 Okay, so we are discussing the angular momentum budget that can hold in the upper branches of circulations that are angular momentum conserving when the Rossby number approaches one, and where they are driven by eddy stresses when the Rossby number is much less than one. Again, let me re-emphasize this point again, it's important. When a cell which conserves angular momentum starts becoming cross equatorial, we have this upper level easterlies that develop over a broad region in the tropics. The eddies that do transport, effect transports of angular momentum are barotropic Rossby waves that propagate in upper level westerly flow. So there is already a hint here that cross equatorial hardly circulations might be more angular momentum conserving because the appearance of upper level easterlies shields them from eddies originating from the winter hemisphere higher latitudes. Okay, so then let's go back, questions? No, let's go back to the aqua planet simulations and here I am looking at a lot of fields and I know that this is a very packed slide, but here the important point that I want to emphasize, this is what the circulation looks like before monsoon onset and before monsoon onset here, I really mean that this very short lived time, this is of course the shallow, makes their depth simulation where things are more or less symmetric about the equator and after monsoon onset I'm picking a time where the monsoon is really well developed. So again, going back to what the circulation looks like, notice how here when things are symmetric about the equator, the circulation is characterized by two cells that again are almost symmetric about the equator. The southern cell is a little bit stronger than the northern cell. Notice how the gray contours represent angular momentum contours. We said that a circulation that conserves angular momentum is such that angular momentum contours and streamlines are aligned. We clearly see crossing of angular momentum contours by the circulation, so the circulation is not angular momentum conserving and in fact the color contours that show at the momentum flux divergence in red and convergence in blue clearly show that this cells are in fact very much in the limit of a small rosby numbers, eddy stresses really constrain the strength of the circulation, these are again the large scale eddies originating at higher latitudes, they propagate in region of upper level, questily flow, once they start approaching the critical line, the zero inline the break, and again they extract momentum from this flanks of the circulation and they converge to higher latitudes. So let's see what happens, just more or less 20 days after, I think it's 25 days after this snapshot and notice how in 25 days that the circulation really has changed quite rapidly from this more equinoxial pattern to this social pattern characterized again by just one single strong cross equatorial Hadley circulation. Points to notice is the fact that if you can see angular momentum contours now are not vertical, which is what you expect if angular momentum is dominated by the planetary component, but in fact they are, they take a horseshoe shape and they follow at least in the ascending an upper branch of the circulation, they primarily follow the stream lines of the flow. So this is a circulation that approaches way more strongly conservation of angular momentum. So why, why is that the case again, the fact that as the circulation becomes cross equatorial upper level easterly start appearing really plays a very important role because again the circulation is shielded by the zero inline from the influence of the eddies. So most of the, especially where the circulation reaches its maximum, it's really in a region where there is very little eddy momentum flux divergence. And so here the argument is that these monsoon transitions that we see in the absence of any lengthy contours that are really driven basically they represent transitions in the leading angular momentum budget in the upper branch of the cell from an eddy driven regime where again the circulation is really slaved to the eddies to a regime that is much more angular momentum conserving in much better agreement with the angular momentum conserving theories that Jeff discussed. So the question is why is this transition so rapid? Why does the circulation intensify so rapidly? In these simulations there is two feedbacks that operate on very short time scales. Again the first one is associated with this interaction between the mean flow and the eddies as the circulation becomes cross equatorial and the upper level estuaries develop. The estuaries shield the circulation from the eddies and so the circulation can become more angular momentum conserving. As it becomes angular momentum conserving you really shift to a much more non-linear dynamics abduction by the circulation really becomes dominant. Again remember that from angular momentum conserving theories as the circulation becomes cross equatorial you develop through thermal wind balance this reverse meridional temperature gradient. So temperature maxima are not found near the equator they're in fact the minimum in temperature near the equator and a maximum at the location of the poor branch of this circulation through convective quasi equilibrium arguments these upper tropospheric temperature structure is related to the lower moisturistic energy structure. We clearly see this the equatorial minimum is not. So I mean it's not really a minimum but you definitely see a much larger values in moisturistic energy in the boundary layer in the subtropics with the edge of the heavily circulation is. And so now as we start developing this reverse meridional temperature gradient in the lower branch the circulation itself through abduction of temperatures really allows very rapidly to push forward even further forward this maximum in the moisturistic energy. That is to say that the circulation can intensify and broaden very rapidly. And again here the key is not the fact that land warms up faster than an ocean because we don't have the difference but it's the fact that the lower boundary that here it says swamp really can allow for this rapid shifts in the distribution of the moisturistic energy and in fact can help push the maximum in moisturistic energy at subtropical latitudes and with it the upper branch of the circulation associated precipitation patterns. I had a question before asking to what extent this maximum coincides with the maximum in solar insulation it does not. Solar insulation maximizes at around 23. This maximum is in fact occurring at about 30. Later in the simulation it actually goes all the way to 30 degrees north. So here the interaction and the advection provided by the large scale circulation becomes dominant. And again this is also a caveat in this argument is that really emphasize the fact that we need to know the distribution, gradients, maximum, moisturistic energy to say something about the large scale circulations is that because this is a couple problem it's really provides that a mechanistic but not a prognostic view of monsoons. We have to run simulations or diagnose fields to be able to look at these interactions. It's very hard to make any prognostic arguments based on this. Okay, so very very short summary. The aqua-planet simulations suggest that rapid monsoon onset and end correspond to transition in leading angular momentum budget in the upper branch of the cell from an equinoct regime where the influence of the eddies is large and really the circulation is constrained by angular momentum budget to a monsoon circulation where the role of the eddies is minor and the circulation can approach more closely conservation of angular momentum. As a caveat this is based on an aqua-planet, right? And it totally neglects zonal asymmetry so I think that there's gonna be more discussion next week at the workshop as to how these mechanisms should be modified to include zonally asymmetric, sorry, asymmetric continents. Oh, sorry, zonal asymmetric continents. No, this is Katrina's talk, sorry, yes. So this is right. So more discussion about what happens when you start introducing some lengthy contrast and to keep things simple we just impose a continent that is completely zonal symmetric but then how these mechanisms are also modified by the presence of stationary eddies that are completely neglected here when you do have zonal asymmetries. And also I have a poster on what we discussed a little bit what is the observed angular momentum balance in the South Asian monsoon. Whether this transitions from a more linear to a nonlinear angular momentum budget is also in the observations. Okay, so then the other thing that I wanted to do because I'm sure there's gonna be a lot of discussion next week on the more static energy budget is, okay, we said that to the extent that a circulation is completely angular momentum conserving, the zonal momentum budget reduces to a trivial balance, zero equals zero, that is verified for any strength of the circulation. So what constrains the strength of the circulation? And so a lot of progress has been made in that by using the more static energy budget. But again, it's really the relevant budget for moist circulations. And in fact, in many ways, it's really the theoretical development to this quasi equilibrium views of the interaction between conduction and large scale circulations that I discussed earlier. So how do we obtain a more static energy budget? We talked before about the dry thermodynamic budget. So that is the, just the first law of thermodynamics. Jeff, I'm sorry, but I'm gonna use primitive equations here. Sorry, pressure coordinates, I should say. So the first law of thermodynamics can be written. So I'm just rewriting in pressure coordinates, Cp, the temperature, d time minus one over rho, d pressure, d time equal to any heating rate, okay? This is the first law of thermodynamics we should all be familiar with. So when we write it in pressure coordinate, then we have Cp. I'm gonna expand the material derivative. We're gonna have a horizontal temperature grid, and it turns out that you can combine the vertical abduction of the material derivative on temperature and this term in just one single term that is equal to omega, which is the vertical velocity in pressure coordinate, omega being dp, d time. And then here what appears is the dry static stability. That is the ds, dp, with S being the dry static energy. We discussed a lot about the moist static energy. It's just Cp, t plus gc. And that is, I should have written it. Sorry, let's do this. And this is equal to the heating rate, okay? Again, this is stability, it's basically d theta, dp, linearized form of stability related to the Brunweiseler frequency. There has been a lot of work that is being done by using the dry thermodynamic pattern. Once you know the distribution of the heating rate and the distribution of the precipitation pattern, so look at what large scale flow is consistent and generated and driven by the diabatic heating. But again, the problem here is that it's diagnostic, but it's not prognostic. Again, once you introduce a perturbation, because the distribution of the precipitation is strongly influenced by the large scale patterns, there is nothing that this budget can tell you, okay? So then how do we make progress? Then we combine this. We're gonna vertically integrate this. And I'm gonna adjust the node, vertical integral like this. And I'm sure that I'm gonna miss a few things, but that's how we write it. Again, I'm just d time, vertical integrated temperature plus the, again, this is just the horizontal wind, so this is just the horizontal direction, okay? Plus the omega, the SDP term. And then what are you left with when you integrate the heating rate is how radiative fluxes or surface fluxes can change your temperature. And so we're gonna have the vertically integrated diabatic heating due to condensation, plus sensible heat from the bottom. And then you have a net short with fluxes. And here what I mean the net is the difference between the net at the top and the net at the surface. And then you have the same for long wave fluxes. Again, net difference between net at the top and net at the bottom, okay? So then we're gonna take the moisture budget and we're gonna do something very similar. We're gonna use it, again, these of course is written in energy units. We're gonna do the same for the moisture budget multiplied by the latent heat. So we're gonna do LV dQ dT plus the horizontal advection plus the vertical advection omega dQ dP. And this will have to be equal to sources and sinks, right? Sources minus sinks. Then you vertically integrate and then you obtain V ddt of Q plus the horizontal advection plus the vertical term. And then what are the vertically integrated sources? And sinks, you're gonna have the condensational moistening. We call it QM. And then you'll have evaporation from the surface. So latent heat from the surface, okay? Then we're gonna sum these two. We're gonna sum the vertical integrated dry thermodynamic budget, the vertical integrated moisture budget and we obtain the moist static energy budget. Let me call this equation one. This is equation two. Taking one plus two. We obtain the moist static energy budget. So we have a term which is the storage of enthalpy in the atmospheric column which is CPT plus LVQ. Okay. Then we have the horizontal advection of the same quantity, vertical integrated CPT plus GZ. Sorry, the vertical integral is here. And then we're gonna have a term that represents the vertical advection or a favorite quantity which is moist static energy because it's the sum of the dry static energy coming from the dry thermodynamic equation and moist term. Say it again? No, I'm sorry, I'll do, sorry, yes, yes. There is no GZ there, yes. There are, there are different ways in which the moisture budget is derived. Some start from a statement that moist static energy is conserved. At the end you get to something similar but this is really the correct way to derive it and in fact in the advection and in the storage you don't have the GZ term. If you start from a statement that moist static energy is conserved materially then you have the extra GZ term. Doesn't make much difference that is a very smoothly varying term but that's the correct way to derive it. And then when we sum the sources and sinks of energy terms we're gonna use the fact that these terms that are the largest terms that appear in the dry and moisture budget actually cancel each other. So we're gonna use the fact that the condensational heating which is equal to LV multiplied by precipitation is equal to minus the condensational mustening. So the two are the biggest term in the individual equations but they cancel each other so they completely drop. So now we don't have any information that is related to the diabetic heating anymore and the sources and sinks are really our sunsets and sinks of a moist static energy coming from the top of the atmospheric column and the bottom. And so these are going to be equal to what we call the F net or net energy input into the atmospheric column and these are equal to basically the top of atmosphere radiative fluxes. Again, those contain the downwelling shortwave and the up going longwave minus the surface fluxes and the surface fluxes in addition to the radiative fluxes also contain the latent heat and the sunsets here. Is it clear? So we're really just saying that whatever is the net energy input that can enter an atmospheric column through radiative fluxes at the top and radiative and turbulent surface enthalpy fluxes at the bottom will have to be balanced by these other terms that are associated with how the dynamics respond. So it's really again bypassing this the large diabetic heating terms and it's really related large scale to the energy sources and sinks in a vertically. Integrated sunsets. Okay, so then approximations that are usually used in the most static energy budget are the following. Study state, so we neglect any storage. So we're gonna assume study state. We also are gonna make use of the weak temperature gradient approximation to at least to a first order drop the horizontal advection terms. Notice how the weak temperature gradient is of course justified for temperature is less justified for moisture. We're gonna say that we're gonna do it, okay? We're gonna drop that. And so then the balance that we have so study state, weak temperature gradients, then we are going to say that the leading balance and that is true in the deep tropics is between the vertical advection of more static energy and the net energy input. Again, if this is my atmospheric column, the net energy input is whatever it comes through the top and the bottom, okay? We also are going to assume that in the tropics, so far I haven't introduced any time averages. I've been a little bit sloppy about that, but we are gonna assume that in the deeper tropics, really the vertical advection is not dominated by eddy covariance is between vertical velocity and H. It's primarily dominated by mean vertical motion. So again, I'm gonna now put the bar and assuming that the HDP bar, this positive is stratified exactly as I showed you before, the fact that H tends to be on average, larger at upper levels than at lower levels, which means that in pressure coordinate, this will be negative. Then what this balance is really stating is that whenever the net energy input is strong as positive, what the atmospheric circulation will do, which means that you are actually gaining heat through the top and the bottom, the atmosphere will respond by diverging energy away through the development of vertical motions, such that omega will also be negative. So the way in which the circulation responds is to develop strong vertical motion in the atmospheric column. If you assume, and that is also a consequence of convective quasi-equilibrium, that really the dominant vertical dominant mode is a mode in which the vertical motion is characterized by one simple structure with maximum in the metroposphere. And then you have lower level winds and upper level winds confined to relatively thin layers close to the surface and the bottom and they basically are opposite sign to each other. Then the picture that you develop is that you have lower level convergent motion. These converging motions are converging moist static energy that is smaller than the moist static energy that is being diverged away by the upper level motions. And so in this way, you can reach a balance again, by which the net energy input coming through the top and the bottom is balanced by the circulation that is exporting moist static energy through the development of vertical motion. Okay? D H by D changes sign. Yeah, and again, this is also where you're using the assumption that the horizontal winds are primarily confined to thin layer close to the top and the bottom so that when you take a vertical average it's really basically the difference between the H and upper level, minus the H at lower levels. And the H at upper levels is larger than the H at lower levels. There is a lot of caveats that go into this and that's where we also are right now moving a little bit away from convective quasi-equilibrium. To what extent this is also true that always true that convective motions have a deep first baroclinic mode structure. There is evidence in the tropical Pacific have in fact circulations in which the expert is occurring at a much shallower level where in fact you are close to the minimum in moist static energy and you can still have convective rain bands such as the one over the Eastern Pacific that in fact is importing rather than exporting moist static energy because again, in this case when the return flow is at lower levels, let's say mid levels where the moist static energy reaches the minimum the lower level converging motion is importing more moist static energy than the one that is being exported by the mid level motion. But these are things that are being exactly next week there's gonna be a lot of discussion about this. There are a lot of different definitions of a quantity which is the gross moist ability. I'm sure that the gross moist ability will be used extensively and the gross moist ability can be defined in many different ways but it's really is a measure of the vertically integrated export of moist static energy by whatever circulation that you have normalized by the mass convergence at lower levels. Again, here all these arguments are based on positive gross moist ability also called GMS but again, there is a lot of work that is being done these days to understand how good of a representation of many tropical rain belts. The assumption that gross moist ability always positive is. Okay, so another point that I want to emphasize that goes back to how we should really think about the, and I should mention that really the first paper that introduced the gross moist ability is also a quantity that is really powerful to, for instance, model tropical precipitation is kneeling and held 1987. And honestly, we haven't done a whole lot of progress since that paper in understanding what really controls the gross moist ability. It has to do with the interaction, reading convection and large scale circulation. Probably I gave you the idea that if we have all figured it out, it's all about convective quasi-equilibrium, in fact, it's really not the case. There is a lot of active work that is really trying to understand where all of these assumptions based on convective quasi-equilibrium really break down and when we need to consider the variation from convective quasi-equilibrium. Okay, so the other thing that I wanted to say, again, because it really, oh, maybe I shouldn't. Okay, I think it really makes the case for how the moist static energy is really the budget that we need to consider, for instance, when thinking about Manzono circulations is the following. Again, the net energy input is the difference between top of atmosphere radiative fluxes minus the surface fluxes. Okay, so the surface fluxes are also the ones that control the surface energy budget. So now I'm thinking about the surface energy budget of a mixed layer, but then we'll talk about that how that gets modified, for instance, over land surfaces. Let me call just big C the heat capacity of whatever mixed layer I have. So the surface energy budget is just the statement that storage, let me call it TS, in the mixed layer depth. So how temperature can increase in the mixed layer depth will be a result of the surface fluxes. And again, notice that the surface fluxes are taken as positive when they warm the mixed layer, that is the surface, we have to switch side when we consider what gets into the atmospheric column. And then possibly if you have ocean heat transport, there will be a convergence of ocean heat transport here. Okay? Okay, so over land, there is of course no transport. And also because the heat capacity of land is small, then this term on any time average longer than a few days will drop out, okay? So land is really different than the ocean in terms of this moist static energy view in the fact that again on time scales of a few days, the surface energy fluxes are constrained to be zero. Okay? So the net energy input into the atmospheric column is really dominated by the top of atmosphere radiative fluxes. Okay? And so for instance, this is why over months in regions you have through season and insulation forcing a strong source of energy through variations in solar insulation. Okay? And so it's the atmospheric circulation because no heat can go into the surface that need to redistribute those, that energy input from regions where you get a lot of energy to regions where you are losing energy. Okay? So that's why we get much stronger in solar circulations over land. It's really not the lensy contrast per se, but it's the fact that surface energy fluxes are constrained to be zero over land. Over the ocean, now a lot of that that comes from the top can be stored into the ocean. Or can redistributed through the circulation. So the ocean can dampen out the atmospheric response which cannot happen over land. So this is again, beautiful series of papers by two annealing. I never know how I'm saying two usual annealing early 2000s. And again, de-emphasizes again the view of monsoons has really driven by near surface temperature contrast which should really be thinking about moist circulations that want to export moist static energy. And we should really be thinking about them more through this view that emphasizes, relates the circulation to the top and surface atmospheric energy fluxes. Okay, so I am left with 15 minutes. I'm trying to decide what I'm gonna do. I think that what I'll try to do is be a little bit more clear as to the consequences of thinking about monsoons as really cross equatorial hardly circulations and also trying to tie back this energetic arguments to for instance the main position of the ITCC which is north of the equator and possible shifts during the monsoon season. Let me do one more thing at the board, sorry. The moist static energy, one flavor, it's really, I'm restating the same things that will make it a little bit more clear the connection between the moist static energy budget that I've just described with this view that is trying to link shifts in the ITCC position to cross equatorial energy transports if now we take a zonal mean and I'm gonna indicate the zonal mean in this way and I'm gonna also neglect storage although the storage could be in fact effectively included in the net energy input. The moist static energy budget has been can be rewritten as the meridional divergence of the zonal average of the vertical integrated total meridional moist static energy transport and this needs to balance the net energy input is exactly the same concept I'm just averaging in the zonal direction and again I am relating any region of net energy input to divergence that is export of moist static energy through the development of a divergent circulation. Okay, so now we can integrate from the south pole you can do the same from the north pole in fact up to a latitude theta and again it's the fact that at the south pole and at the north pole there is no meridional energy transport and so we can express the energy transport again here it's really the total you can decompose into an amine and a net decontribution at any given latitude theta has one over the cosine of theta of the integral from the south pole to that latitude theta of the net vertically sorry this is also zonal average I'm also gonna take a zonal mean of a cosine of theta in d theta again you can do the same from the north pole and this is really just to say that if the net energy input is completely hemispherical symmetric then you cannot have a cross equatorial energy transport you can have a cross equatorial energy transport only if you have a symmetry in the net energy input between the north and the south pole and these then going back to the schematics that is really relevant to many things including the northward shifted position of the ATCC in the annual and zonal mean again going back to why is the ATCC north of the equator is really related to the fact that there must be an asymmetry in the net energy input with the north and hemisphere receiving more energy than the south and hemisphere and the question is exactly what is it is it through top of atmosphere fluxes is it through surface fluxes has John discussed on Monday it's really not through the top of atmosphere radiative fluxes in fact the short word term is remarkably symmetric the long wave term in fact is such that if anything just based on top of atmosphere considerations you would expect the ATCC to be south of the equator the north and hemisphere radiates very efficiently in desert regions so again if the ocean didn't do anything the ATCC would be south of the equator and this is confirmed in idealized simulations that we've done in our group who recovered the north and hemisphere with just a very simple land and without any ocean heat transport the ATCC is sitting south of the equator so the reason why the ATCC is north of the equator is because the ocean heat transport is transporting energy in the Atlantic marionnel of returning circulation from the south and hemisphere to the north and hemisphere in fact in excess to what would be required by the top of atmosphere radiative imbalance and so now that excess of energy that is transported into the north and hemisphere by the ocean needs to be transported back by the atmosphere and the way the atmosphere does it again is by shifting the ATCC in the north and hemisphere and again here these are just showing schematics that are showed before again in this framework north which shifted ATCC position is accompanied by cross equatorial energy transport in the opposite direction because again the Hadley cell on average is an energetically direct circulation and transports energy in the direction of the upper level flow so this framework, Sarah was really influential in the development of this framework really emphasizes how the ATCC position is anti-correlated with the cross equatorial energy transport if we include any perturbation to this already is only a symmetric present day climate configuration that for instance puts more energy into the north and hemisphere than a more northward shift shifted position of the ATCC will be accompanied by an increased southward cross equatorial energy transport I'm sure that another thing that will be discussed a lot next week is the energy flux equator which is a proxy for the ATCC that again has been developed based on these energetic arguments again to the extent that the circulation has this structure more static energy has this very simple stratification then the position of the ATCC that is the dividing boundary between the southern and the north and cell is where the mass flux but also the energy flux will go to zero so the ATCC in this framework has been argued if not necessarily collocated at least covary with the energy flux equator again where the energy goes to zero from being southward in the southern cell being northward in the north end cell so this anti-correlation between the ATCC shifts and changes in cross equatorial energy transport has been shown to be robust in GCM simulations forced through different forcings this anti-correlation is shown here this is the annual mean ATCC change as a function of the changes in annual mean atmospheric cross equatorial energy transport and with the sensitivity of so you need to obtain a three degree shift in the ATCC position you need one petawatt of change in cross equatorial energy transport okay so let me emphasize how while this energetic framework has really been used extensively to understand annual and zonal mean shifts of the ATCC there's still a lot of open questions the first question is to what extent is even this zonal mean framework useful in the sense that two different forcings is it true that in different monsoon or ATCC regions is the zonal mean framework indicative or representative of any different sector means the verdict is still out there I don't think there is any agreement that has emerged yet and there is a lot of work that is being done with different GCMs more or less idealized of course again here we have totally exactly as I did for the zonal momentum budget we don't have any consideration of zonal fluxes zonal shifts in the precipitation so how do we extend this theory to account for those and there has been recent work that has taken steps forward in this direction and then the other big question is here really we're assuming that a big assumption in all these arguments is that shifts in the ATCC are primarily due to changes in the mass flux of the Hadley cell without any change in the efficiency with which the Hadley circulation is transporting energy and it turns out that that is not always the case we cannot assume that the gross moistability and the efficiency of energy transport is always constant this is work that Sarah has done looking at the response of the ATCC to CO2 forcing we've also looked at changes in the gross moistability through seasonal cycle with aqua planet idealized GCMs so it's important to keep in mind that again sometimes the Hadley cell adjusts to radiative perturbations again not by shifting its ICDC but actually changing it's hard to change the moistatic energy stratification but you actually can change the Hadley cell vertical structure for instance through the development of return flows that don't go all the way to the detroposphere at level where the moistatic energy is large but can in fact occur at the levels of minimum gross moistability therefore changing the sign of the gross moistability okay so in this situations then cross equatorial energy transport and ITCC positions are not associated or related in any linear ways okay or anti-correlation okay so if I can have two more minutes the final thing that I wanna do is talk about the existence of tipping points in monsoons two minutes it's not even my work but I thought it would be interesting so how we define tipping points so these are really really very somewhat broadly defined again we'll or can we expect that monsoons will shift rapidly from very different states let's say wet and dry states for small changes in radiative forcing past a critical threshold and there has been some work that has argued that as the total top of atmosphere of veto gets above 0.5 monsoons will totally shut down there is evidence in paleo records of rapid changes in monsoon I will also say that probably there's gonna be discussion next week as to what extent these paleo records are really providing evidence to rapid changes at a specific location or more gradual changes of patterns that have rapid spatial patterns so again this is something that is to these days being discussed in the literature so why should we be thinking that monsoons have tipping points and I think that the argument that has been used is the fact that monsoon onset is a very nonlinear process can these nonlinearities that act on the season hours of seasonal timescales also act in response to a given changes in enforcing and of course here the concern is that through land use changes maybe areas or maybe increased greenhouse gas concentrations the monsoon will shut down okay so of course usually the tipping points are studied in very simple models I won't present work from previous work but I'll primarily focus on recent work by Bill Booze and he used a simple model that is basically just the moisture energy budget that we have described actually has two equations for temperature and moisture, vertical integrated those should be thought as fluctuations in temperature and moisture again we have the vertical terms that represent the antibody cooling in the low level moisture convergence meridiano winds are assumed to be proportional to the meridiano gradient the sign is the low level flow simple closure for precipitation you have an heaviside function well let me first of all there is observational evidence that precipitation is strongly related to how much moisture you have in the column and then so precipitation increases with moisture in the column but decreases with temperature and if the temperature becomes too warm the column becomes too dry and then you have a relaxation time skill and a heaviside that first of all guarantees that precipitation is non-negative and again that tells you that when you have too dry and too warm atmospheric column precipitation will not occur no rotation, no non-linear momentum of action no evaporation so in this simple model actually you see and the solutions for precipitation is the blue and the solution for the wind is in red again when you combine these two equations in one single equation for you actually find that the relevant parameter is again the net energy input into the atmospheric column is this Q parameter here and again you see that there is no evidence of any abrupt change in the monsoon there are some maybe non-linear increase of V and P as Q is positive once Q becomes negative again this is the net energy input into the atmospheric column no precipitation and then the circulation reverses so how do we explain the absence of tipping points in the simple models with previous work that have argued for the existence of tipping points so previous models especially this paper by Leatherman et al basically used some similar arguments as the one provided by the moist static energy argument but they neglected some key terms in the resulting equations they neglected the vertical term in the dry static energy budget that is the adiabatic cooling that is also the vertical motion that sustains precipitation they also neglect completely the lower level convergence the dress retain the abduction bi-rotational flow of moisture and they argued that that is the relevant non-linearity for the monsoon so to test that that is indeed the case that it's really not accounting for these terms that are so important and that really represents our current understanding of moist circulations in the tropics so then here what is being done you take the same model and by basically pulling the dry stability the DSDP term that has cast before it to zero then you obtain the following solutions basically as Q decreases plus this threshold you basically your monsoon completely disappears okay so again here what I would like to emphasize is that again our current understanding of monsoons is not in line with the existence of tipping points and I'll stop here