 This next part is try to build our intuition a little bit about why this interaction between the ocean and the ice matters so much. And so we're going to do some more modelers tricks to explore the hierarchy in ways that will teach us something new. And the first thing I'm going to do, actually, this is the same kind of experiment that I've already shown you in a much more complicated model, but now I'm going to take this same relatively simple complex GCM, this Ridge World model, and put it into slab ocean mode. So the most interesting thing in that model that we've been looking at is the ocean dynamics. So let's get rid of it. And this is now the same experiment that I showed you the animation of with the big fancy model. I'm doing a pure slab. So no q-flux, just whatever, 50 meters of water. And this is time series now of what the model will do if you insist that you just have a pure motionless slab. And I can start from the warm state. I can start from the cold state. And of course, what this shows is that in both cases, actually unlike the big fancy model, which equilibrated somewhere here, these ones go into the snowball. So this used to be my slide for convincing people why it's useful to think about the ocean. I have a nicer slide now, so I showed it to you at the beginning. But without the ocean moving heat at all, we get the snowball in this model. It's consistent with what I've been telling you so far. So what we're going to do is we're going to play some modeling games where we represent the ocean through q-fluxes. And so we're going to use the slab, but we're going to input energy sinks and sources into the slab to mimic what the ocean actually does in the coupled system. So we have to think about what's a useful way to do that. And so to that end, I'm showing you here observational estimates, again, in black of the present day ocean heat transport pole to pole. And plotted over top of it in colors are the ocean heat transport as simulated in various configurations of that idealized GCM that we've been looking at in both warm states and cold states and in the pure aqua planet and in the ridge world. Those are all plotted here. It doesn't really matter for this purpose what's what. I'm plotting them here just to give us a sense of what's a kind of dynamic range for ocean heat transport in the fully coupled system. In all cases, the ocean is moving a lot of heat out of the deep tropics. So we have these peaks in all cases. And we have where the graphs are sloped this way. There's convergence. So there's heat coming out of the oceans. There's a lot of details that vary in the mid to high latitudes. Is the ocean moving heat to the pole? Or is it doing almost all its work in this sort of equator to mid latitude scale? So that gives us a sense of what's possible in a model that sort of solves the equations of fluid motion. And we're going to use that as inspiration and do something analytical and simple. So I'm just going to adopt this parameterization here, a geometrical formula that says that the ocean heat transport follows these smooth curves that always have a peak. And so in all cases, the ocean is moving heat off the equator and converging it somewhere in the mid to high latitudes. And I have a little number here. This is just sine latitude times cosine raised to a power. And the number, the power I'm raising the cosine to here, just controls the spatial structure. We're going to impose this into the model, into the slab ocean version of the model. So n equals 1 means I'm going to insist that the ocean is moving heat right to the pole. What's plotted here is actually the convergence of these graphs. So this is actually what you plug directly into the slab. So it's a cooling signal at the equator. It's a warming signal somewhere else where the warming peaks is determined by this number n. And I have another parameter that says how large is this peak. So I have a two-parameter system. So I'm just going to map out my model's response to various shapes and sizes of imposed ocean heat transport. I've taken the dynamics, the ocean dynamics out, replaced it with this two-parameter space, just to get some insight into how the climate depends on the shape and size of ocean heat transport. All right, so that's the question I'm asking. I'm going to start these simulations initialized from both warm and cold initial conditions and see what happens. So this is one example. Here's the latitude. Again, now the latitude here indicates the size of the ice cap. So I start from cold initial conditions, the ice is here, and warm the ice is here. This is one out of my whole set of parameters, n equals 3. The shape of the ocean heat transport for n equals 3 looks like this gray curve. The colors indicate the amplitude of the peak. So as we go from blue to red, we're making the ocean a much more effective heat transporter. Going above and beyond the dynamic range that I showed here. The largest peaks here are less than four petawatts. So we're deliberately going past that in this parameter sweep. OK, and what happens? So these are just time series of the adjustment. The adjustments are quick because we're in a slab now. We've taken the long memory out of the system by taking away the thousands of meters of water and replacing it with a shallow slab. So these are quick simulations to do. But what do they do? Well, it turns out in this case, only one of these that started cold sort of stays about how it was. The others diverge, right? This one melts away. These ones go into snowball. These ones, on the other hand, like to stay warm. So for this blue one, which took a while to figure out what it was doing. And this is some evidence of this long adjustment time when we're close to bifurcation points. But eventually, it went into the snowball, all right? So now that we're oriented on that, I'm going to put a whole big panel of these plots on. OK, so this was the one we were looking at. And the panels here are just my numbers N, again, which are sketched in gray. With zero, with no Q-flux at all, of course, we get snowballs. When N is a small number, and we're insisting that the ocean move heat into the high latitudes, what happens? Do we find any stable states with partial ice cover? No, OK, right? These states all either diverge into the snowball or into the warm state. This one that we saw at the beginning, only one of them happened to find an equilibrium with partial ice cover. But as we get into larger N, meaning the ocean is moving heat over shorter distances, then all of these stable states with partial ice cover pop up, OK? Furthermore, how much ice is there? Well, it seems to be pretty strongly determined by how strong that transport is. As we vary N and we vary the amplitude, the size of that ice cap just grows or shrinks proportionally. So there's a range, there's a whole range of possible climates here, depending on the shape and size of the ocean heat transport. I can summarize these results in a graph like this. I have this two-dimensional parameter space of shape and size of ocean heat transport. If I summarize those on a single axis just by quantifying how much heat is the ocean carrying across 30 degrees latitude, that turns out that's half of the Earth. It turns out to be a convenient way to summarize this. Then I get this whole cluster of possible climates that have partial ice cover, OK? If the ocean, either through parameter N or through parameter amplitude, is carrying more heat across 30, the ice cap gets smaller. And the planet, this is now temperature, global average temperature, but it's basically a direct measure of how big that ice cap is. There are a bunch of warm climates up here, too. The astute observer will, of course, see that these actually get warmer as this goes up. And that's something that I probably won't have time to get to today, but you can speak with Cameron Renkrel, who's back there, because he's working on a project that follows that question more closely and with more sophisticated models. Why does the planet warm up when the ocean carries more heat out of the tropics, even in the absence of ice? It's no longer a nice albedo feedback problem, but it's a very interesting problem. But of course, this signal is much larger, right? The slope of this line, degrees of warming per petawatt of heat carried out of the tropics is much steeper because of the influence of the important amplifying effect of the albedo feedback, all right? So this means that for given OST, we have two states. That's right. So again, by stability here, I could say I don't have a unique answer from this model. If I know how much heat the ocean's carrying across 30 degrees, that doesn't uniquely determine whether I'm in a warm state or a half ice-covered state. So to summarize what we learned from that, so this idealized GCM has this continuum of cold icy climates, which the ice edge is basically slaved to the location of the strong convergence of heat transport in the ocean. In fact, I think I skipped a slide, which I don't want to skip. Let me put it back. Let me make this point more clearly. I'll go back here for a minute. So here's my access of ocean heat transport across 30. Here's my continuum of different possible sizes of ice cap to emphasize the connection between the magnitude of the convergence of heat transport at a certain latitude and the location of the ice edge. Well, what I'm plotting here is now the ice edge latitude, same set of simulations, all those continuum of cold icy climates. All right. Here's different ice edge latitudes. The continuum here goes from about 25 degrees latitude out to mid-latitudes, 50 degrees latitude. The red dot here actually represents what the coupled model that I already showed you actually does. It finds a state like this. The slab model, if I make the ocean carry heat over smaller ranges of latitude, is very happy to find equilibria with much larger ice caps. But the point of this diagram is I'm saying, well, what is actually the magnitude of the Q flux of that convergence of heat transport around the edge of the ice? And it's large. Nowhere does it exceed 30 degrees, not degrees, 30 watts per meter squared. And we can think of that as a limit associated with having to pass a lot of heat through ice would make the ice thin. And so to find an equilibrium, we have to arrange ourselves so that there's a lot of heat coming out of the ocean into the atmosphere on one side and very little on the other side so that that ice can continue to exist. Otherwise, the heat passing through it is just going to thin it and melt it. OK. So the sea ice edge is poleward of any location that's receiving somewhat less than 30 watts per meter squared of heating from the ocean. That's kind of the conclusion of that idealized set of experiments. But the idea is that any size of ice cap within this broad range of climates that span a huge range of global average temperatures is possible if the ocean, depending on what the ocean can do, if the ocean can move a lot of heat from the tropics to the subtropics, then very large but quite stable ice caps are possible. So I'm setting myself up for a punchline here. So I want to go back to this idea. We saw this animation where we saw the model, the coupled GCM. Now we're going back to a fully coupled model with the ocean dynamics. We've seen this already. We saw this transition occur where I put in, and I want to emphasize, since I didn't properly emphasize last time, the forcing here is completely arbitrary. I've just decided to play God and turn up and down the sun on a long time scale, just as a way of forcing a transition from warm to cold. We saw this. We went from no ice to this mid-latitude ice edge. I've done a bunch more of these kind of calculations. And the red curve here is the one we just saw the animation of. We started warm. We turned down the sun. I've changed the units here. I've multiplied by four. And I apologize. There's two different ways we can talk about the solar constant. But it's the same calculation here. We've turned down the sun. We've warmed it up. This is now, again, the ice edge latitude. The red curve goes up, up, up, and it turns cold. And then it warms up. That's the animation that we saw. But the purple curve here, which is just the same idea, but a slightly larger magnitude of forcing, what did it do? Something different. There's a whole other equilibrium state that we've discovered here. And it turns out that this in the purple side, when we tried to warm it up again, it didn't work. This model is now stuck in a, turns out, a much colder regime. OK. The ice, well, we're going to look at it in a little bit of detail here. So if you believe what I've said so far, then you should expect that this state of the model exists because somehow or other, the ocean has arranged itself to move a lot of heat over short distances. And that I'll emphasize here. This was discovered entirely by accident. And this is one of the great fun things about working in climate sciences. There are still really interesting new things to discover just by doing a random walk through subjects that interest you. And we knew about these. And we were doing these simulations to look at the dynamics by which we get from one to the other. And one of these experiments did something wholly unexpected. I didn't predict this. It came out of the model, but I learned something from it. And I think what we learned from it is worth learning. So there are four stable states in this model. And in fact, these four states exist in both these configurations of the model, with and without the ridge. This represents, these pictures are equilibrium pictures. They represent a lot of computing to run the model out to genuine, or at least as far as we can tell, genuine equilibrium, where there's no drift and the model's conserving energy and so on. So we have a warm state. We have what I was calling a cold state. And then I'm calling this new thing the water belt, called a water belt because they have a relatively small amount of open water. The ice is now coming down into the subtropics. And the whole planet is much, much colder, as shown by the colors here. And of course, we still have the snowball. Get no intuition whatsoever from the Boudicco Sellers model that we started with at the beginning that this ought to be possible. But it is, and it is because of the spatial structure of ocean heat transport. And let's emphasize that in a few slides here. Well, first of all, to connect one more time to paleo, why these sort of make interesting laboratories for thinking about Earth history? If we just think about the pole to equator temperature gradients in these various states of the model, here we have a warm planet with a weak gradient. The Earth has spent a lot of time in regimes where the pole to equator temperature difference is a lot weaker than it is today. And that's what this model does in its warm state. In this cold state, the gradient is stronger than it is today. But the state looks a fair bit in some ways like what the last glacial maximum looked like. And I think David is going to say a lot more about that tomorrow, maybe. And then, of course, we have these mysterious snowball Earth phenomenon. And we don't have nearly as good measures of 700 million years ago. And so there's still debate about whether Earth looked more like this or like this at that time. But we can use models like this to inform those debates to a certain extent. OK. So the sea ice in this water belt state is sitting in the subtropics. So again, if you believe what I've been saying, it must be the ocean doing the very hard work to stabilize this large ice cap. And so just a couple of slides to show what that looks like. What I'm showing here is ocean heat transport, a bunch of different simulations, and the observations, again, in the gray. I've turned the whole graph around. So now here's the south pole. Here's the north pole. Here are these peaks, the ocean moving heat out of the tropics in all cases. Here's my water belt state, OK? I have a peak, but I have a steeper slope here. This goes to zero much faster than those other curves. To look at it in a more spatially resolved sense, what this map shows you is an annual average sense. Where's the edge of the ice? And what is actually the, what would be the Q flux in this case? What's the annual mean net surface heat flux? These are large numbers. Lots of heat going into the ocean at the equator, a whole lot of heat coming out of the ocean at the edge of the ice. There's some interesting zonal asymmetry here having to do with the presence of the ridge and boundary currents that keep this part of the planet warmer than the rest of that latitude. If I try to match this to some of my idealized curves that I used in the slab model with this parameter n, well, it turns out to match n equals 14 pretty well. That's a very small scale equator to subtropics kind of transport. And in those, why don't I just flip back for a moment to this panel? Whoops, n equals 14. OK. So this is just to say that the model is sort of consistent with itself, right? In slab form, if I put n equals 13, I found various equilibria that I could all describe as water belt states with very large ice caps. The coupled system has found a configuration that looks like n equals 14. That's the story. So why? Just a few words about the dynamics. Well, it turns out that the reason why has to do with winds. And this is kind of interesting because it's a fundamentally coupled problem. We need the ocean and the atmosphere and the sea ice to all be consistent with each other to get this. And so you would never find it in a model that wasn't fully coupled. But what I'm showing you here are contours of zonal mean wind in the cold state in the atmosphere, of course, in the cold state and in the water belt state to emphasize that the winds have actually converged toward, they've moved toward the equator. So the jets have shifted. As the climate has gone from cold to very cold, the global wind systems have actually contracted toward the equator. I'm also showing you potential temperature contours here to get some sense of how cold it is and what the stratification looks like here. But the main message is that the winds have sort of contracted toward the equator. And that matters because the winds are driving the ocean. And yes, please. Is this true for the surface? The zero line, is it so different? So I think I have a plot of the surface stress coming up, which might be better to look at. Or did I take it out? I can show it to you if it's not in these slides. So here are now half of each of the ocean's sort of mirror image. So here's the equator. These are all symmetric about the equator, so I only have to show you half of each. But now we're looking at cross sections of the ocean. So here's our cold state with our wind driven overturning that's very effective at moving heat into the mid latitudes. And the edge of the ice is sitting here. And here's our water belt state where there's still easterlies giving way to westerlies. And so we still have this not fundamentally different overturning circulation that's essentially forced by trade winds moving warm water this way, subduction of warm water in return. But the whole thing has been squished. And where are we going with this? I guess I don't have any more slides to really make this case any more strongly, but let's say why has the winds been squished toward the equator? It ultimately has to do with the fact that the ice edge itself has moved toward the equator. The winds exist because of baroclinic instability in the atmosphere, giving rise to eddies that are pumping westerly momentum into the region where the eddies are forming. And so in the cold state, that's the mid-latitudes, much like it is in present day Earth. That's where the strongest baroclinicity is. Strongest baroclinicity is in the mid-latitudes, first and foremost because that's where the gradient of incoming sunlight is strongest because we live on a sphere. And the ice is just helping here. We're creating strong temperature contrasts between the warm and the cold parts of the planet. And the water belt, something a little bit different happens. The temperature contrast between the tropics and the subtropics becomes very large. And so essentially the baroclinic zones where all the storms are forming has to shift the equator with the ice, which would just be a curiosity except that that shift in the storm tracks affects the winds which are driving the ocean. And the ocean is holding back the ice. So this three-way coupling gives rise to something that looks quite different from our familiar climate. And in this model, at least, permits the coexistence of these different states. So it's the same argument in cartoon form that I put up earlier. It's just we have to squish this whole sketch toward the equator. The model has two different configurations in which the ocean is holding back the ice at a certain latitude. Kind of interesting. OK. Let me just skip the text and just show you the pictures here. So I'm going to go back to this basic idea that I started with. We solved the one-dimensional Boudicco Sellers model and got this bifurcation diagram that we had our little star passing through that said, if we start warm and we try to cool down, we have a range of stable climates with partial ice cover, then an instability. And then if we want to get out of the snowball, we have to crank the heating up very high before we can jump back here. OK. And that model knows nothing about the ocean. Knows nothing about the spatial structure of ocean heat transport that ultimately exists because of the winds. And then I presented, I tried to play games with these curves to flip them around so they go the same direction. I presented a toy model that does know about the spatial structure of ocean heat transport and does know about the interaction with sea ice to the extent that the ice is an insulator. So heat transport under the ice edge has to be very small. And we found suddenly a prediction of multiple stable ice caps from that toy model. She didn't show this graph before, but this appears in the paper that first described the multiple states in the GCM and showed how one can quantitatively fit an energy balance model to those results by encapsulating this idea of heat transport by an overturning circulation. Giving rise to this sort of ledge of stability here. But these graphs both look different from this, but they're both incomplete based on the last section that I showed you because the model has an additional stable state. And so the fully coupled system actually has a bifurcation diagram that looks like this. And this is probably the last picture I'm going to show you. But I'm going to spend some time on it because frankly, I spent a lot of time number crunching to make this picture. And the reason is every dot on this picture represents an equilibrium solution of the fully coupled model with the full ocean starting from various initial conditions. This is my attempt to map out the full shape of this diagram for this numerical model. So many, many, many thousands of years of simulation go into this. It's pretty interesting. There's all these folds in this diagram that exist based on what I've been arguing today because of the dynamics of the ocean. I'll walk you through it. The color codes and symbols here represent initial conditions. Did we start in the snowball or the water belt or the cold or the warm? So my little cartoons here help to guide us. So if we start in the snowball and then we're changing again the solar constant as the parameter we choose to vary, to map out this solution space, if we start in the snowball, we stay in the snowball. I have to go way out onto the beach there on this graph to get out of the snowball. That's not the point of this talk, so we're not going to do that. If I start warm, that's the red. Anywhere along here, if I start warm, I'll stay warm. So I haven't really plotted too many red curves here, but I could put a red curve here, here, here, here. These are a couple of red dots that started warm and just barely stayed warm. Here's a red dot that started warm and actually ended up here in this water belt state. And here's some that went all the way to snowball. Okay, it depends on how bright the sun is shining. There's all these bifurcation points here, so the details matter as to what we're going to end up with. If I start in this cold state, I'll stay in the cold state over this range. If I go beyond here, we've already seen an animation of going beyond this point and having the planet rapidly warm up. We saw a loop of that actually happening over those four to 8,000 year simulations. We also saw an example of one that jumped down here. And that's how I first discovered the existence of this whole branch. But we can then map it out by starting from this state and those are the diamonds here. So actually this stability ledge here, the water belt state actually exists over a very wide range of the parameter space. We can turn the sun up or pretty much equivalently think of increasing CO2 in the atmosphere to move along this way. And the water belt pretty much stays as it is. I mean, it gets a little warmer and a little less icy as it warms up and the winds are gonna shift a little bit back toward the mid latitudes. But this is a feature we knew nothing about, but it actually characterizes a much, a broad part of the solution space of this model. And I think it has something interesting to teach us about what happens to Earth when Earth gets very cold. Of course, if we warm it up enough, we end up up here. So we can think of taking this model and so the dashed lines are just kind of schematically illustrating the unstable branches of the solution that we will never be able to find in a numerical time-stepping process. But the model tells us that a whole huge diversity of climates are possible and it does depend on how we get there. It's a system with four stable states. So the history of the system is very important in figuring out where we end up. Okay, this will be comfortable with this graph. You say so comfortably that it's the same or kind of forcing you change. The doubling you do is the same as solar. But physically, I mean, principle is something quite different to change the solar input or to change the absorptivity. So it's a... Not that different though. Did you do the... I have done a few cases of changing the long wave absorption parameter. Done a lot more with the solar constant. What's the difference between increasing CO2 and increasing the solar constant? Well, the solar constant changes a forcing that has a more detailed, a gradient, right? When we turn up the sun, we're increasing the differential heating of the system. When we turn up CO2, we're applying something more like a globally uniform warming. That's gonna matter quantitatively. So the details of the bifurcation points on this diagram will probably change a little bit. But this is what we've got so far. But I am pretty confident that the basic story of having the multiple states and having various pathways by which we can get from one to another would not change. Yes? Several surprising results and interesting but surprising. So when I see your region, you did so many simulations, right? Just so many long simulations. How many simulations you did? Maybe... You count the dots. I mean, not only that, but also other things. So I think this is so important in my opinion. So is there any effort from other groups to reproduce these things? Yeah, that's a great question. So, I mean, if I could just modify your question just a little bit and say, we can ask how robust is this? If I take somebody else's GCM, am I gonna find analogous multiple states? How dependent is it, for example, on the geometry of the... We've set up this idealized world with a stick continent. I mean, the first response to that is that we've found analogous multiple states with and without the stick, so that tells us something about the robustness. But it's very difficult to rule out that a model has multiple states, right? You have to look for them. And that's... So you're absolutely right that, and I already said an enormous amount of computing and simulation went into this. This wasn't where it started. It started from finding evidence of multiple states and then digging deep into it to understand it. I think it should be a priority to look for. The reason that I'm asking is, this is so important and some surprising reason. And so that society has to attention on that. But how we can believe your regions. And it may be really big projects to do so that not many groups cannot do such things. We can't have a multiple equilibrium MIP. Something like that. This is what I'm suggesting. Global warming research, that's the reason. I mean, we're spending hundreds of millions of dollars just for the kind of things. I mean, if we spend a bit of money on basic science, we're going to be done. So, I mean, as I, I mean, I can propose to WCRP to make some effort. I mean, I, or some encouraging institutions to do this business. Well, I'm all for that. I mean, I think this is really fundamental stuff. I mean, the question of how unique is the climate? We have tools to address it and it's just waiting for people with the patience and computer time to sort of go after these questions. And that's been my hope that people will follow this up with other kinds of models in other ways. Not yet follow. What's that? Not yet follow. I haven't seen anyone publish results like this with other models, nor have I seen anyone try and fail to reproduce these results. Maybe a friend and we could see it. So. Very interesting. The women's global world. So not everyone is doing global warming experiments, but I mean, I certainly want to encourage people here at this workshop to take the first step, which is to build the Albedo feedback into the model that you're working with this week, because all those results I showed with the Q-fluxes are things you can explore very nicely in the ISCA model, as long as you have the feedback. And that gives you an opportunity to do things like ask how sensitive are the results to, if you're coding in the Albedo feedback as a one parameter thing where it's, the Albedo is high where it's cold, well then you have a decision to make about what that contrast is in Albedo. And as I said at the very beginning, that matters. That's going to affect how bi-stable or multi-stable the system is. So that's a great question to ask. Yes. So one thing I want to clarify is does your model include some kind of cloud related feedback? Yeah, good question. So I didn't say much about the GCM here. It does include clouds. It's basically, the atmosphere is basically speedy, which means something to some people in this room. So it's a relatively simple atmosphere, but one in which sort of has a full set of moist feedback processes, including clouds. So the short answer is yes. It knows about water vapor feedback. It knows about clouds and their impact on the planetary energy budget. We can certainly argue about whether they're done correctly and how we can look at how they're influencing the results. But they're there. OK. Yeah, just in terms of cloud related feedback, I think Fred kind of briefly find out the intrusion of the ice into the top of the region in your senior sample simulation. So in the same region, the eye, there are many reflective clouds. So it just kind of maybe shrink the albedo difference between eyes and the nose. And I think that is the key to why that CESM simulation, the fancy movie I showed at the beginning, did find a stable, apparently stable equilibrium with very large ice cover. When we set the ocean to be a motionless swamp, it didn't go into the full snowball. It got very, very cold. I do believe that clouds kind of changing in a way that essentially neutralized that strong albedo contrast at the ice edge is a big part of why it became stable. So relating that to the simple model arguments, again, this parameter that controls the albedo difference in that sense is a function of the climate state you're in. And so that would alter the shape of the stability curve in ways that one could explore. I haven't done the hard work to sort of figure out exactly what's going on in the CESM simulation. So you also came back to John's puzzle yesterday, right? So that despite the surface albedo is much higher in northern hemisphere, but the planetary albedo is for some reason quite similar. So the clouds apparently are doing something. I'm not saying, you know. Yeah, and it's great to thank you for bringing it up, because I've spent a better part of two hours talking about ice and snow albedo feedback. It may give the impression that the top of atmosphere albedo is determined by the surface, and it's not. It's determined by rays of sunlight passing through the atmosphere. And there are clouds in this model. I haven't shown you any pictures of what they're doing. There's much more complicated clouds in the CESM simulation. And those details matter. Ultimately what it comes down to is, because these are instabilities fueled by albedo feedback, the details that set the albedo and its spatial structure and how it changes as the climate changes affect every aspect of a graph like this. And that's where we get ourselves into some trouble thinking that we've got all the answers on this page, because we're dealing with a system where if we want to know, for example, where is this bifurcation point where we jump into the snowball? It turns out that the details of how we treat snow sitting on the top of sea ice model sort of dependent details matter. And in the snowball Earth modeling literature, this has become a big theme that how likely a GCM is to give you a snowball for a certain reduction in CO2, for example, becomes a very model dependent question. Every model's going to jump into a snowball at some point. So that was my argument number one, and it's true. But where quantitatively is a tricky thing to nail down, because the details matter. Yeah? I'm interested in the unstable branches of the equilibrium. Did you see any signs in the transient phase of the model hanging around the unstable equilibrium like some subsystems? Yeah, I don't have the slide here, so I'll have to show you offline. When I say there's many thousands of years of number crunching here, some much more than others, because I was very careful when I made this graph to only plot things that had really come into equilibrium to the best of my ability to judge, but some of them took an awfully long time. I showed you those transients with 4,000-year transitions. Some of these close to the bifurcation points take more like 20,000 years, so there is this phenomenon of the time scales getting very stretched out when you're close to a bifurcation point, and the GCM does that. And that's part of what makes it very expensive to build a graph like this, but also why it's hard to be confident when you say it's hard to rule out the presence of instabilities in multiple states in models in general, because often we just don't wait long enough. You don't have particularly elegant ways of determining whether a model really has reached equilibrium other than looking at whether it's drifting. But if it's drifting very slowly, then it's drifting very slowly right at the edge of a bifurcation, then surprises can await you. And here I kind of had a good idea where the bifurcations were, so I was able to be careful about it. But that's usually not the case. John. Do you think that the present climate has, if it does, that's pretty important knowledge to have? Well, the argument here is that yes, it should, because we have posited that the ingredients for multiple equilibria are an ocean that's capable of transporting heat out of the tropics over relatively short distances driven by the wind, stabilizing large ice caps. So we haven't relied in building that argument on any specific details of the geometry of this model. So we hope that the argument holds when you put in Earth-like geometry. And then we'd say, OK, yes, we should be able to take Earth as it is today, if we magically cool it down to a point where the ice is coming down into the mid-latitudes or the subtropics. It ought to be able to rearrange itself in a way that is stable. But that's a question we can explore with models, right? So if we got to a high end. Well, we do just like I did in this model, which is to choose a parameter like the solar constant or the CO2 and artificially turn it down. And then wait. You have to, you can't just paint the ocean surface white. That's not going to work, because you have to allow the stratification of the ocean to rearrange itself in ways that gets all the heat content out of the ocean. The best way to do that operationally is just to turn a parameter down that forces the planet to cool down and let it run freely. And hope it doesn't go into a snowball. OK, so if you do that, you'll get to some glacial state where there's large ice caps. So what do we do now? You turn the parameter back up. And hope that it stays there. Yeah, but you have to have done it patiently, where you've actually allowed the model to really find an equilibrium that's cold. Because if I am permitted to go back to the animation here, there's a transient. Not that this is a perfect analog for what you're talking about, but what happens when we first start to cool it down? A little ice cap forms. Oh, it goes away. I don't know if people paid attention to that the first time. But what went on there was that the polar sea surface was allowed to get cold, but it was stratified by salt. There was all this warm water underneath. And so for a while, and it was a long while. It was hundreds of years. There was a little ice cap over the poles with very warm water underneath. And that eventually got mixed away. And that huge heat reservoir came up. And from then on, it took another 1,000 years to get the ice cap to form, because we had to cool down 3,000 meters of water. And that takes a long time. So that's why I'm saying we have to be a little bit careful about finding the right initial condition from which to start our experiment of warming it back up, or seeing if it warms back up. But this is doable. It just takes patience, and it takes computer time. We should do it. How do you manage computation? Or what is computation? Well, these are relatively cheap. Not only that, so you made hundreds of simulations. Yeah. How are you going to do that? I'm just a patient person. Well, this is much, much cheaper to run than something like the CESM. So that's part of this story. I can say do the 8,000 years here on a handful of cores on a cluster over a few weeks. That's the kind of scope that we're talking about. Because it's not going to parallelize well past a handful of cores. But if I have a cluster, I can do many of these simulations simultaneously. It's not on the scale of doing something like this with a big model. And the reason really is that the atmosphere is relatively simple, and cheap, and fast. And that was the point of this model configuration, is that it allows us to study genuine coupled problems, but long time scale coupled problems that are beyond the scope of cutting edge GCMs. But yeah. But it does take patience. Yes? No, respect. You argue then, you have to learn to go once you learn to borderize. Yeah. Yeah. It's tough.