, in the colours, the low-level wind is really tilted. And if you look at an animation of this, you can see it nicely flips about just like it does in the North Atlantic. So, and in time, Martin showed this morning that the speedy seems to emulate the behaviour in the North Atlantic, and in the very, very simple model quite well. So, OK, that's good news. So we wanted to use this setup, since it works so nicely in the time-varying picture, we wanted to see if, in the kind of time-mean picture, it also works. And so, on the right here, is the speedy, is the speedy experiments compared to the Pima experiments. And the model runs are still quite limited. We, like I say, it's still work in progress. But you can see that there are, apart from this annoying red line, there is some hope, I think. There is some hope that these patterns will be similar to these patterns. Having said that, if you look at the speedy response, if you look at the spatial maps of the response, they are a lot more complicated. There's more complex, especially around the triangle. There seems to be perhaps unrealistic structures when you force it with the friction. So that's kind of a problem. So I went back to Pima and tried this triangle experiment in the simpler model. And I get the same structures. So now I'm trying to design a different forcing, create a different storm track, if you like, using a heating dipole instead of the triangle, to see if these unrealistic features can be eliminated from the model runs. So this is where we are so far. And the plan is to, when we have a good speedy result, then we want to move to the open IFS. And the open IFS has a more realistic planetary boundary layer. And so we wanted to see how these kind of, you could say, simple ideas, how they apply to the very complex and smaller scale circulation features. And yeah, and eventually we will look at climate models. And this is, like I say, this hierarchy of models is a real time saver because you don't have to do all the experiments in each, all the experiments in complexity in each individual model. So, yeah. So do I have time still? I don't know what time this is. Can I just go over the conclusions? Is it time? So we found a relationship in a very simple kind of conceptual, even model, which shows that if you force the baroclinicity, you get a response in the edis. And if you force the edis, you get a response in the baroclinicity. It did not, at first it did not seem plausible, but A, there seems to be quite a bit on the literature, in the literature on the baroclinic adjustment area, on the baroclinic adjustment idea. And then we looked at it in the model and it seems to work. And it's not just a model property because we tried different types of models and we tried different complexities of models. And this is a very good approach to kind of, if you can't look at this in observations, in long time series of climate models, then using this hierarchy is very good and efficient way of being able to tell whether this is a property of the system. And our next step is to look at this dipole storm track in Speedy and also look at the open IFS for more realistic features of the forcings. Thank you.