 So I'll start by summarizing a bit the paleo context, which essentially means giving you some indication of what type of paleo climate change I'm interested in and which part of the last few million years we are interested in. I'll give a quick summary of the multiple state dynamics, and that's essentially a bit of a repeat of what Brian did yesterday. Then we'll get into the subject, which is what transition between multiple states that we have and their dynamics is interesting to interpret DO events, which are dense car, dense garr, OSGAR events. I'm going to define all of those terms in a minute. Then we'll switch to glacial interglacial cycle. I took a bit about stochastic resonance and how stochastic resonance and the use of multiple states can be used to interpret glacial interglacial cycle. And then there may be a bonus track if I'm not too late. So paleo climate context, as Brian mentioned yesterday, if we look at the Earth climate history over the last four billion years, Earth has been going through very, very different states, but we do have some indication of what were those states with some interesting information, at least over the last few million years, few hundred million years. So that panel shows what's called the neo protozoic, actually there's a spelling mistake, snowball Earth. So we think that at maybe 500, 700 million years ago, Earth went into a state where most of the planet was covered with ice or land ice or sea ice. Perhaps there were some openings in there, and there are plenty of questions about what were exactly those openings, because life made it through. So there was some place where life could survive. So there's plenty of interesting questions, but there's pretty certain evidence that the Earth climate was very, very cold and nearly entirely covered with sea ice. Closer to us, there was a state like the Cretaceous, where there wasn't any ice at all. So probably no ice at the poles, no ice in the Arctic and Antarctic. There are some indication that the equator to pole temperature gradient was weaker than it is now. It's very much subject to debate, but clearly the climate was very different. The deep ocean was probably way warmer than it is now. So nowadays, the deep ocean is just a few degrees, three, four degrees on average. Maybe it was 10 degrees, so it's a huge change. And that's an indication of where the water was formed. Well, they are formed usually in the coldest place at the pole. So the poles were probably warm. And obviously, we have the present climate, which has a bit of ice, but we live in a place where we are not entirely covered with ice. So we went through those three states. Oh, by the way, do you know how also we know that there wasn't any sea ice at the poles? Alligators, yes. Ta-da. Yeah. So apparently, there were alligators there and palm trees. And if we think that those alligators and palm trees are as they are, they are analogs nowadays, they can't survive if it's freezing. So clearly, it wasn't freezing at that point. And any time in the year it was freezing, that's also subject to a lot of controversy. But it would just take it for granted. So Earth's climate went through very different states. And perhaps it was driven by change in CO2. Perhaps it was driven by change in the continental configurations. Perhaps it was driven by the fact that Earth is endowed with multiple states. That's one option. If we get on a way shorter time scale, which is still a million year or half a million year, we have the glacial interglacial cycle. So that's a plot of temperature at the top of the Antarctic ice sheet. That's obviously a proxy. There isn't a thermometer there. There's a proxy that we think is measuring the temperature at the top of the ice sheet. And what you can see is that over Antarctica, there have been oscillations quite regular every about 100,000 years with changes in temperature of about 10 degrees Celsius. So it's a big change. And in fact, we have plenty of evidence that those oscillations or associated with large global scale change in climate. So in the North Atlantic, well, in the Northern Hemisphere, there were ice sheets over Canada and part of the US. There was an ice sheet over the Scandinavian countries, maybe going down all the way to the British islands. The global mean temperature was probably a few degrees colder than it is now. PCO2 was 100 ppm lower than it is before the industrial times. So massive changes. And the leading order of hypotheses for why those oscillations happened is that they are driven by the Milenkovich cycles. So the Milenkovich cycles are those oscillation of the orbital parameters of the planet. So we are talking about obliquity, which some of you are studying during the lab session. But also the precession. When is it that summer happens on the trajectory of the planet around the sun? Is it happening when the sun is far away or closer to the? Sorry, the planet is far away or closer to the sun. And finally, the eccentricity, which is a measure of how much of the trajectory around the sun is a circle or is an ellipse. We'll come back to that later in a minute. And then if you zoom on that period, what you find is that time series, which now is taken at the Greenland on top of the Greenland ice sheet, you clearly notice that there's way more noise in that first part than in the other. And it's just a sampling issue. The further bark back you go in time, the harder it is to capture the high frequency variability. But there is no reason to believe that the same variability wasn't happening in all the other glacial states. So during the glacial state, there is a lot of variability, at least over Greenland. And it has timescale of thousands of years. And you will notice that those oscillations, they go almost back and forth between the climate, the cold state, and the interglacial state, which we are living now. So it's almost 3 quarters of the way out of the glacial into a warm world. So they are very large, but they are probably mostly limited to the North Atlantic. So they are no longer global. Those are clearly of global scale. Those are probably more regional, at least in the sense of hemispheric scale. Although there is some signal associated to that in other parts of the world. So I'm just repeating this one, the last 100,000 years. If you zoom in and even further zoom in on just maybe one or two of those oscillations, what you see are called the DIO event, so Danzga-Hosger events, which have a very, very characteristic shape. So sorry, now time is going this way. So that corresponds to an abrupt warming, a somewhat slow cooling, sometimes abrupt cooling, and then a cold phase. So they all have that very characteristic shape of abrupt warming, slow cooling, which you find almost. If you zoom in on each of those events, you can spot that characteristic. So the interest of why am I pointing that out is that some of those transitions between a cold state and a warm state happens in decades. So they are extremely fast. Obviously, they are much faster than the characteristic time scale of the oscillations themselves. And a recurring topic when we talk about those climate change of the past, those abrupt, is how do you get those fast time scale? And that's where the multiple states could be a very useful framework to think about those fast time scale transition between states. So here, I'm just giving you an example of a multi-policilibrium problem. I don't know if you've ever done kayaking. If you've done, you know that that can happen. And you don't want to be there, but it's very stable. And obviously, Danzga is very nice. I mean, that hand looks like it's not moving anymore, but it's going to pull him out. So clearly, you also know that that state is stable. You can stay there as long as you don't mess around too much. So that's a stable state. That's a very stable state. And it may be a dead state, an infinitely stable state. I'll just give you an example of why those multiple states can be useful, because obviously, going from there to there is very fast. It's very easy. And you don't need to push a lot to get there, right? So if you think of flipping around, you don't need to have a force to pull you down all the way back with your head under the water to get there. You just need to go over some threshold, and gravity is going to do the rest, and buoyancy, whatever, and you're going to finish there. So one characteristic of that problem is that when you drive a system from one stable state to the other, you don't need to have a forcing that drags the system all across from one state to the other. You just need to pass over a threshold. And then the intrinsic properties of the system will carry you down to the next potential. So effectively, what you need to do for that ball to go there is just to move it here. The intrinsic property of the system will get it there. And that's a very firm fundamental difference between a system which has multiple states and maybe one which wouldn't have that, where you would need a forcing to drive the system from one state to another and maybe keep that forcing to stay there. While here, the system is using the intrinsic properties due to the nonlinearity. And this is just an example to show the abruptness of it. But essentially, it's giving you the same message as here. So by using those multiple states, we can, one, address a question of how do you relate the changes to the forcing and how the abruptness of the transition can be addressed, too. So that's why it's a fun link to make. Oh, OK. So can multiple equilibria of the climate system play a role in Earth climate history? That's clearly not a new idea. Many people have thought about that before, obviously. There is quite a long list of papers which have thought about using that nonlinear properties of the climate system to explain the variation of the past climates. A recurring problem when you try to do that is you have first to convince yourself that Earth's climate has multiple states, which is not a trivial matter, because we obviously don't have any record showing that the Earth's climate has multiple states, which we have or theoretical models or complex GCM to do that. So now if you look at simple models, analytical models, low-order models, it's quite easy to build those models such that they have multiple states. It's, again, a long literature about that. And I'm going to come back to that in a minute. If you look at GCMs, which is the next step on the complexity to build your confidence that multiple states could be relevant to Earth's climate, it gets way more complicated, because it's not easy to find them in a GCM. And Brian talked about that yesterday a bit. So just to clarify, when I'm thinking about simple, low-order model, I'm literally thinking about any models which have a couple of equations, like an energy balance model, which we have seen yesterday. GCM can take a very wide range of meaning here. So it can go from intermediate complexity. So typically, that could be models where the atmosphere is only averaged. So there are no ideas in that atmosphere. Sometimes the ocean is only averaged. Sometimes there is one basin. They would still be called GCM, because they have an ice sheet. They have a land vegetation. They have some information of the realistic distribution of continents. And in that spectrum, it can go all the way to state-of-the-art IPCC class of models, which may have an easier resolving ocean and are extremely expensive to run. OK, just a word about multiple equilibria, which have been appearing in the literature. And that's one which is important. It's the multiple state of the overturning circulation. So I'm assuming you know that there is an overturning circulation in the Atlantic Ocean? Yeah. Yeah. And there is not one in the Pacific? No. No, OK. A coffee, maybe. You need a coffee, guys. No? OK, so there is an overturning circulation in the Atlantic, which is depicted through that figure. So it's just showing the stream function of the zonally averaged flow in the basin. And to first order, we have warm, somewhat salty water coming in from the southern ocean, being carried all the way to the Nordic Seas, where they are transformed. So they are made more dense through lots of buoyancy at the surface. And some of that water is then still modified through entrainment and density current along the topography and exiting out of the basin at mid-depth, 2,000, 3,000 meters. And that's coming from a data re-analysis product. So people have thought about the dynamics of that overturning circulation and the possibility that that circulation has multiple states. Oh, OK. That was weird. And one famous model is the Stomall model. You might have come across that. It essentially describes the overturning situation as the flow over between two boxes. So there's a box in the low latitude where you have evaporation and a box in the high latitude where you have net precipitation. And in between, there is a flow carrying TNS properties. And the key in that model is that the flow between the boxes is proportional to the density difference between the boxes. So if it's dense here and light here, the flow will go one way and vice versa. Now if you write just a budget for that model, you can see that the flow of salinity is q times s. And q is itself a function of density, which is itself a function of salinity. So readily, you have a non-linearity in the problem because you're going to get s squared. And that's really all there is to get a non-linearity in the system, and that allows for multiple states. So this is an hysteresis diagram for that type of model. So what it shows is the intensity of the circulation between the two boxes as a function of the freshwater forcing, which is at the top of the boxes. And what you get here is that you have multiple solutions. There is a range of freshwater forcing for which you have multiple possibilities of the thermo-line circulation. The one which we care about more at this point is that branch. So it's a high-intensity overturning circulation. And there is a low-intensity overturning circulation. And that's a diagram. That's not an exact solution of that equation. But it's a recurring pattern you'll find in those type of models. And so this one is what is called the on-branch. So there is an overturning, and it's not small. It's transporting properties efficiently between the two boxes. And it's a thermal mode, meaning that it's driven by the temperature difference between the two boxes. There is a second limit where the circulation is way weaker and driven by the salinity difference between the two boxes. And there's a range of parameters where these two properties can exist. So why this is interesting is that, especially to interpret DO events, people have used that type of multiple state a lot. It was first introduced by Broker in the 1980s. But there is a very long literature of using this type of multiple state of the overturning circulation to interpret those climate change. And you can already see that it's easy to produce abrupt changes. And the overturning is transporting heat. So it's changing the climate. So it has a number of ticking box to be very attractive to paleoclimate to explain what have been observed. Those type of multiple state are quite easily found in coupled GCMs. So what people do, they call that water-ozing experiment. Essentially, it boils down to you take your model. There is an overturning circulation in that model. And you start to dump fresh water into the high latitude of the North Atlantic. So say you start your model, which has a high intensity overturning circulation. Let's say that 0.1. There is a fresh water forcing. And you artificially increase the fresh water forcing until the model drifts to the 0.2. And if you add even more, what's going to happen is that AMOKE is going to collapse into an abrupt event into a state where the AMOKE is very weak. You can carry on maybe pushing your fresh water forcing further, and then start to remove the fresh water forcing. But now you're on the lower branch. So you're going to move to 0.3 and carry on like that back to 0.1. It's very easy to do. And people have done that a lot in the coupled GCM. So that's a plot from an intercomparison project where many people have taken their coupled GCM and they've carried out exactly this type of experiment. So they drive the system through transition and back and forth. And they create those hysteresis diagram. And so many of those models have that type of hysteresis of the overturning circulation, which obviously has reinforced the interest that people have for this type of model. I should say that a lot of those models of intermediate complexity, meaning that one or two of their components may be simplified, for example, having a zonally averaged atmosphere. So they are not high order. Well, they are GCMs. But they are not state-of-the-art coupled GCMs. If you go to coupled GCM, it's actually getting harder and harder to get this type of diagram. So there is obviously a computational cost here. Maybe we don't find them because it's just too costly to find them. But people have put a lot of effort into understanding those diagrams. And as you get more and more complex models, they realize that there are other feedbacks than the ocean in the climate system, which posteriori sounds not like the Nobel Prize discovery. But they found that the ITCZ is responding. It's changing the freshwater flux perturbation, which is imposed by the operator. So the user of the model is again fighting against the feedbacks into the system. The balance into the Atlantic of the freshwater depends on how water coming from the southern hemisphere goes into the Atlantic basin. And again, it's very much dependent on the currents and how they are resolved and the role of ADs. So it's getting really not trivial that those multiple states exist for more complex model than the intermediate complexity. There is another difficulty is that if you read the numbers here, maybe it's too small, the width of the heat hysteresis is 0.2 Sverdrup. It's actually not a small number in comparison to how much water would go into the North Atlantic in a real system when, say, we have a degliaciation. So obviously in the real system, the argument is that maybe an ice sheet is melting, or CIS is melting, and it's freshening up the upper ocean, which drives the system across the hysteresis and back. But we have estimates of how much water could come from an ice sheet, maybe from Scandinavia or Canada. The numbers are barely reaching 0.1 Sverdrup. So we are right at the margin where this could happen, but it's not trivial that there's ever been enough fresh water dumped naturally into the system to drive those states. Anyway, it's still very popular, and it has merits. I don't want to come across as saying it's uninteresting. So another type, which Brian has described in detail yesterday, are multiple states which are driven by the CISL video feedback. This is just a schematic taken from one of Brian's paper showing a summary of what is an energy balance model. You've seen that yesterday. But just to summarize, it's a model of the zonal mean temperature profile between the equator and the pole. And the ingredients are that there is short wave coming in at the top, long wave coming out at the top of the atmosphere. And there is a transport laterally between the equator and the pole, which is proportional to the gradient of temperature. And the nonlinearity that makes it having multiple states is that the albedo, which is hidden in that short wave term, the albedo is a function of temperature. So when it's cold, we assume there is ice, and the albedo is high. When it's warm, we assume that we have ocean, which has a low albedo. And that's the hysteresis diagram. Again, Brian has shown that and discussed that yesterday. For some range of parameters, you have two or three or four possible equilibrium. Some of them stable, some unstable. So those states, they haven't been studied as much. And in fact, in the literature, there is very little, very few examples of this type of states. At least when we started, there were just a handful of studies that were really interested in that type of multiple states. And again, to be contrasted with this, people had carried out intercomparison projects where 20, 30 people carried the same experiment. So I'm just citing a couple of examples here in atmospheric only GCM. So maybe some of you can reproduce that during the lab session. In this paper, they found multiple states of the sea ice cover in an atmosphere only GCM. And this paper looked at a warm state, which is like present day climate and a snowball. As pointed out yesterday, a snowball probably always exists. If you start a model simulation with ice everywhere, it's white. There is nothing to pull the system out of the cold state. At least if you consider CO2 or other external parameters. So probably a warm state, a snowball always exists. So that's the one, sorry, that's the multiple state we are most interested in. This is probably just a repeat of what John said. But how did we go after this type of multiple states? We used the idealized geometry and went through a series of simulations with very simple geometry where we changed the shape of the continents. I think John has discussed that at length on Monday. All those states have different, all those simulations have different states. And they are mostly driven by when we change the configuration of the continent, we change the ability of the ocean to carry heat to the poles. And so some have sea ice at the poles, some don't. Just a word about the model we are using, because I'm trying to give you a sense of where we sit on that spectrum from intermediate models of intermediate complexity all the way to IPCC model. So we kind of sit in the middle in the sense that we have an ocean-atmosphere-couple model which has primitive equation in both atmosphere and ocean and is 3D, fully 3D dynamics in both fluids. In the atmosphere, it has a coarse resolution, but it's enough to get some synoptic ADs in the atmosphere. So this is a snapshot of the temperature at 500 millibar. Obviously, in the ocean, because of the coarse resolution, there is not, the ADs are not resolved. So we have to rely on AD parametrizations. And really what makes the model flexible and cheap enough to run for many thousands of years is that we are using the simplified atmospheric physics of Franco-Molteni. And the model is coupled. And there is the possibility of CIS. So when we think about that range of model where people have been finding multiple states, we are above the one equation, clearly. We think that in terms of dynamics, we are above most of the intermediate complexity model. We are obviously not anywhere near IPCC class model. And so there's still lots of work to be done. But that's what we have now, just a movie. So that shows 500 millibar temperature, specific humidity, air-sea fluxes, and mixed layer depths. It's in one of those aqua planets. So again, the point is that we have idealized geometry, clearly, and that's an issue. But the dynamics is complex, in the sense that we can have Rosby wave and synoptic eddies going around. We have trade winds, westerly winds, and exchange of energy between ocean and atmosphere. You can see it's a bit tough to see, but you have intense fluxes coming out of the ocean in the cold sectors of synoptic storms. And mixed layer depths is responding by deepening. So it's not a lower-order model. And Brian showed that yesterday. Actually, he added a state in there, but I'm going to stick to that old figure here. So in two of those configurations, we have three possible equilibrium. So in the ridge world and the aqua planet, we have a state which we call warm state, which has very little sea ice at the two poles. There is a cold state which has big ice caps, and obviously there is a snowball. But I think, again, any model would probably have a snowball. If you compare, for example, the equator-to-pole difference in these two states, we have one which is about 28 degrees C. So it's kind of like our climate now, and one which has a very large temperature gradient between the poles. So those states are stable, meaning that we can run the model for thousands of years, and the system stays in that state. And they are run with the exact same parameters and exact same forcing. So they are really truly multiple states of a complex dynamical system. So why do we have those states? It boils down to the shape of the oceanic transport. Again, it's a repeat of Brian's talk yesterday. The big point that Brian made is if you look at the shape of the oceanic transport as a function of latitude, it peaks around 20 north and 20 south. So if you compare to the atmospheric heat transport, which has an atmospheric scale, and peaks almost at 45 degrees north, the shape of the oceanic transport is very asymmetric in a sense. It's large here, and then collapses to almost zero as you go north of 50 north. It doesn't mean that that little leak of heat into the high latitude is not important, but if you care about the convergence of heat, which is how much that curve changes with latitude, it means that you are pushing lots of heat up to here, and then you stop pushing heat. And by conservation, it means that you are releasing a lot of heat in that area, and you are releasing it to the atmosphere, at least to the surface, so atmosphere or sea ice. And that shape, we understand why there is that shape. It's not coming out of the blue. It's that to first order, the wind-driven, the transport in the ocean is wind-driven. It's due to the fact that we have trade winds, which are pushing heat water at the surface away from the equator through Ekman dynamics. That's the first order. We have warm water at the equator. The trade winds are pushing to the right in the northern hemisphere, to the left in the southern hemisphere, so we are just pushing water out of the equator. And some of that water comes back after releasing its heat to the atmosphere in the western boundary current, so essentially it's an over-turning circulation in the vertical plane, which is pushing warm water to the north and cold water to the south. And it doesn't extend all the way to the pole. That's why we have that particular shape. So we can have in that system, we can have a steady state without any sea ice or very little, little enough that it's not enough to trigger a sea ice albedo feedback. And you have to think that on top of that, there is the atmosphere pushing heat to the pole. So even if there is a bit of sea ice and a bit of albedo feedback, there is still the possibility for these to be pushed back by heat transport in the atmosphere. Now if the sea ice albedo feedback is strong enough that ice starts to grow on its own, just expanding because it's white and it's reflecting heat and light and starts to grow and make the system colder, it can reach a point where this albedo feedback is stopped by the heat being released from the ocean to the sea ice. So essentially you can think of this as there's a big radiator here, heat is released by the ocean and just stops the advance of the sea ice. If the system is able to go over that threshold, then the system will run all the way to snowball, except if, as mentioned yesterday by Brian, this part of the heat transport is able to contract following the ice edge. But if it's not able to do that, once the ice has gone over that threshold, it will carry on and expand all the way to the equator. Why this is really important, the shape of the heat transport? Because that shape that we see in those aqua planets is very much similar to the one we see in observations. So this is the observed ocean heat transport, estimated from ocean reanalysis and direct measurements. So clearly as you can see, there are bigger bars there. We don't know that ocean heat transport well. But it's pretty clear that even in observations, heat is pushed out of the tropics at about the rate of one or two petawatt on each side of the equator. So that big bulge is there in observation and then as you move poleward of that 50-40 degree of latitude, the heat transport goes to nearly zero. At least there's a most effective 5 or 10 between these two. So even in the ocean, in the present day climate, you have that very characteristic shape is present, which obviously gives us hope that in the real world, the mechanism we see as aqua planets could be happening. I'm going to skip that because Brian has been discussing that. So now that we have those multiple states, we can think about how to make transitions between those states. So that's showing you a plot that's been done with the ridge world here. And it's been very done very simply. You have two curves here, the red and the blue. So the red, that's the ice edge. It's 90 degrees, ice edge means there is no sea ice, 30 means there is ice down to 30 degrees of latitude. So we have a red curve which starts from an ice-free state and a blue curve which starts from a state which has a big ice cap. And then we drive those systems by simply cranking up and down the solar constant. And really we are not thinking about that as representative of Milenkovich forcing, right? It's just a way to get the system to transit between the states. The Milenkovich forcing are way more complicated than that. But we are just forcing the system to go over the threshold and collapse into the next potential well. So what you see here is that if you start from an icy ice-free state and you drive it with a cooling, so decreasing the solar constant, the systems start to grow ice and then ice disappear again. You get an ice-free state for a few hundred years and then slowly the system goes into a cooling, a very slow cooling of a thousand-year timescale, flips around happily and then pops back very abruptly to an ice-free state. It doesn't matter if you start from another point, if you start from an icy state. Again you get a warm transition into a warm state which is very fast and you get this interesting blip where CR is formed and then disappears before collapsing into an icy state again. So again not saying that what we are looking at are DO events but it's quite interesting to make the parallel between DO events. So I'm just plotting here the curve of the Greenland record for delta-18 which is kind of telling us that here it's warmer and here it's colder but it's interesting to see the transitions between those states where going from cold to warm is abrupt and going from warm to cold is a bit more gradual so you would compare this to this type of curve. So perhaps we are looking at something which is relevant to the DO events at least in their dynamical aspects. Okay, I'm going to skip this one but because the nudge here is to think about how the salt is changing in the system. So this is a plot of the salinity profile in the model as a function of latitude and depth for various years into the transition between ice-free, icy and back to ice-free. And this is indicating whether you have sea ice or not that those purple blocks there. So when we start in an ice-free state what we have is the usual figure the usual picture we see in observations for example you get salty waters in the mid-latitude and you get fresh waters in the high-latitude and that's just because it evaporates in the net in the subtropics and in the net it's raining in the high-latitude there's not much to that if you're in a steady state the ocean sea surface salinity is just reflecting the fresh water being dumped on the top of the ocean. So now we start to cool the system and what happens is that obviously as we cool the temperature gets to the freezing point in the high-latitude and sea ice starts to grow but sea ice is made of fresh water so as it grows it's leaving the salt behind into the ocean so we could that brine rejection and what it does is making the surface water saltier and denser up to the point where the top of the ocean gets denser than the bottom of the ocean so in the high-latitude a characteristic of the ocean stratification is that it's warm at depths and it's cold at the surface because obviously the surface is in contact with the sea ice and the column is stratified by salinity so if you remove that salinity stratification by dumping a lot of salt at the top of the ocean this triggers convection and this brings warm water to the surface and warms the ice so the ice just melts away so we are cooling the sea ice has disappeared now and we have deep convection top to bottom and then from there the whole system is going to cool down by cooling from top to bottom of the ocean so there is a permanent convection from top to bottom and the system is going to cool down up to the point where that whole water column is at the freezing point so it takes a few hundred years to completely bring that whole water column to minus two degrees of the freezing point and then sea ice will start to grow again but at this point there is no stratification the whole water column is at the same temperature and salinity and as the sea ice progresses in front of the sea ice there is deep convection top to bottom which is needed to remove the heat which is stored inside the ocean and that is released by the convection then after a while the system starts to warm again at the peak of the glaciation so now the sun is turned up again sea ice is melting but when sea ice melts it is releasing fresh water so it is dumping light water at the top of the ocean which doesn't trigger convection so the melting process is not triggering any convection and so the heat capacity of the melting process of the melting phase is only important for the top hundred meters and the system is going to just melt away so the key difference here why are those timescales between warming and cooling very different is that when you cool you have to cool the whole depths of the ocean so 3000 meters but when you warm there is no convection and the effective capacity of the ocean which is in contact with the atmosphere is only the depths of the mixed layer so maybe 100 meters depths so the timescale comes from that big difference in the stratification that's why that's necessarily a slow process and that can be a very fast process and that's probably something which is relevant to the DO events just to finish the first hour just to point out that as I said earlier when it comes to DO events people have been thinking about overturned by stability multiple equilibrium state of the overturning circulation a lot as a framework to think about the DO events there has been a few recent paper where the people have tried to push a shift in how to think about those events and thinking about the sea ice ocean interactions so that's a paper by Duncan et al and I'm really just plotting the summary point here and I'm not going to go through the details of that because they've used lots of paleoproxy to get through those those ideas but essentially what they are after is to point out that during what they call stadium conditions is the bottom the coldest phase of the DO event interstitial is the warm phase of the DO events so in the cold phase there was probably sea ice covering the whole of the supolar gyre down to England while during interstitial the warm phase the sea ice was retreating and really that's a schematic but it was retreating maybe all the way to Greenland what they are suggesting is that this oscillation has not a lot to do with the biostability of the overturning circulation but it's a couple problems between ocean and sea ice cover so from the paleoproxy they could infer that in the cold state there was actually still an overturning circulation going on bringing warm water under the sea ice cover and that heat is being stored under the sea ice cover up to the point where the water column become destabilized and start to overturn and in that process you are bringing the warm water to the surface and melt away the sea ice and that's how you transition into this interstitial warm state where there is still an AMOG going so in both situations there is an AMOG transporting warm water from the tropics into the high latitude the difference is that whether that warm water is going under the sea ice or is done is going at the surface no need to go a lot into the detail but I'm just pointing out that there are some paleoproxy evidence that maybe the bi-stability AMOG framework that has been used to interpret the DO events is not necessarily the right one and sea ice has to be put a bit better into the picture and that's just an example that some models that's a series of very interesting papers by Vitority and Peltier where they have self-sustained DO events in a model what they do is that they start with a complex IPCC-like climate model which exhibits self-sustained oscillations so that's a very colorful figure that they've produced but really the interesting bit here is that this is a curve showing the intensity of the AMOG so in their case the AMOG is going up and down in a natural way so they don't have any forcing in that model but the interesting bit is that what's really happening is that the system is oscillating into a big ice cap which is covering the whole of the North Atlantic and a system where there is a huge polina in the middle of the ice cap and again what happens is that the AMOG is transporting heat under the ice cap to destabilize the water column and there is overturning and melting of the ice at the surface and I'm going to stop there we need a bright no yeah even for that you