 It really made it easy for me. I can really skip a lot of more introductory material today thanks to his great lectures yesterday. So I decided to use this three hours, how many do we end up being, to really set the pace for a lot of the discussion that is going to happen next week at the WCRP workshop on tropical rain bells and monsoons. And really, this talk, or series of talks, is really meant to provide some introduction to theoretical frameworks that have been developed in the past 15 to 20 years for a lot of the recent advances in our understanding of what controls, for instance, the mean position of the ATC in response to perturbations and monsoons as well. I kind of divided the material in three main topics, but you would see that especially the first two blended in. How do we think about the interaction between convection and large-scale tropical circulations? And here, by large scale, I'll really be focusing on the large scale overturning the Hadley cell and monsoona circulations. And then to move it towards modern theories for these systems. And then if I have time, because this is one of the themes of this summer school, I'll try to address the question, are there tipping points in monsoons? This is not research that I've done myself, but I think it fits very well if we get there to some of the themes that will be discussed before then. I also would like to emphasize that all of these questions are really at the core of a lot of my research activities. I spend a lot of time thinking about this fundamental interaction between how large-scale tropical circulations on Earth and other planetary atmospheres as well interact with the condensate species and therefore interact and shape the hydrological cycle. OK, so I promised that I had decided to put a movie and animation even before seeing Jeff's talk yesterday. And this is an animation of the cloud field for one specific month, the month of July, specific year, I think, in 1994. So Northern Hemisphere Summer. So these are observations. And so clouds, in some ways, are really a manifestation of convective activity. And one thing that I wanted to spend some time doing is using this movie, and I'll look it through several times, to really emphasize some important differences between tropics and extra tropics. OK, so I'm sure that you have seen similar movies, similar animations before. But if you haven't, I think that one thing that really strikes your attention is the fact that the cloud field is really chaotic and turbulent. And this is really a reflection of the chaotic and turbulent motions in which clouds are embedded within and in which they develop. Of course, after staring at this field for a while, despite the fact that, of course, yes, the turbulent nature of the cloud motions, which involve interactions on many different important spatial scales, you see that some patterns start to emerge. And here I really want to emphasize the key differences between the cloud field and the tropics, broadly defined as the latitude belt, 30 degrees north and south of the equator, and the extra tropics, everything forward of that. So notice how, first of all, in the tropics, weather, here as represented by clouds, tend to move from east to west in association with prevailing with Easterlies there. Whereas in the extra tropics, clouds tend to move in the opposite direction in association with prevailing westerly winds there. You also might notice that in the tropics, the cloud fields has a more granular structure. Of course, what I mean to say is that you see clouds forming at small scales. In fact, one single individual cloud has a typical horizontal scale of about one kilometer. Of course, convection in the tropics can take the shape of more complex and larger scale organization. I think that here you also see tropical cyclones that is spinning off the ITCC. You also see typhoons in this region along the coast of East Asia. But these scales are different than the ones you see in the extra tropics. And this is particularly evident in the southern hemisphere because this is winter, the winter hemisphere, where you see that, in fact, clouds tend to be organized along filaments that have very large spatial scales. We're talking about several hundreds, thousands of kilometers. And these are, in fact, the typical extra tropical weather systems, patterns, cyclones, and anti-cyclones that control weather in the extra tropics. Another point that I would like to emphasize, notice how convective activity is intense over the oceans in narrow, in the meridional direction regions that are, however, extended in longitude. You see, again, this is something that we'll keep discussing and learn more about this morning. You see a lot of widespread convective activity over the summertime subtropical continents in association with monosomes there, Indian, Western Africa, and to a much smaller scale even over North America. OK, so this is, of course, just, in many ways, just snapshots. Now, of course, we do have measurements of precipitation, although precipitation remains a very hard quantity to measure, to model, to predict. We have global maps of precipitation, so let me show you one such global map that shows the long-term annual mean precipitation over the Earth's surface. Of course, blue, it's intense rainfall. Again, we see how most intense rainfall tends to be concentrated in very meridional and narrow, longitudinally extended rain belts over the oceans. Those are the features that we usually call intertropical convergence zones, ITCC for brevity. You see that, of course, intense rainfall is also seen, and in fact, moving further away from the equator than what we see over most ocean basins, over subtropical land masses. We will see that that is, at least to some extent, really the manifestation of the strong seasonality of precipitation there. And we also see that outside of the tropics, precipitation is primarily organized along tilted storm trucks. And this is, again, where those systems that I showed you before, those filaments of clouds, again, those weather systems tend to be primarily forming. If now, in addition to taking a temporal annual mean, for each given latitude, I also take a zonal mean. I obtain the following distribution of the zonally averaged annual mean precipitation as a function of latitude. And so we see the very familiar pattern of alternating wet regions, wet region in the tropic. This is the wettest region, dry region in the subtropics and two other wet regions in the extra tropics in both hemispheres. So it's no surprise that the wettest region, the wettest then, occurs on Earth around the equator. But it might be a surprise, although this is something that has already been discussed in previous lectures, it might be a surprise that, in fact, the maximum precipitation is not found at the equator, or the distribution of the precipitation is not symmetric about the equator, but maximum precipitation, in fact, is sitting north of the equator at about 6 degrees north. So why is the IPCC north of the equator? Why does a precipitation prefer one hemisphere versus the other? It's really important to emphasize how if the two hemispheres were completely symmetric, and we'll try to understand what I mean by that a little bit more later on, if the two hemispheres were completely symmetric, there would be no reason for precipitation to prefer to sit on one side of the equator, or at least not having a symmetric distribution around the equator. So the fact that the IPCC is shifted northward of the equator implies the existence of an isymetry, hemispheric isymetry. And what is the relevant isymetry has been discussed at length in the literature. One might guess that, for instance, the fact that the northward displaced position of the IPCC associated with the fact that in the northern hemisphere we have more land masses. Other hypotheses have been suggested being the orientation of the coastlines in the American associated interactions with ocean circulations as the seas and clouds, maybe the presence of the Andes. And I will say that maybe all of these mechanisms are plausible, but consensus has emerged. And not many years ago, but only in the past five years, that most likely the primary source of isymetry is the fact that the ocean is transporting energy across the equator from the southern into the northern hemisphere. And we will see that this requires corresponding transport of energy by atmospheric circulations in the opposite direction, which manifests itself as the ITCC shifting northward of the equator. Of course, these precipitation patterns are clearly linked to the large scale atmospheric circulation patterns. Here I'm showing the distribution of the nearest surface, annual mean winds, contours, represents speed, of course, the vector's direction. And again, of course, the ITCC really is associated with the location where we have strong horizontal lower level convergence, which needs to be balanced by vertical divergence. And therefore, it's the development of vertical motions that support precipitation there. Again, in almost everywhere over the ocean, you see that the winds in the tropics are the easterly trade winds. Almost everywhere, with the exception of the north and Indian Ocean, where you see that on the annual mean the speed is weak. And in fact, there is a very slight southwestly component. I hope that you can see that. And that is really the signature of the annual mean of a very strong seasonal cycle of lower level winds over the Indian Ocean. And I'll show you an animation of that later on, in which the near-surface winds reverse quite rapidly, in fact, through the course of the seasonal cycle, and quite remarkably, from blowing from the northeast to the southwest as everywhere else in the tropics during the winter. And they reverse completely, and they blow from the southwest to the northeast during the summer in association with the Indian Monsoon. Again, precipitation is strongly tied to vertical motions. One way in which we really like to depict the general circulation of the atmosphere is by looking at the meridional overturning. And this is the Eulerian mainstream function that has been discussed before. I don't think that anybody has shown, though, the real pattern, the exact pattern of the annual mean derived from observations. So we see that in the tropics, this large scale overturning is characterized by two hotly cells that are almost, but not quite symmetric, about the equator ascending motion near the tropics. Poleward flow at upper levels in both hemispheres. This ascending motion in the subtropics at around 25, 30 degrees north and south. And equator flow at lower levels to close the circulation. It is clear that maximum precipitation, at least in the zonal mean, coincide with the center of the ascending branches of the two hotly cells. And the fact that the ITCC is displaced north of the equator really results from the fact that the two cells are not entirely symmetric. The southern cell is a little bit stronger and broader than the northern cell. So ascending motion does correspond with maximum precipitation. The dry belts in the subtropics coincide with the descending branches of the hotly circulation. This is because air that arises all the way from the higher troposphere is very dry as it moves down where it gets heated up adiabatically. And so these tend to suppress any convective activity. So it is clear that, at least in terms of the zonal distribution of precipitation, really the hotly circulation shapes that distribution in fundamental ways in terms of where its ascending branch is located, the strength of this returning, and where the descending branches are located. So we really would like to have a close theory for all these features of the hotly cell in terms of planetary parameters or climate parameters, such as the depth of the troposphere, the vertical stability, the pull to equator temperature gradient, the rotation of the radius of the planet. And yet, as I think it emerged quite clearly from Jeff's discussion yesterday, that theory has not emerged yet, which of course also makes the interpretation of expected changes with warming a little bit more difficult, based both on observations, for instance, projections based on Simi-5 models. One important aspect of this hotly cell is that that is a thermally direct circulation. What I mean by that is something very simple. Relatively warm air tends to go up. Relatively cold air tends to go down. So this is a circulation that is converting potential energy into kinetic energy of the large scale. We will see that this is also an energetically direct circulation. Again, I'll try to be a little bit more clear as to what I mean by that. Outside, and I don't think that we will discuss much the ferrule cells, but outside of the hotly cells, we see these weaker cells that in fact are indirect. And what I mean by indirect is that they are circulations in which relatively cold air goes up and relatively warmer air goes down. You need to do work to make this happen. And in fact, these cells are not thermally direct. They are indirect and they are completely driven by eddies, large scale eddies in the extra tropics. And again, I will, at one point, go to the board and try to develop at least two, just by looking at the zonal momentum, but with some arguments to try to understand at least the direction of the upper level flowing the ferrule cells and how those cells are really driven by large scale eddies and how they transport momentum in the meridional direction. To make the connection with the near surface winds, the hotly cells occupy the latitudinal belts where the surface zonal wind is easterly, no big surprise, below the ferrule cells. We have surface westerly flow. We have talked very little about clouds in the summer school. I won't really talk about clouds today, but I really would like to mention those are really understanding cloud processes has proven very, very hard. Even the sign of cloud feedbacks as the climate is changed remains poorly understood and poorly constrained, but it is clear that the tropical overturning impacts fundamentally the clouds and different regimes across the tropics. And here the overturning both represents this meridional overturning associated with the hotly cell, but also zonal overturning. So if you fix latitude across, longitudes, for instance, associated with difference in surface temperature patterns, probably lengthy contrast and walker circulation. So in ascending motion regions, we find the development of deep cumulonimbus clouds as we move towards regions where the ascending motion gives rise to increasing inversions and stability. These deep clouds transition to shallower cumulus clouds all the way to stratocumulus clouds tend to be found over the eastern sub-tropical ocean. For instance, for those of us who live in southern California, the stratocumulus clouds tend to be very, very persistent. Sometimes it's really disappointing. You go to the beach in July and you find this completely overcast conditions. It was really a surprise for me when I first moved to southern California coming from Italy because I thought that summer was supposed to be hot and humid in southern California, especially along the coast. It's not necessarily the case. And in fact, in May and June, these stratocumulus clouds that can move thanks to the breeze that moving from the unsure flow from the ocean into the land. These overcast conditions sometimes can come all the way 30 miles, 50 kilometers inland, even to where I live in Pasadena. And this is very well-known for southern California. It's called May, Gray, and June gloom because conditions are really very, very gloomy. Again, this is, I think, all I will really say about clouds. But at least I did say something. And let's move back to the distribution of the annual mean precipitation. And of course, I think that we somewhat understand, again, how the large-scale Hadley cell controls this alternating part of wet, dry regions. But of course, this is only true in the zonal mean. If now we start looking for any specific latitude, at changes in longitude, we find that these changes are pretty remarkable. For instance, 25 degrees north, just to peak one latitude, you see that over Asia, East Asia, it tends to rain a lot in the annual mean. And yet in Africa, Saudi Arabia, California, it tends to rain very, very little. And of course, I cannot argue that all these zonal asymmetries can be explained through the seasonal cycle and temporal variations. But at least some of these variations are explained, indeed, by the fact that especially over subtropical land masses, we tend to have very strong seasonal cycle of precipitation. And so to show you this, let me now show you the corresponding long-term map of precipitation for the month of July, northern hemisphere summer, and the corresponding one for January, that is, southern hemisphere summer. I'm going to be toggling for a few times between the two. First of all, look at the Pacific Ocean. There you see that, of course, there is a seasonality of precipitation, but that is quite muted. But in terms of changes in intensity and position of rainfall, in particular, notice how over significant stretches of the Pacific Ocean, maximum precipitation remains north of the equator even during southern hemisphere summer. That is, maximum precipitation is not always following the maximum insular installation. But now I want you to focus over subtropical land mass. Pick the one that you like the most. Pick India, pick Western Africa, or somewhere in the southern hemisphere. And I'm going to be pointing to the South Asian mountain region because I spend a lot of time thinking about the climate of this region. But look at how there the seasonal cycle of precipitation is quite remarkable with very, very dry winters being followed by the opposite direction being followed by very, very wet summers. So it's really this seasonal migration of the primary convergent zones in the tropics where precipitation tends to be concentrated into the subtropical land masses away from the neocotorial ocean that now we understand is really the manifestation of the development of monsoonal circulations there. And one point that I really tried to make evidence about these hours is really the fact that despite the fact that for decades monsoons were really defined as systems with seasonally reversing winds both at low levels and upper levels, highlighting more original character of monsoonal circulation that is now becoming quite clear that in fact monsoons really need to be interpreted as a fundamental part of the seasonal cycle of the overall returning circulation in the tropics and associated precipitation pattern. So let me try to make this point a little bit more clear right now, again, I think it will hopefully become even more clear later on. And so now let's look at what the Hadley cell looks like when we take a complete zonal average for the month of July. And these similar patterns have been shown by Jeff yesterday. Again, this is the global zonal mean. So we see that the equinoxial pattern that I showed you before for the annual mean conditions characterized by two cells that are almost symmetric above the equator is now replaced by a soustitial pattern which is completely dominated by a single strong broad cross equatorial Hadley cell. This is the winter cell. This is the southern cell that has strengthened and has moved its ascending branch in the summer hemisphere. There would be here also a summer cell but for the choice of contours that summer cell is so weak and narrow that you don't see it. And it's obvious that now here really most of the ascending motion is not occurring at the dividing line, the dividing boundary between the two cells but it's primarily concentrated in the ascending branch of the single cross equatorial Hadley circulation. So now let's go back to try to understand as to what the monsoons have to do with that. And so now again I'm gonna show you this map again because now I'm gonna do the same thing. I'm gonna try to compute a meridional overturning circulation and a caveat here is that of course when we do that over just the sector which means that I'm focusing only over the longitudes between 60 degrees in east and 100 degrees east where the Indian monsoon tends to develop in July there. We don't have a two dimensional non divergent flow. There are contributions to the mass balance through the zonal fluxes but at least for the summer months that tends to be a smaller contribution and so we're gonna try to define an overturning that develops just over this sector over the summer months and this is exactly what you see. You see that the development of the monsoona circulation is indeed associated with the development of a local strong and cross equatorial monsoonal Hadley circulation with ascending branch where most of the precipitation tends to be concentrated cross equatorial flow both at upper and lower levels and descending motion in the opposite hemisphere. So in many ways monsoona circulations really are cross equatorial Hadley circulations that projects strongly on the source to zonal mean and if you're interested there is a series of papers where we really try to make this case more strongly. I'll discuss some of this in a poster next week. One big difference that I would like to emphasize is that if now we look at the distribution of the surface zonal winds, zonally average over the entire long latitude circle we find that more or less everywhere in the tropics may be the exception of right at the equator the winds tend to be still Easterlies. In the monsoon sector you see that there is a strong reversal of the low level flow in the summer hemisphere from about the equator up to the regional strongest vertical motion low level winds in the monsoon sector are westerlies and we'll try to understand why that is the case. Okay, so these are the large scale circulations that I'll be focusing on and I'll try it now to go back to this question. So it is clear that within the ascending branch of these motions convective activity is plentiful. There is a lot of convection clouds precipitation development. So how should we think about this interaction? How should we think about how convection shapes or determines the existence of this large scale circulation vice versa? And I'm sorry, I will have to say that I won't be able to provide any alternative explanation than the one that Jeff provided because I think this is really the theoretical framework that has emerged in the past 20, 25 years and I'll try to clarify some points. Okay, so then in fact the tropical dynamics text books and literature to these days is dominated by statements that it's really the latent heat that is being released when water vapor changes face and condenses out that really provides the fuel, provides the energy that drives large scale circulation and perturbations in the extra tropics is really the fuel that allows for perturbations to grow in intensity and spatial scales. And so why has this thinking prevailed for so many years that is associated with the concept of conditional instability? And I'm hoping that you're all familiar with that. I'll try to briefly review what this implies if there is anything that is not clear, please, please ask. So this is a schematic representation of the sounding. So with the thicker line here representing in schematic temperature profile, this is what for instance radiosounds and given locations would measure how temperature changes with height. On this diagrams we also are drawing some fundamental lines can be interpreted as processes. For instance this straight line here represents a dry adiabat. This represents how a parcel that lifted from the surface so the temperature, the rate of temperature with height of a parcel that lifted from the surface before it reaches saturation would follow and temperature decreases at a rapid pace because at higher pressure the parcel expands and undergoes an adiabatic expansion before it cools off. And the nice thing about the dry adiabatic lapse rate is that it is really just a constant. And I'm gonna put a minus sign here to make this a positive number. This represents again how temperature changes with height following a dry adiabatic expansion and that is equal to G divided by Cp, Cp in the specific heat of contents pressure for air and this is about 9.8 Kelvin per kilometer. It's really a constant that makes it very easy. When we try to define a saturated lapse rate that represents how temperature changes in a displacement in which a parcel goes up saturated we are not that lucky. We do not find a single number. This is something that changes with height. It depends on temperature, moisture constant content but let's say that depending on where you are this is about three to 6.57 Kelvin per kilometer lowest where you have more moisture lower down. It becomes a little bit harder now you're higher up and then as you really start going up and up and up because you're getting rid of all the moisture at very high at very low temperatures then the saturated lapse rate approaches the dry adiabatic lapse rate. This is the moist adiabat that is drawn here and we schematically represent it by this line. The important thing here is to remember is that of course it is less steep which means this number is smaller than the dry abatic lapse rate because as a parcel reaches saturation above its lifting condensation level then any excess of water will have to condense out and so latent heat will punctually compensate for the cooling associated with the adiabatic expansion. Okay, so now let's consider a parcel that starts from the surface unsaturated and let's see what happens if we displace it at any height below this level here which is called the level of free conduction. Again, before it reaches saturation the parcel moves along a dry adiabat. So let's suppose that we place it here is the parcel colder or warmer than the environment? Again, the environment is this thicker line. The parcel is following a dry adiabatic lapse rate. So is it colder or warmer than the environment? Colder, right? So it will want to sink back. Okay, then let's introduce a larger perturbation. Let's suppose that you can lift it above the lifting condensation level and then we place it here, right? After the lifting condensation level it starts following a moist adiabat. So again, I place it here. Is it colder or warmer than the environment? Still colder, so it still wants to sink back. So this is to say that we have to lift it above the lifting condensation level. I'm sorry, the level of free convection before it starts becoming positively buoyant and is allowed to freely conduct. One point that I really would like to emphasize is that if you take a parcel from any given height and you just displace it by a very small infinitesimal displacement, conditional instability, conditionally unstable profiles will always give stable displacement for small perturbations. To get conditional instability you really need finite amplitude vertical displacements. Of course, you have to do work before you reach the level of free convection. The work that you need to do in this schematic is represented by sin. It's called the convective inhibition. It's really the area between the temperature lapse rate and this process is describing how parcel goes up adiabatically. Whereas the cape that is the convective available potential energy that you can release and turn into kinetic energy of sun motion is the area from the level of free convection to the level of neutral buoyance again of the difference between the environmental lapse rate and the moist adiabat. Okay, so when we started taking soundings back in the 1950s most of the soundings were of course over land areas and in particular over the south center, mid-eastern United States you find soundings like this that do have significant amount of convective inhibition. Then this really has led to believe that convection that really has led to the belief that convection in most of its forms is triggered which means you again have a large enough perturbation that can overcome the sin and then let the cape be released. This also implies that cape can build up with time through large-scale or radiative processes before it is actually released. And in fact, the large amount of cape, again, I don't wanna emphasize that they never occur. They do occur especially over the continents. Large amount of capes are for instance seen in very severe storms such as rotating storms that for instance generate the supercells that generate tornadoes. But let me emphasize how the evidence, the unambiguous evidence of condition and stable profiles really only have been shown to exist in continental areas. Okay, so the concept of cape being able to build up has really allowed to be thinking that it is that source of energy once convection is able to get going and the associated late and heat release that can drive larger-scale flow. And in this view, you really are treating the late and heat release as, yes? Why condition and stable? I'm gonna, do you mind if I answer the question in just the following slide? Yeah. The prevailing thinking now is that no, the tropical atmosphere, especially over oceans, soundings are close to being almost neutral in a moist sense. And there is several evidence building on that. And again, the point that I will try to make is not that cape is necessarily zero, but the rate at which cape changes is very, very small. Which means that whatever cape is made available again by larger-scale processes or radiation, convection consumes it pretty rapidly. At a timescale that is much smaller, then again, the large-scale over which larger-scale radiation slower processes can create cape. Okay? So again, the fact that late and heat can in fact provide energy for the drive large-scale flow implies the late and heat typically exceeds the energy required to maintain the kinetic energy of the large-scale motion against dissipation. And of course, this view really emphasizes how that late and heating can lead to kinetic energy production. But again, here at the point that is really missing is that for this conversion to happen, you need positive correlation between vertical velocity or heating fluctuations and temperature fluctuations. And there is no reason to believe that when you have an interactive system as larger-scale flow and convection, that correlation is always, always positive. In fact, late and heat release is really largely primarily balanced by radiative and antibiotic cooling. As you start developing convective-scale upward motion, those can be locally very, very strong. They consume the cape, but everything else around the conductive down drops, the up drops that in fact occur in very, very small fractional areas, you have the sinking motions of the nearby atmosphere. So really, any residual is really just a small percentage of this large compensating term. So there is very little that is really being left to drive large-scale motion. So how then should we be thinking about the interaction between convection and large-scale circulations? This is what is called convective quasi-equilibrium. I should mention that this way of thinking, of course, led to the development, for instance, of convection parametrizations that are being used in climate models. And really, this line of thinking is reflected in convection schemes that parametrize precipitation in terms of moisture flux convergence, with the idea that it's really the latent heating that drives the flow, that provides the moisture convergence, which reinforces the latent heating. And in fact, it has been shown that those convection schemes are really ill-posed and they lead to inconsistent, for instance, water vapor, but yep. May I ask a question at this last point? Yes. Essentially, if I think about the thermodynamic equation, whatever q on the right-hand side is q, what you're essentially saying is q is very small. No, the q is large. It is large where you have latent heat release. But again, it's basically primarily balanced by strong vertical motions with adiabatic cooling resulting from this strong vertical motion in very small areas. Is exactly what Jeff very nicely draw yesterday, the fact that again, most of the strong vertical motion in cloudy updrafts occur over a fractional area that is as most 10% and everything else has very slow sinking motions nearby. And you can reach an equilibrium where, in fact, this balance is exact. You don't need any additional large-scale accent. The accent is occurring in the narrow updrafts, it's consuming all the cape that you have, it's releasing latent heat, but you need, on average, you don't need to have a mean vertical ascending motion associated with a larger-scale perturbation. So you have that w here that told me that would be the large-scale vertical motion. So if there's q and if there's a stratification from convection, there's a reciting vertical motion. Yes and no, because again, the adiabatic heating, it depends, of course, on how you define it, but of course you have balancing cooling outside of the convective updrafts. In the area, every heat is balanced, but the differential means that they are spatially different when heating. You have to impose, but you have to impose, exactly, you have to impose the spatially varying differential heating. If you don't have it, even if you have a conditionally unstable sounding, it's again, it is all consumed at the convective scale, but you don't need to drive any larger-scale circulation that is driven by the diabatic heat release. Yeah, if heating involves rising motion. Of course, but the heating, yes. Okay, can I get back to that? And this thinking about the dry thermodynamic budget and that is something that I hope to get to maybe in the second hour is somewhat misleading, especially when you think about tropical circulations. And again, by what I mean tropical circulations, I'm thinking Hadley circulation, Monsonna circulations, because of course, here you need to know what the diabatic heating is, which means you need to know the precipitation. Sure, there is outstanding literature that for instance, by using linear wave dynamics, shows how if you know the imposed, the latent heat pattern, if you know, for instance, the precipitation distribution, through the dry thermodynamic budget, you can, for instance, understand some aspects of the large-scale flow that is consistent with this heating pattern. The problem is that when you perturb the system, because the precipitation is strongly linked to what the large-scale circulation is doing, you don't know what to do with Q. And so now the prevailing thinking is that it's not the dry thermodynamic budget that we should really be thinking about is the moistatic energy budget that we will see by summing the vertically integrated thermodynamic and moisture equation gets rid of this. The largest, but canceling terms of again, diabatic heating associated with the latent heat release and convective moistening. Okay? And again, I hope that, keep the questions coming, but I hope that, yes, Miigata. Can you repeat what you said about the probably mass convergence-based convective parameterization? Yeah, so those, for instance, they do not really, so that they're basically closure assumptions that are based on the moisture budget. They don't give a consistent moisture budget. They also, again, are based on this idea that the latent heat release is really associated with the moisture flux convergence. Again, external forcing drives moisture flux convergence that reinforces the latent heat and so on. And for instance, again, I wanna get into that because I'm really hoping to cover a lot of material, but so one of the ideas about, for instance, SISC, which is Conditioning Stability of the Second Kind, was trying to think about linear instability exactly the same way in which we think about linear instability, for instance, in the extra tropics, again, to think about how the presence of vertical instability associated with CAPCO, for instance, lead to generation of hurricanes. And it turns out that when you try all of this linear instability analysis, what you find is that the most unstable scales are always the smallest scale. They're always the convective scales. You never can find modes that grow because you have vertical and stable profiles that are on the large scale. In some way, all of those moisture-based, for instance, the COO scheme are based on, the closure based on moisture, and they neglect some fundamental terms in the moisture budget. So the moisture budget is not really concerned. So then, how we should be think about these interactions between convection and large-scale circulations. Again, this concept of convective quasi-equilibrium, I think, well, it actually dates back to our Kaua Schubert, 1974, but it was really conceptualized by Emmanuel Aral, 1994. So we really should be thinking as convection to be in statistical equilibrium with the large-scale environment. Again, the concept of statistical equilibrium requires separation between spatial and temporal scales over which convection acts. And again, spatial and temporal scales of larger scale processes, such as the large-scale flow or radiation. So convection really acts on very small and very fast time scales. And what this means is that as soon CAPE is made available or is produced by radiation of large-scale flow, convection consumes it very rapidly. Again, we're talking about just a few hours. So this means that CAPE can be non-zero, but CAPE cannot accumulate. And in fact, its rate of change is approximately zero just to give you orders of magnitude for typical tropical conditions. In general, net surface fluxes and radiative cooling generates about this much, but CAPE values rarely exceed a quarter of that. And I hope that this answers at least part of your question, the fact that in fact, you never almost ever find over a tropical ocean's large amount of CAPES. And this invariance of CAPE with time, again, with the caveat that this needs to be averaged over time scales that are larger than the convective time scales, this is, that is true. So the fact that CAPE is largely invariant really has important implications for the temperature of convective atmosphere. So the way we should be thinking about what convection does, at least again, when we are considering large spatial averages, long time averages that moist convection, again, by being active, primarily almost all the time, really sets the temperature stratification of the tropical atmosphere and it maintains the free tropospheric temperature close to a moist adiabat. And this really closely couples the temperature distribution in the free troposphere to the moist energy content in the boundary layer. Yes. The statements that CAPE has consumed very quickly and then the rate of change is approximately. Say it again. The statements that CAPE has consumed quickly. Yes. And then the rate of change is approximately zero, feel like a contradiction to me. What am I just saying? I'm not sure, but let's just say that again, you have some instability and radiative and large scale process that we're talking about tens of days, more or less those are typical, either at active or radiative timescales. Radiation tries is always destabilizing temperature profiles, but as soon as CAPE largely increases, convection is quick at removing that. That's really all I'm saying. I'm saying that again, if I now consider how CAPE changes with time, because convection is a fast process, this rate of change is zero. Does it make sense? And again, the important thing here is that of course, we cannot be looking at this time derivative cannot be taken over the rate over which convection is developing and consuming CAPE, it needs to be larger than that. So it's really, this thinking really applies to large scale circulations. Even for instance, when we start thinking about, again, a lot of this has informed that it orbits very same fact, some convective finalizations that preceded this theoretical arguments use more or less similar approaches. Derakawa, Schubert being a convection scheme being one example. Again, for instance, one thing that quasi equilibrium convection schemes don't do well is for instance, the diurnal cycle. So when we start looking at the diurnal cycle, there is obvious this is where things already start breaking down because of course, there is some memory in the system. In general, the convective quasi equilibrium schemes will give you a convection that starts around noon, whereas especially over land convection is a little bit delayed. So obviously, there is some delayed, there is some trigger, there is some in that respect that convective quasi equilibrium schemes do poorly. But at least when it comes to thinking about again the interaction of larger scale circulations such as the Hadley and Monsonla circulations on, even time scales over a few days, these approaches work well. Yes. Does this only apply? Can I get back to that? So this statement is really true in the deeper tropics but thanks to the weak temperature gradient approximation that Jeff was discussing, that temperature stratification that being set to follow a moist study about in deep convective regions is spread out to remote areas. And in fact, Jeff showed how remarkably uniform free tropospheric temperatures are in the tropics. Okay? Keep for there being free tropospheric temperatures. Free, not the boundary layer. The boundary layer and in fact, the tropical Pacific is a clear example of where you can have very strong sea surface temperature gradient between the eastern and the western tropical Pacific but there you're happy because you have additional terms that for instance arise from what friction does and turbulent motions in the boundary layer that can give two large deviations from the weak temperature gradient approximation. Okay, but I'll try to go back to this point in a minute and to talk about what temperature looks like in the, for instance, in a cross equatorial Hadley circulation. Okay, so here I am really condensing in two statements a lot of theoretical development and I'll spare you that because I don't think it's really important but here the point that I would like to make is that in this view, again, what determines the moist adiabatic lapse rate is a much moist energy you have in the boundary layer that is how warm and moist a parcel is when you lift it up. That sets the moist adiabatic. And so a qualitative statement on that association is that changes in free tropospheric temperatures are really in equilibrium with changes in the boundary layer of moist static energy. I think I have an equation but let me rewrite moist static energy here. I'm really sorry but moist thermodynamics is really very confusing. There are more variables than letters of the alphabet and so the moist static energy is sometimes referred to as M, H, many other symbols but it's really the sum of dry enthalpy. We are familiar with that. CPT plus potential energy. GZ that is not an important term in the boundary layer tends to be small but it's really important higher up and plus you have latent energy, LVQ. It turns out that this quantity is really important because from a parcel perspective, it is conserved if you follow adiabatic displacements that are also are in hydrostatic balance and also it turns out that this is really the relevant energy for a moist circulation, okay? So it has two important interpretations. So schematically, what do I mean by saying that the stratification is really set or is in equilibrium with changes in the boundary layer moist static energy and this is the statement that upper free tropospheric fluctuations in free tropospheric temperatures are a couple to changes in moist static energy. In fact, if you really want to be more precise you should use moist entropy but moist static energy is the linearized version of moist entropy. So let's suppose that we start from a situation we are over a tropical ocean, nothing is happening, right? We have very, very shallow, maybe some clouds but those are not deep clouds. Moist static energy in the boundary layer in equilibrium with the upper tropospheric temperature. Let's suppose that now some perturbations, for instance, in the surface fluxes or other perturbations lead to an increase in the boundary layer moist content. Now you are in this equilibrium, you have a lot of moist and warm air sitting below. If you want to go up, it gives rise to the development of deep convective clouds and now convection heats the free troposphere. That's exactly what convection tends to do and a lot is also in fact due to the compensating descending motion in surrounding areas because in reality the convection does also something to the boundary layer moist energy. The warning of the free troposphere is not exactly in equilibrium with the change in the boundary layer moist static energy because there are down drafts that are evaporatively driven that slightly cool off or reduce the initial perturbation in the moist static energy in the boundary layer but at the end of the process, again, what convection has done, we don't need to know anything about the latent heating but really what, again, this has been dissipated but what convection does, it restores temperature in the free troposphere to be in equilibrium with boundary layer moist static energy. So you are, again, in a situation where you do not have any conditional instability. It has all been released by this convective process and the only thing that we care about is, again, the fact that upper tropospheric temperature, the stratification of the upper tropospheric temperature is really set up to follow moist static and he's in equilibrium with the boundary layer moist energy content. So let's try to apply this to the concept of a cross equatorial hardly circulation. This could be the annual mean hardly cell, this could be a monsoonal hardly circulation. I'll show you why this is the case but the polar boundary of this cross equatorial circulation coincides with the maximum in upper tropospheric temperature which means that because fluctuations in upper tropospheric temperature are tied to fluctuations in the moist static energy in the boundary layer, the boundary of this cross equatorial circulation also sits where the moist static energy in the boundary layer maximizes. Most of the ascending motion is just a equator word of the simple or boundary of the circulation and so the precipitation will be just slightly equator word of the maximum in moist static energy. Because, again, notice that again, this is a situation where how much moist and warm air is in the boundary layer, more or less sets where convection is developing in the ascending branch of this hardly circulation. Again, this sets the temperature structure of the upper troposphere in the convective regions but because, again, temperature gradients tend to be weak, they are spread out both through the influence of this overturning circulation that exists to transport energy where you receive more energy to where you receive less energy. The temperature structure is communicated. You have very weak temperature gradients outside of the boundary layer and now you have very stable conditions from in the descending region, from where you have much lower moist static energy in the boundary layer and a very warm and a very dry air above it. So this coupling between boundary layer and moist static energy and the temperature of stratification is really true only in convective regions but that thermal stratification in the free troposphere is communicated elsewhere. The important point here that I would like to emphasize is that to the extent that monsoons are viewed as cross-ecotorial hardly circulations that should not be thought as being driven by the near-surface temperature gradients. If there is anything that you care about is the moist static energy. You might wonder, well, but the distribution of moisture is strongly tied to temperatures that is too over the ocean, it's not too overland. So it's not necessarily the case that temperature and a moist static energy gradients always go together and I'll try to show you a couple of examples before we break. So we all studied monsoons. This is in fact how my older son learned about monsoons as part of his science curriculum in fifth grade and I tried to argue with him and then he said, oh, but my teacher said so and so I have to stop and couldn't confuse him anymore but if there is one thing that I hope you will remember is that this view that you find in a lot of textbooks is wrong and I'll try to say why it is wrong but again we should really not be thinking as monsoons as sea breeze circulations that are primarily driven by contrasting thermal properties between land and the ocean because this view really emphasizes the importance of the near-surface temperature gradients during the summer, land heats up faster than the ocean because it has much smaller heat capacity therefore the resulting temperature and pressure gradients drive the flow towards the land. These are flow with a lot of moisture, supports precipitation in the winter, the cycle reverses. The emphasis on the near-surface temperature gradients can lead to very wrong predictions about the behavior of monsoons. So how should we thinking about Hadley and monsoons as regulations? We should really be thinking about the fact that they exist because you need to transport energy from regions or hemisphere for the matter where you receive more energy to regions or hemispheres where you receive less energy. And this is what we for instance see in the annual mean. This is a very schematic representation. The southern cell is a little bit larger and stronger, broader I should say. Then the northern cell, the ITCC sits in the northern hemisphere. Again, the relevant quantity, the relevant energy that is being transported by the moist circulation is the moist static energy. Notice how the moist static energy has a minimum in the metroposphere and that is because if we were in a dry atmosphere, the only thing that matter would be the dry static energy, CPT plus GZ, which goes like this. But because in a moist atmosphere, we care about the moist static energy that also includes the presence of latent energy and because moisture is primarily confined in the bottom, then you get a profile that more or less goes like this, which is what I dematically depicted there. What this means is that if we think about a hotly cell as more or less it's always the case as characterized by lower level branch and an upper level branch that are confined to thin layers close to the bottom and top boundary, then the effective stratification of this moist circulation that is the difference of the moist static energy at upper levels and the one at lower levels is not as large as the one that you would have in a dry atmosphere. Okay, so what this means that, well, first of all still because of the GZ term at higher level because both temperature and moisture decrease with height, the GZ term wins out. So you have more moist static energy at upper levels and lower levels. So this circulation is thermally direct in the sense that it's transporting energy in the direction of its upper branch. And so that is why, I'll say why, but in general Northward shift deposition of the ITCC corresponds to energy transport by the hotly circulation away from the ascending branch in the opposite hemisphere. And let me go back to this point is that the fact that moist circulations have a weaker stratification than dry circulations implies that everything else being equal to accomplish the same amount of energy transport, a moist circulation will have to be much stronger than a dry circulation. That is something that F asked to the group or groups who are working on the comparison between moist and dry hotly circulations to verify. But there are, again, very simple physical arguments for which we really believe that that is the case. That is to say that moist circulations are less efficient at transporting energy than dry circulations. Again, because moist static energy is positive stratified, hotly and monsoona circulations in general, that's a big caveat, there's a lot that we're learning about the extent to which this statement is always true and this is very active research being done right now. Monsoona circulations transport energy in the direction of the upper level flow and the fact that the ITCC is shifted into the North and Hemisphere implies that the North and Hemisphere receives more energy than the Southern Hemisphere. And it turns out that is primarily through the transport of energy by the AMOC, the Atlantic Meridiano Returning Circulation. The atmosphere needs to compensate for that by transporting energy in the opposite direction and it does so by shifting the ascending branch of the animal mean hotly cell. So I'll stop here for five minutes. I'll provide some evidence of to what extent these arguments really are verified in observations in monsoon regions and then we'll dive a little bit deeper into modern thinking of monsoons.