 We'll have the second lecture for the day. Professor Eric Maloney from Colorado State University will present this. Eric has made highly influential contributions on various topics related to tropical meteorology observations, modeling, and theoretical studies of interseasonal variability in the tropics, easterly waves, including a lot of work on NGO theory. So there's some of them that Chidong just cited. Eric has also worked on mid-latitude air-sea interaction, regional climate change, tropical and extra-tropical interactions. And today's lecture will be on the MGO teleconnections. Eric was the former chair for the Whitney MGO task force and the NOVA map model diagnostics task force. And yeah, Eric has been involved in many field campaigns as well, such as Dynamo, the years of maritime continent and Otrec, a recent field campaign in the East Pacific. Thanks again, Eric, for giving our lecture. OK, let me try to share my screen here. Can you see my screen? Yes. OK, good. Let me put this into presentation mode. Thank you very much for the invitation to present at this prestigious colloquial omination. I really enjoy giving talks and meeting all the students and postdocs at these sorts of events. And I was actually an ASP postdoc back in 2000 to 2002. And really enjoyed meeting all of the researchers across the country and world at events like this. So thank you again. So as Anish mentioned, I am going to talk about tropical meteorology and teleconnections during my talk here. I'm going to talk a bit more generally about teleconnections, but a lot of my discussion here is actually going to relate to the MJO as the MJO is a major player in S2S prediction across the globe. So just to point out here, I'm going to cite a lot of references here in this presentation. And I wanted to note right before I started that all of the references that I mentioned are actually included on this page right at the beginning. And so if you see a paper that I cite, then you want to go back and take a look at it. It's contained within this reference list here. So this is part of the presentation just for your reference later on if you want to look at something. OK, so what is the problem that we want to look at? And so basically what we want to look at here is the issue of if you have a precipitation anomaly and heating anomaly in the tropical Pacific or Indian Ocean, how does that influence the middle attitude flow? And this is a pattern here that we might call a teleconnection. This is from a famous paper by Harrell and Wallace in 1981. And this is, for example, an El Nino heating anomaly in the central Pacific. And what you could see in this particular figure is that this El Nino heating anomaly induces a wave-train pattern, as we call it, into the higher latitudes consisting of alternating high, low, high, and low geopotential height anomaly centers into the region over North America. This stationary wave pattern, as many people have alluded to before, can have substantial impacts on weather across the mid-latitudes. If I have time, I'll talk about some of these teleconnection effects on things like atmospheric rivers, droughts, heat waves, cold outbreaks, things like that. But this is the basic topic that we're going to cover in this lecture. How does this particular heating anomaly produce a teleconnection pattern like this? And as I mentioned, the MJO is going to be a major source of this heating. What kind of heating can produce teleconnection patterns? These can actually occur on a variety of time scales. We're going to talk a lot about the MJO here, as Qi Dong mentioned and introduced very nicely in his previous talk. This is a composite lifecycle of the MJO produced by Adrian Matthews, where you can see the MJO ticking through each of its eight phases of its lifecycle. But teleconnections can actually be induced by a lot of different mechanisms. So El Nino can introduce a teleconnection. And you could also induce teleconnections by shorter time scale heating. There was a very nice paper by Graham Branstetter in 2014 showing that just a two-day pulse-like heating can induce a teleconnection pattern. So these teleconnection patterns can be induced by a variety of things. But I'll make the point that the MJO heating structure is actually somewhat optimal for producing teleconnections that have very strong implications for a sub-seasonal prediction over North America. So to think about this, let's start from the tropical thermodynamic energy balance. And so this is the tropical thermodynamic energy balance put in terms of dry static energy S here. So on the left-hand side, we have tendency and invective terms. On the right-hand side, we have a quantity called the apparent heat source that includes things like radiative heating, the effect of condensation minus evaporation, and then the effect of motions on the sub-grid scale, eddy fluxes. I ignore ice here for simplicity, but there's also ice processes that go into this equation as well. So near the equator in the tropics, you can do a scale analysis of the thermodynamic energy equation and equations of motion that actually simplifies this thermodynamic energy equation quite a bit. So you can actually show that near the tropics, the thermodynamic energy equation is approximated by a balance between Q1, which is the apparent heat source, and adiabatic cooling given by omega dSDP on the right-hand side here. So in the tropics, the balance is relatively simple. So what this implies is that if you know what an apparent heating is associated with something like the MJO, and you know what the stratification of the atmosphere is in terms of how dry static energy changes with height, you could use this to derive a vertical motion out of this dominant thermodynamic energy balance. If you look at what dSDP looks like, or the dry static energy change with height, you could show that dry static energy increases with height. Or in other words, you get a negative dSDP since pressure goes down. And what this implies is that if you know what the diabetic heating is and it's positive, you could show that vertical velocity in regions of positive diabetic heating has to be upward, characterized by a negative omega using this dominant thermodynamic energy balance. So because we're near the equator, you get something called weak temperature gradient approximation that can be used to derive the vertical velocity. So people like Qidong, actually, have exploited this dominant balance to derive the vertical motion field and the divergence field if you assume a diabetic heating anomaly in the tropics. And so this is actually something in this figure that comes from Qidong's paper with Samson Hagos in 2009, where they apply different convective heating profiles. This one is a deep convective heating profile shown by the colors here, and the right-hand side is a stratiform heating profile. And what you could show is that if you apply, for example, a deep convective heating profile, you get upward motion through much of the depth of the troposphere here in the heating region, which is consistent with this equation with divergence in the upper troposphere and convergence in the lower troposphere. Stratiform heating is similar. You get upward motion in the region of positive heating, actually downward motion in the region of negative heating, but even for this profile, you see divergence occurring in the upper troposphere. The actual heating profile in MJO convective regions, for example, is probably a combination of this deep and stratiform. So if you put these two together, you could see that in MJO heating regions, you'll get divergence in the upper troposphere associated with heating. So this is key. So you get divergence aloft occurring here. Another thing that's really key here is that when you produce divergence in the upper troposphere and divergent winds in the upper troposphere, the effect of that doesn't stay in the tropics. And so this is a really nice figure from Sartor-Schmuck and Hoskins in 1988 that shows if you put an idealized heating and divergence patch here in the tropical Pacific and look at the divergent wind field that's produced by this heating patch, you could see that the divergent wind field actually has a projection into higher latitudes, extending out of the tropics. Similarly, this study in 1996 showed the effect on the divergent heating field of a heating anomaly near Darwin, Australia. And you could see that the divergent wind extends into higher latitudes away from this heating anomaly. So if you have a heating anomaly in the tropics, again, the effect of that isn't just felt locally in terms of local divergence, but it also has a divergent wind component that extends into higher latitudes. So why is this important? The reason that this is important is that this extension of that divergent wind into higher latitudes can force a Rosby wave source at higher latitudes. And this was nicely shown in this study Sartor-Schmuck and Hoskins again, 1988. They used a non-linear vorticity equation which is shown on the top here. And so on the left-hand side, you have a tendency and eviction of absolute vorticity by the rotational wind. So that's what the fee is here on the left-hand side. And on the right-hand side, you have two terms. You have a dissipation term F and you also have an S term here, which is of the Rosby wave source. And breaking out the Rosby wave source, you can see that the Rosby wave source is given by v-chi here, which is the divergent wind field. So basically you have infection of absolute vorticity by the divergent wind as the first term of the Rosby wave source. And the second term is divergence in the presence of a non-zero absolute vorticity can also generate Rosby waves. It turns out that it's this first term, infection by the divergent wind field across an absolute vorticity gradient. That is the most important way that a heating anomaly associated with something like the MJO can actually generate a Rosby wave source. If you remember, in my previous slide, the divergent wind actually extends out into the tropics. And so if this divergent wind experiences a very strong absolute vorticity gradient, it can help generate a Rosby wave. So this is where jet streams come in. So this is an analysis that one of my former students, Stephanie Henderson, who's now at the University of Wisconsin did. The upper left panel here shows the wintertime mean 250 hectopascals zonal wind in reanalysis data from era interim. And you could see here, the presence of a very strong seasonal mean North Pacific jet stream occurring in the North Pacific. Let me see here, let me get a pen out here and see if I could, doesn't look like I could get a pen out here, that's okay. On the South flank of this jet, there's a strong negative relative vorticity region on the Northern flank of this jet. There's a relatively strong positive relative vorticity region due to the shears of the zonal wind. And so you actually have a very strong positive absolute vorticity gradient across this jet. And so if you have the divergent wind field associated with something like the MJO blowing across this jet, you can generate a very strong Rosby wave source according to this equation that I showed down here. The other thing that Stephanie showed is that climate models produce very, very different manifestations of the climatology of the North Pacific. Some models have jets that extend too far east. Some models have jets that extend, are too strong and have too strong of vorticity gradients. So, teleconnection biases can be generated by the presence of mean state biases in these jets because the Rosby wave source is wrong. I won't talk about that too much here, but I just wanted to point that out. So anyways, if you have the divergent wind blowing across this jet and the strong absolute vorticity gradients with this jet, you can generate Rosby wave sources. And so this plot here from one of my other former students, Kai Chi Sang, shows Rosby wave sources for one particular phase of the MJO. This phase of the MJO, which we call MJO phase two is associated with positive MJO Indian Ocean Convection and a negative MJO Convective Anomaly Center over the Western Pacific. It turns out that the divergent wind field associated with this MJO heating configuration produces a Rosby wave source that looks like a dipole. And so there's actually a negative Rosby wave source on one flank of the jet here, around 180 degrees. And there's a positive Rosby wave source more in the Asian sector caused by Indian Ocean heating over this region. And this sort of Rosby wave source dipole like Rosby wave source is actually very, very effective at producing a teleconnection pattern due to constructive interference. And if I have time, I'll talk a little bit more about this later. And the teleconnection pattern that this Rosby wave source configuration produces looks like this. It's associated with, in this case, a suppressed dilution low over the North Pacific, low pressure over Alaska, and then higher pressure over the Eastern United States. So maybe if I have time, I'll get back to talking about this. But because of the MJOs heating anomaly, it is very effective at producing a Rosby wave source and a teleconnection pattern like that. Okay, so I talked a little bit about the Rosby wave source. You also have to think about the pathway that Rosby waves take. There's actually a large body of theory that borrows from optics and indices of refraction and Snell's law, basic physics to try to explain the pathway of MJO Rosby wave propagation. There's a quantity called stationary wave number that's sort of analogous to a refractive index that we can use to explain why Rosby waves take the pathways that they do in the mid-latitude atmosphere. And this is given by essentially the absolute vorticity gradient divided by the mean zonal wind square root. And Stephanie Henderson plotted out the wintertime stationary wave number here that has some very interesting characteristics. You can see that stationary wave number is high in regions of the jet stream. You can see that it generally increases as you get towards the equator, generally decreases towards the poles. There's a lot of really interesting things that you can do with stationary wave number to think about the pathways that Rosby waves take in the extra tropical atmosphere. I won't go into that theory. Let's see. In its entirety right now because it would take up an entire lecture in itself, but there's a really nice paper by Hoskins and Ambrisi in 1993 that talks about the pathways that atmospheric Rosby waves take. If you know the characteristics of the flow and the stationary wave number distribution in the atmosphere. So for example, on this upper left figure here, you could think about the y-axis being latitude, x-axis being stationary wave number. You can see generally here that stationary wave number in this plot increases as you get towards the equator. You could show, for example, that Rosby wave pathways refract towards regions of higher stationary wave number. So this is a general comment that is true based on this theory. You could also show, for example, if you know what the spatial scale of your disturbance is in terms of a zonal wave number, you could show that all Rosby waves associated with this spatial scale have to refract before they reach a latitude where the total stationary wave number is equivalent to that. So you can see that all Rosby waves with certain wave numbers have to bend. You could also look at other things. All Rosby wave numbers at any spatial scale have to refract before the stationary wave number reaches a value of zero. You could also think about what happens when a stationary wave number goes to infinity. It gives a possibility that a Rosby waves are absorbed at those latitudes. Variety of different things you could do with this theory. If you have a jet stream with a maximum in stationary wave number, you could see that Rosby wave energy is trapped in the jet. So really nice discussion of linear Rosby wave theory in Hoskins and Mbreese 1993 that actually encourage you to take a look at. Oh, let's skip this for now. So because we have a distribution of mean zonal wind associated with climatology that has jet streams occurring in certain locations, easterly winds on the equator, various other characteristics of the mean flow, you could show that preferred teleconnection patterns tend to pop out given this background basic state wind distribution. Sarge Mac and Hoskins talked about this quite a bit. There's other papers that have looked at this, but a preferred teleconnection pattern that tends to pop out is something that we refer to as the Pacific North America pattern. And so on this particular plot, you could see that if you have a heating, for example, that's imposed in the Central Pacific, this tends to produce a wave train associated with one center over the North Pacific, another center over North America, and another center over the Southeastern United States. Regardless of where you actually put the heating in the tropics, you tend to get a very similar pattern. You see that the magnitude of the pattern may vary depending on where the heating precisely is. And so over the Western Pacific, you could see that heating pattern or the teleconnection pattern is a little bit more muted, similar for Eastern Pacific heating. You could also see that there's slight subtle shifts in the teleconnection pattern depending on where exactly the heating is. And so for example, you could see here in the Eastern Pacific, the illusion low has moved more towards the coast than for a Central Pacific heating pattern. These have tangible impacts on teleconnections was actually complicate things in terms of, for example, being able to make S2S predictions of West Coast precipitation, but the same general pattern tends to pop out with subtle shifts from in latitude and in longitude and things like that. So certain MJO phases actually have really strong and prominent teleconnection patterns. And this is a composite lifecycle of MJO teleconnection patterns as a function of phase and then lag in time after the phase. And so you could see that MJO phases three, two and three and maybe also six and seven tend to be where teleconnection patterns associated with the MJO are maximized. And the reason is that this happens is basically because of the reason I told you before in that teleconnection patterns tend to be optimized when you have more of a dipole heating structure associated with the MJO and a dipole rosby wave source structure associated with the MJO on the equator. So I showed before that MJO phases two and three tend to produce a dipole-like heating structure and a dipole-like rosby wave source that produces a very strong teleconnection pattern. The opposite phases would also be true if you looked at MJO phases six and seven, it would also tend to produce a dipole-like heating source and rosby wave source of the opposite sign that would also tend to produce a very strong teleconnection pattern. So this is sort of an optimal configuration as far as MJO forcing the extra tropics. And we've quantified this also in this plot, which I won't get to in any more detail here, but just to point out that we looked at this in more detail in this paper by my former student, Kai Chi, saying in 2019. Okay, so Anish, how much more time do I have here? Maybe about three minutes, Eric, and then we'll have 15 minutes for Q&A. Okay, sounds good. Why do we care about this teleconnections? This is something I'll skip and we'll get into too much more detail, but these teleconnection patterns modulate tangible weather on places like the West Coast. So for example, you can show that atmospheric rivers along the West Coast are preferentially modulated by the MJO because of these teleconnection patterns that occur. There's a lot of complications with this and that QBO phases also matter, but there's a lot of potential for prediction based on the fact that there's these relationships between the MJO and teleconnections. Okay, so last thing I'll talk about here is the topic of how these teleconnections might change in the future. So remember that heating in the tropics is balanced by vertical velocity based on this equation here. In a future warmer climate, one very robust prediction about the tropics is that the tropics are going to preferentially warm in the upper troposphere. And this is shown in the study here that I did with Anhelidamus and my former post-Aquine buoy. And we showed that in our CP 8.5 scenario, climate model simulations, there's a very robust warming of the tropical upper troposphere and this actually increases the magnitude of the vertical dry static energy gradient in the upper troposphere. And a prediction from this balance is that a weaker vertical velocity is needed to balance a diabetic heating in the tropics. So if you have a weaker vertical velocity per unit MJO heating, for example, this is likely to weaken MJO teleconnections in a future warmer climate. And is this true? Does this actually occur? And we've actually done some work to look at that with my former students, Brandon Wolding and Stephanie Henderson. And we took a state-of-the-art climate model called the Superparandri CESM, ran it in current climate and ran it in four times CO2 world and looked at the strength of the MJO teleconnection. And what we showed is that indeed because of the increase in tropical static stability and weakening of vertical circulations with the MJO, we actually got a weaker teleconnection associated with the MJO in a future warmer climate. This compares two phases here and you could see the weaker North Pacific teleconnection and we did a scale analysis of the response and it definitely does scale with changes in tropical static stability. The complication here is that there are other things going on as well. So in this particular plot, you could actually see that, yes, the response has weakened but the teleconnection response actually shifts eastward. And so that might actually increase the effect of the MJO teleconnection on the west coast of the United States, even though you get a weaker teleconnection pattern. This was actually highlighted in this recent paper in 2020 showing that the effect of an eastward shift to teleconnection does increase the impact of the MJO on California precipitation, for example. Studied by Joe Adult 2020. And I think this issue was actually brought out really nicely in this particular paper by a former student of Elizabeth Barnes and Dave Randall at CSU where they looked at mechanisms driving the MJO teleconnection with warming and CMIP6 models. They make the point that the MJO teleconnection is sensitive to a number of factors including the mean state dry static energy change which I highlighted but it's also dependent on the mean flow and the propagation and intensity characteristics of the MJO itself. And so this paper shows that decreases in MJO teleconnections due to tropical dry static energy changes are robust but there's a lot of uncertainty created due to mean state winds changing in a future warmer climate that produces a lot of uncertainty in future MJO teleconnections. So their grand conclusion here is that you may get a reduction in a boreal winter MJO teleconnections across most CMIP6 models but there's a lot of nuance over North America due to eastward expansion of the MJO's teleconnection due to jet stream shifting and things like that. So a lot of future work that needs to be done on this particular problem. Okay, let me just leave some key questions up here for possible discussion. So there's a lot of interesting questions here about how will the MJO change in the future that we have not addressed yet? How will tropical teleconnections associated with the MJO change in the future warmer climate? This is dependent not only on how the MJO changes but also mean state wind changes that add complications to things. And then you have to worry about what the implications are for middle attitude S2S prediction based on changes in teleconnection. So a lot of interesting stuff there to study. And then more basically I think, how can we fully exploit our current knowledge about teleconnections for S2S middle attitude prediction? This is something that I think machine learning and techniques and things like that that we'll learn later in the week are gonna bring a lot to bear in terms of approving our prediction skill for California precipitation, for example. So with that, I think I'll wrap up here and hopefully I've left some time for questions. So thank you. Thank you very much. It was an excellent summary of a lot of work.