 Good morning. So today I'm going to talk about coupled tropical-extra-tropical interactions and the globally unstable mode. This is a continuation of yesterday's talk. Yesterday I talked about the tropical-extra-tropical interactions between NGO and NAO. Today I will talk more about the theoretical work on this topic. So first I will say a few words outline what are the existing NGO models in the series about this NGO generation. And then I will spend most of the time to talk about three-dimensional instability theory of intracenial oscillation and the convectively coupled equatorial waves. And then I will show there's some comparisons between observations and theory. All right, so here's a list of historically proposed theoretical models for the NGO generation. These slides mainly for those theories that look at the NGO as the many tropical phenomenon. For example, at the first paper by Martin Julian in 1971, they look at this oscillation they said in the paper it cannot be covered with. So it's not covered with. It's different. But two years later, 73 Parker, they say, oh it's a covered wave because it's very similar with number and propagation. And later Linzen, Lao and Pan and Chang and Lin, they look at the theory for the NGO theory and they said it's a covered wave sustained through a wave and the conditional instability of second kind, the CISK mechanism. And later Wang and Zui and Sao Bi, they modify that theory and say it's a covered wave sustained through a frictional wave CISK mechanism. And Emanuel and Linien, they look at another mechanism and they say it's a covered wave sustained through evaporation and the wind feedback. So it's a little bit different from the wave CISK mechanism. And from observation, and Wider Kedades and then this, they look at the spectrum and they look at the peak. It's distinctively different from common wave. So they say it's not common. So there's not a mixture uncertainty in the explanation of the NGO phenomenon in the tropics. And there's a question, what is the minimum mechanism or processes that is responsible to produce the NGO in the tropics? And the work by Maida and the station man, they design a skeleton model. They look at very simple, what is the minimum to generate this process. They use multiple interactions between three processes. It's the dry dynamics and the lower troposphere moisture and the envelope for synoptic scale activities. So those multi-scale interactions, they show that their model is able to generate some oscillations that is very similar to the NGO. So those just lists have those theories that is focused mainly in the tropics. And they say it's a tropical phenomenon. And yesterday, my talk and the next talk, we will show some influence from exotropics that can also be a possible mechanism to generate the initialized NGO in the tropics. And another kind of view for this oscillation is global view. This is not only a tropical phenomenon. This is a global oscillation. It's a linkage together, tropics and exotropics. So from the observation, Maida and the Phillips and the Hsu, they look at the coherent variation of the tropical wave and the middle attitude of the wave change. So they link that together and they see that that is the global phenomenon, not only in the tropics. And the theory is co-worked by Fred Bixon and they analyzed the instability of the global three-dimensional basic state and the form mode that is very similar to the NGO and the interest in the variability. So that is the history of this theory. So today my talk is based mainly on these two papers. The first one is by Fred Bixon 2002 as a genesis of interest in the oscillation and the equatorial waves. And the second paper is by Fred Bixon and myself. We compared the theoretical waves with observations to see if there is consistency between theoretical work and observational work. So Fred Bixon's theory, the look at instability are for interest in the oscillation and the connectively coupled equatorial waves. They, because it's a linear theory, so they use a basic state that is January 1979. There's some questions for why they don't use like a DJF mean and the multi-year average. And I talked with him, he said it's better to use one single month because if you use a multi-year average, you smooth out those features that is critical for this instability like that. And the theory is instability, you need to include convection and evaporation in the model. And they analyze the frequency, wave number frequency modes generated from this eigenvalue, eigenvector analysis. And we also compare these observations. I will show the properties of a theoretical interest in the oscillation that is broadly similar to the observed NGO. It is coupled tropical, extra tropical mode, sustained through moist baryclinic, barytropic instability. And the property if you, I will show later, the wave number frequency and the dispersion relationship is comparable with the coupled Kelvin wave, Rossby wave, mixed Rossby gravity wave, and the Goose waves near the equator. So here is the basic state for January 1979. This is an observation for 300 million bosom wind, 700 million bosom wind and moist static stability. This is always positive. So that means there's no mechanism to generate wave CISK mechanism. So it's just exclude this mechanism. And this one is the evaporation and the room of wind feedback. So this is one of the important terms in that equation. So the evaporation wind feedback the parameterized that impact using this equation. And this is coefficient and the thousand millimeter bar density of air. And this is the wind speed at the near ground level and multiplied by the difference between the saturated specific humidity and the specific humidity at that level close to the ground. So they use this parameterization to represent evaporation and the wind feedback. And for the convection, they use a simple that's a generalized cool type parameterization to represent the convection in that equation, in that model. And the linearized with respect to the January 1979 wind global field, it's a three dimensional field. So this will produce linear equation and they solve this eigenvalue eigenvector problem with 2480 by 2480 big matrix for the three dimensional basic state. And then they find the bunch of modes unstable modes from this system. And then they look at the dispersion relationship the frequency and the number. And okay, here it's a list of the modes. Okay, they have a different switch to the switch of for example, dissipation. So here include evaporation mechanism. Here is the another type of experiment. The last column is the dry model. There's nothing. Okay, so they have the first line that's for the code NGO. So what we can see is here is the mode number 66. And the period of that oscillation is 34.4 days. And here is the e-filled in timescale. And they said this one is the most closest mode to the NGO. And also they got other waves like Kelvin wave, equatorial inertia gravity wave, and mixture gravity waves. So here is the wave number frequency distribution for those theoretically generated mode. For example, this line is a wave number from zero in the center. And the negative that's the westward propagation and the positive that's the eastward propagation. This is frequency. So what you can see is that along this line, that's a Kelvin wave. That's almost the wave number and frequency. They are linear related. And the NGO, it's here. It's wave number one. And it's different from the Kelvin waves. And they also have the equatorial rotate wave on this side and the mixed rotate ground wave and the inertia gravity waves. So they represent this spectrum distribution relationship with this kind of diagram. And then compare with the Witter-Kinadius diagram. And they say the comparison is good. All right. So what is this? I think that's basically what I said. Okay. This is a comparison with Witter-Kinadius diagram for the observation. So this is the anti-symmetric part because in the analysis of Witter and the Kinadius, they separate this analysis into anti-symmetric and the symmetric part. So the symmetric part, they have the Kelvin wave at the NGO in this area. So that's why Witter and the Kinadius paper say this NGO is distinct. It's different from the Kelvin waves. All right. So here is a comparison because in this paper, in Frederickson's paper, they didn't separate to the symmetric and the anti-symmetric part. So they include everything in this diagram. So this light blue area corresponding to Witter-Kinadius diagram in this part. So that's including the initial gravity wave. But in this part, the white area is this part. So that means the Kelvin wave and the NGO and the Equatorial Respite wave, they compare quite well with the observation. They compare with the observation. Okay. Now, look at in detail the NGO mode and we'll find the structure and the propagation and the comparison. Okay. Now is the leading, this is the leading intracellular oscillation and that's in NGO mode. This panel shows 500-millimeter bar stream function. What you can see is there's not like patterns, normally patterns in the northern hemisphere. So that is, there's some similarity to what I showed yesterday from the observation. This is a whole global theory generated. And this diagram shows the 300-millimeter bar velocity potential. So that is a really tropical divergence field. So there's a connection between this kind of northern hemisphere pattern under the tropical divergence. So the varies with the period of 34.4. That's close to the NGO time period. This is a half molar diagram for the 300-millimeter bar velocity potential from zero to 20 degrees. I think the time goes up. This is the longitude. You see the eastward propagation of the divergence field. And compare with observation. Observation, you see this velocity potential. This is a composite from observations. So the propagation there, there's similarities between the theory and the observation. Okay. This is another comparison with the, I think, stream function. Okay, velocity, right? This is a zonal velocity for the shading and stream function. I think it's the same one, that's the last one. Yeah, it's the same one. So now we compare the analysis between the theory and the observation. So we perform analysis similar to the in 2009 and regard the time series of evolution of theoretical ISO mode as very similar as the observational time data set. And to look at the relationship between the face of the convection in the tropics and the development of the entire pattern in the nothing hemisphere. So instead of using observational data, we use the model output, the model generated evolution to do the analysis. We also examine the extent to which the wave flux associated with the theory are similar to the observation. Okay, again, this shows the Wheeler-Hunden index in the face space from face one to face eight. This one showed yesterday. And also this one I showed yesterday. This is a composite for precipitation anomaly, anomaly equator from face one to face eight. So now we do the same composite, but for the stream function for 200 millibar. So again, you see this with eastward propagation. For example, the face one, you have divergence, this is the upper divergence from the Indian Ocean that propagate eastward. That's consistent with this precipitation anomaly, eastward propagation. Okay, this is an observation, but now the same calculation was done for the theory generated the velocity potential for different in the cycle. Okay, so what you can see is that the velocity potential from the theory for the NGO mode also propagate eastward. And if you put them together, you can find quite a lot of similarities. So that means that the theory can like the mode in the tropics is very similar to the NGO signal. We also did the UF analysis. This is an observation for the LLR. It's very similar to what I showed yesterday for the UF1. It's a monopole structure near the Indonesian continent, Maritime Continent Area. And the second mode is a dipole structure. So this mode is very similar. It's well correlated with Widow Handling Index, RM1 and RM2. And you see if you do a time mark relationship, you can see that the UF1 did UF2 by about 10 days. So we can do velocity potential regression with respect to the PC1 and the PC2. So instead of showing the relationship, this is LLR. So this is not surprising that the velocity potential have this kind of larger scale features also. And another thing is the NNO pattern. As very similar to what I talked yesterday, we project the stream function 500-millimeter-bar height. I think it's the stream function 300-millimeter-bar to this pattern to get to the NNO index. All right. So this is the evolution of the NNO index for different phase. But the phase in the theory is different. In the theory, it's a cycle. So you have to use the phase from minus 80 degrees to positive 80 degrees. That can be mapped to the phase of the MGO by looking at the location of the convection of the stream function centers. So what this says is that when there is NNO index, when there is MGO is in phase five, that's about 10 days after phase three, you see a positive NNO kind of association in the metamattitude. So this is very consistent with what we see in the observation. And look at the anomaly map on the right-hand side, and that's the observation. On the left side is the observation. The theoretical mode at the left side, observational component at the right-hand side. So the comparison is, for example, after phase three, phase four you see the similarities. For example, the development of the positive phase of NNO and in phase five. So there's some similarities between the theory and the observation. Okay, we also look at the wave-active flux as I showed yesterday from Takaya and the Nakamura. And here is the theoretical mode, wave-active flux for phase three, phase four, and the phase five. So you see the development of the wave flux activity in the NNO specific, and then extended to NNO's America. And another phase after, you see the source of propagation of the wave-active flux. That is very much consistent with the observations. So, okay, yeah, this is a showed comparison in the same regions for the wave-active flux. So the theory matches quite well with the observation. So, okay, this is the second leading mode for the ISO oscillation. I think the comparison, I think this one, I covered most of it. It's the X-tropical waves and the tropical divergence field. Okay, so another thing we look at is to see the sensitivity to the basic state. Instead of using 1979 January mean state, we tried 1988, and they also averaged from 1980 to 2009. So the second leading mode, theoretical ISO mode for the January 1979 line after phase three by 20 days, the period is 44, 25 days. But with 1988 basic state, we also find the leading mode, it's lagged by 12 days. The time period is a bit shorter, but it's still in the interest in the time scale. And we've used a 30-year average January basic state. We find the lag to phase three is about 12 days. The NNO lags by 12 days. So the period is about 30, 38 days. So there's some difference among this basic state, but they all have the interest in the variability that that has showed the tropical convection and the association with the NNO. So those kind of results since it's quite robust. So this bariclinic zonal and the meridional wind for January 1988, and the comparison with 1998 to 2009, you can see that there is some small difference, but mostly it's very similar. By eye, I cannot see much difference. So I think I will conclude. I just mainly cover this part because most of the third work is done by Fredrickson. So I just mainly focus on the comparison with the observation. So the model I also have appeared from 30 to 50 days with the first internal mode, tropical structure and the equivalent barotropical, extropical structure. So the theory captured the complex phase relationship between NGO connection and the NNO. And also I didn't show the TNA teleconnection. The tropical, extropical interaction of the theory I also seen in Will Flux also are very similar to those in the application. The second leading ISO mode for January 1979 has appeared 44 days. And I think that's the best structure I've simulated. But with different basic state, we can still simulate, but it's a bit different like a period. And the gross rate is a bit different. All right, thank you.