 We'll start with theory today. I would like to welcome Chidong Zhang, who will be doing the first lecture for the day. Chidong leads the Ocean Climate Research Division at PMEL. Chidong has also led many successful field campaigns. Dynamo is one of them, which was studying the Madan Julian Oscillation's origins in the Indian Ocean, over a decade ago or about a decade ago. Chidong co-leads the international program, years of the maritime continent that investigates weather and climate processes in the Indo-Pacific maritime continent region and their global impacts. Chidong had been doing research on the Madan Julian Oscillation, I think at least for the last three decades now, two and a half decades, has led many great research on both the theory of the Madan Julian Oscillation, modeling, model deficiencies, and observations of the Madan Julian Oscillation. Today, Chidong will be giving a presentation on the theory for the Madan Julian Oscillation and a few different theories, I think, and how they compare and contrast. Thanks, Chidong. Thank you, Anish. I would like to express my appreciation for Anish and the Judas for organizing this symposium. I remember the first symposium I attended when I was a graduate student. And I still vividly remember some of the lectures and debates and that has benefited the rest of my career. And I hope the students participant here will have the same benefit. So let me share my screen. And because after I share my screen, I cannot see anything. So if anything goes wrong, just give me a holler. OK, sharing. So we don't see your video again, Chidong. Oh, I see. I'm sorry. I think once I click sharing, somehow the video disappeared. OK. OK, perfect. Let me try again. Did you see my screen? Yeah. You see my screen? Yeah. No, my presentation. It's not full screen yet, but. How about this? Yeah. Well, OK. All right, so I'll start. So today's topic is theories of tropical intrusion oscillation, but mainly we can talk about theories of the MJO. And for all of you who are interested in tropical intrusion oscillation, have some background knowledge about the dynamics through theories on MJO will be very beneficial because it will help you to understand the dynamic process, not just the MJO itself, probably the MJO influence on the global weather and climate. So the materials I'm going to present you today are pretty much based on these four publications. The first one is an MJO review. Sometimes go in this paper, Section 3 mechanism includes some of the discussions of early attempt of understanding the MJO through theories. And then the second paper in 2020 is a review paper of four, particularly four MJO theories in a very detailed comparison of four theories. So if anyone who is interested in the detailed theories about MJO, this would be a good paper to study. The next one also published in 2020 is a much broader review of the MJO, especially the recent progress on MJO. And in this paper, Section 3.2 specifically discussed the modern theories of the MJO include many MJO theories, except the last one, which just published earlier this year. So this one is not included in that review paper. That's why I listed here. So in this lecture, first I will provide some background to give you a context of the MJO theory. And then we're going to set a standard. What we would call a theory of the MJO and what's the difference between theories and hypotheses and assumptions, and what we should expect from a theory of the MJO. And then we're going to demonstrate the current very broad and diverse thinking of the MJO theories. You will see that there are many, many different ways to describe MJO dynamics. And if we have time, we're going to dive into three theories and give you a little bit more details. So as a background, we have a lot of theories about tropical atmosphere through water circulation, hotly circulation, and ITCZ. And these two are closely related. Quasi, biannual oscillation, or QBO. And this is an excellent example of how the discovery of this phenomenon from observations led to a complete theory in a very short time period. This is probably one of the best theories about the tropical atmosphere. And that, of course, we have many, many different theoretical approaches of autumn monsoons, about tropical cyclones, and the easterly waves, and equatorial waves. And equatorial waves is another wonderful example of a elegant mathematical solutions to atmospheric motions. And the theories of the MJO is pretty much based on equatorial waves, as we will see. First of all, let's set our standard. I would have to emphasize that conceptual models or hypotheses or assumptions are not theories. No matter where you get developed, conceptual models from observations or from numerical simulations, and they cannot be treated as theories. Because conceptual models usually give you, describe verbally or graphically, some important physical process, dynamical process, but it's not quantitative. And we have a lot of conceptual models about MJO, and they usually come with nice graphics and emphasize on certain aspects of the MJO. And in the literatures, there are many, many of them, and not all of them are theories. So we'll emphasize on theory. So what is an MJO theory? First of all, it has to be quantitative, and if you want to be quantitative, it has to involve equations, first principle. So the MJO theory would have to be based on the linear stock equations. That's the first thing. The second thing is, no matter what theories you're going to make, you have to have assumptions and approximations. And for an MJO theory, those assumptions and approximations will have to be testable against observations when those observations are available. That's the second criteria. The third one is, specifically for the MJO, you will have to explain the most fundamental features of the MJO. And they are the intracisional times, the intracisional scales and the planetary scales, so the time and the spatial scale, and the eastward propagation. And sometimes you can replace one of them using the eastward propagating speed. You have to explain those fundamental features quantitatively. So those are the requirements for MJO theories. And if you use this, compare with the sum of the hypothesis and the assumption you will find out, those hypothesis assumptions are hand-waving. They probably sound very reasonable, but they are not qualitative. So that's the fundamental difference. So I assume all of you are familiar with the MJO, so I don't have to say too much about the MJO. I'm showing this just to put us on the same ground. The figure on the left is the classic original schematic of the MJO, drawn by Menden and Julian in their phenomenal pickers. So in the right is the modern representation of the MJO in terms of precipitation anomalies in eight phases based on the RMM index. Well, I'm showing this to emphasize that precipitation and the convection has been integrated part of the MJO from very beginning. Just keep that in mind. The next one, showing you the horizontal structure of the MJO. And if you are familiar with the GIL solution, which is showing in the upper right, and you will know that once you have connected heating in the tropics, and you will generate a raspy structure, let me show you here. Can you see my cursor? I assume you can see it. So you will generate a raspy gyres to the west of the conductive center, which is showing in the upper part, and a Kelvin wave structure to the east. And this is a very classical solution to the flow pattern in response to a conductive heating. The MJO horizontal structure in the lower panel shows a very similar structure but with a little bit different. The red dot represent the connective center of the MJO. This is composite. To the west, you can see these two big gyres represent the raspy waves. To the east, you can see this extended the zoom flow near equator, which is the structure of the Kelvin wave. But what's different between this MJO structure and that the classical key solution is you have another pair of the raspy gyres. And this one can be explained as the raspy response to the negative anomaly of a connection associated with the MJO. And we all know that when the MJO has the active, connectively active and the inactive phase, two phases. So this green dot, blue dot, represent the inactive phase of the MJO. So these inactive phase of the MJO also generate raspy waves to the west, but with the opposite sign as the raspy wave west of the active connective center. So you have these two pairs of raspy waves which sometimes people refer to as quadruple vortices. So just keep it in mind because some of the theory will including those structures. Okay, one fundamental problem related to the MJO is why MJO properties, right? That's one of the most fundamental feature of MJO. And if you read the literatures, the most common explanation is MJO propagated eastward because the low level moisture is higher to the east of connective center of the MJO than to the west. So this schematic diagram just illustrates that. The tall cloud represent connective center and the green represent the moisture so you can see moisture is higher to the east. Is this the right answer? If you look the MJO observations, every single event, you will see this. If you look at MJO composite, you will see that. If you look at the numerical simulation by global models and if they can produce MJO, you will see this feature. So everything you can observe, you will see that. So this sounds like very reasonable answer. But I'll call this elephants trunk explanation and the reason is if you ask a naive question, why do elephants prefer to move forward instead of backward? You take observation, you will find all elephants move forward because they follow their trunks. Their trunks always lead their ways, right? So then you have answer is MJO prefer to move forward because of their trunks and you may all laugh but the logic is exactly same as we explained MJO in terms of low level moisture because you observe that and no exception so you take that as a reason, as a dynamic reason. Go back to the MJO. You can simply ask why this low level moisture does not occur west of the connection center so then you move westward. That's a very logical question. So just use the low level moisture to understand MJO eastward propagation is not sufficient. So let me introduce you a conundrum in tropical meteorology and that is very simple. If you're familiar with the Matsuno solution, this is the Matsuno's shallow water equation. It leads to a set of solutions represent a series of equatorial waves. It's a very, very nice mathematical solution to the atmosphere flows. But there's no MJO solution. If you look at the observations and they are using either presentation or cloud, you'll find the spectrum peak that line up very well with the predict dispersion relationship from Matsuno solution except in observed spectrum you have MJO signal at the bottom and there's no MJO in Matsuno solution. So what happens? Well, in the community we think the reason the Matsuno solution does not include MJO is because some critical component of MJO is not included in this simple linear shallow water equation. So what is missing? As we saw earlier, MJO is very closely related to conduction. So maybe what is missing is diet by heat. So maybe we should add that diet by heating to this equation. And MJO signal is always related to the moisture variability. So maybe we should add moisture to this equation. And maybe this equation just represents a single vertical structure. MJO is much more complicated. So let's add vertical structure, for example, boundary. Or maybe we can add surface conditions. For example, evaporation from ocean surface. Or maybe because MJO is a non-linear process. So this linear equation cannot give us MJO solution. So maybe we can consider non-near energy. And this equation, the Matsuno solution does not include any viscosity. So maybe we should add viscosity to this equation. And maybe there's something else missing and we have not discovered. The basic approach to MJO theory is to add additional terms, additional variables to this simple mathematical shallow water equation. Let's see whether we can do that or not. So that's the early attempt is basically follow this type of thinking as a viscosity, as diet by heating, especially at the interaction between diabetic heating and the wind. Add the surface evaporation and add a boundary layer. And we're going to discuss in details how each of these components play a role in the modern MJO theory. So this table lists currently available MJO theories. We call them modern theories because they are all the recent theories during the last decade or two. The first three, the top three in the red box share a lot of similarities. They all think moisture vapority is the key. They all include moisture and the convection coupling. They all think cloud radiation feedback are critical to the MJO. What's different is the first one, rely on assumption. We call it with temperature gradient. And based on this assumption, precipitation and moisture can be directly related. And the second one rely on surface moisture. And the third one rely on assumption of equilibrium, quasi-equilibrium in the boundary layer. So in addition to those details, these three share very, very common basic dynamics. The third, the next one, the trail interaction basically emphasize on boundary layer convergence as the key. The skeleton one emphasize the interaction between MJO and synoptic and mesoscale systems. And they call this skeleton because at that time they think this is the simplest MJO theory, but it turns out it's not as we will see. Everything above this green-yellow line represent a group of theory that emphasize the interaction between connection and the circulation. The next one, the larger scale vortex. This one emphasize on the vorticity generation at a low level due to stretching. It does not explicitly include the interaction between connection and circulation. And it does not explicitly include moisture. The gravity wave theory emphasize on the difference between eastward and westward of propagating inertial gravity waves. And the MJO exists because of those gravity waves. And it does not include explicitly moisture either. The solid wave is only nonlinear waves. They think MJO is a solitary raspy wave, which is nonlinear. And the last one is harmonic oscillator. They think the MJO is basically a configurated or transformed Kerbin waves. When you include the viscosity, the Kerbin will just become the MJO. So those are the general ideas of the MJO dynamics based on different thinking. So let's see what's the difference and similarity between those theories. As I said, there's only one nonlinear MJO theory. That's the solitary wave. And most of the theories including collective coupling with the circulation. And the two, there's a two that don't. Five of these theories emphasize the moisture variability. So they only include prognostic equation for moisture. And the rest of four do not. And for those that include moisture variability, moisture play a key role for MJO propagation. In theory, most time when you want to explain a perturbation, you use the approach of unstable mode. You assume a solution which is unstable. And then you look at what scale the unstable mode grows fast. So most of these MJO theory take this approach. Assume MJO is unstable mode. And they look at the reason why this unstable mode grows fastest at the intracisional time scale and at a planetary scale. And four of the theories do not assume MJO as an unstable mode. In some of them, MJO is neutral. In some of them, MJO is damped. And again, if you include moisture in the MJO theory, moisture would play a role for MJO growth. So five of those theories include this. Now, cloud relation feedback to circulation is important in four of the MJO theories, not in five of them. And as we discussed, MJO has this raspy carbon wave structure. And very interesting among all those theories, three of them, including both the raspy and carbon wave structures. And three of them include the only carbon wave structures. And four of them include only the raspy structure. And the momentum damping, the Masuno solution, Masuno equation does not include the momentum damping. Three theories include the momentum damping, but only one, in only one series, momentum damping plays key. Atmosphere boundary layer, three of them include the atmosphere boundary layer, the other stone. So you can see that there is a lot of different thinking, a lot of different process, and some of the process play key roles in theories, others not at all. So those are the diverse thinking of MJO theories. Okay, so I only have five minutes left in my 30 minutes' alignment. So let me quickly go through three theories if I can, managing five minutes. So the moisture mode theory is currently the most popular theories and the well-accepted. The essence of this theory is the intracisional time scale is determined by the feedback between water vapor and the convection. It based on a very simple hypothesis from observations. So this shows the precipitation versus moisture in the tropics, and you can see there's a exponential, quasi-exponential dependence. And in this theory, they took the middle of that and linearized this exponential curve so they can find another solution. So this is how the assumption is made. The variability of column moisture is directly related to the variability of precipitation, and this gives the time scale of the MJO. And the planetary scale comes from the long-wave cloud radiation feedback because in the upper troposphere, conductive cloud will generate a big envelope cloud and spread into a large area, and that, the feedback, give you the large planetary scale of the MJO. And lastly, the eastward propagation, as I said, is due to, as I said, the moisture is always high, low-level moisture is always higher to the east, and this equation explains exactly why. It's because the caravan and the rust-wave direction in the lower troposphere produce the higher low-level moisture. So you can see that there's nothing wrong to say moisture is higher to the east, but you have to explain why, and this theory explains why in terms of moisture direction. Let's go quickly to the next one, the trail interaction theory. The trail interaction represent interaction between boundary layer moisture convergence, convection, and rust-wave-caravan-wave circulation. So that's the three-parts interaction. And this diagram pretty much illustrates what the essence of this theory. In the boundary layer, when you have easily wind, then corollary force will create a convergence, and then convergence will push moisture upward and generate new convection, and this is exactly why the MGO move eastward. And the planetary scale and the intracesional time scale of the MGO all determined by how the caravan-rust-wave responds and interact with die-back heating and with basic moisture structure. The last one is the harmonic oscillator. I include this because this theory is the newest one, and it is not including any of the MGO review papers I introduced you at the very beginning. And this is a very simple theory. It just simply say, if you include viscustic momentum damping in the Matsuno shallow water equation, then caravan-wave will slow down and become a harmonic oscillator. And this harmonic oscillator will respond to stochastic background forcing and a resonant at the intracesional scale and the planetary scale k equal to 1, zonal-wave will number equal to 1. And not only the caravan-wave slow down is structure also changed. We all know the caravan-wave structure in the low-level is such that the pressure is in phase with the zonal-wave to the left, or to the right, this is the caravan-wave structure. But when you slow down, the structure gradually changed. The pressure is no longer in phase with the low-level zonal-wave is in quadrature with the low-level zonal-wave. So the low-level pressure is at where the connection is. And this is the MGO structure. So this theory basically say MGO is simply a transformed caravan-wave in response to stochastic forcing at the present of momentum damping. And so far, this is the simplest theory of MGO. Okay, my time is up and let me just quick make a conclusion. And as we see, there are very rich and diverse thinking on the dynamics of the MGO through theories. And so if you ask the question, which one is correct? And I'm afraid I have to say you may ask a wrong question. To me, the question is, does the MGO have to be driven by a single mechanism? Or can some of them, or even all of those MGO theory, all are correct, all are part of the big elephant that we feel? And however, the current MGO theories does not cover everything. It does not cover MGO initiation. So if we have a theory that can explain MGO initiation, that would be a great advance in MGO studies. And some of them may know that the recent discovery, a recent wonderful discovery is that MGO is modulated by a QBO, the quasi-bionic oscillation. But we don't have a theory to explain that. And some of you probably also heard about the barrier effect of the Meurntin condiment. That is, when MGO propagates over the Indo-Pacific Meurntin condiment, some MGO can propagate through and some just stall there and die. They cannot propagate through. So that's why it's called barrier effect. We don't have MGO theory that can explain this. And the last one is, we have lots and lots of observations showing a very specific small scale at the conductive level or even smaller scale related to MGO. And none of the theories at this moment include this small scale process. So those are the potential topics that can be advanced in terms of a theoretical understanding of the MGO dynamics. I'll stop here and answer questions. Thank you very much, Chiran. It was an excellent summary of really difficult topics developed over many decades. So thanks again.