 Okay. All right, well, I'm gonna talk about something fairly different from the last talk, but thank you to the organizers for inviting me. This is my first systems workshop coming from the ice sheet modeling community. And where I'm gonna start today is actually not too different a place. So starting with water on the landscape and what it means for communities. I am Alex Roble, I'm an assistant professor at Georgia Tech School of Earth and Atmospheric Sciences. And today I'm gonna be talking about a stochastic ice sheet model that we've been developing in my group with some collaborators. And at the end, I'll briefly talk about some hydrology modeling that's in progress as well. All right, so this is sort of the, you know, ultimate motivation for this work. So this is in my home state of Georgia. This is Highway 80, which connects the city of Savannah, the Tybee Island. It's the main inhabited barrier island on the coast of Georgia has about 5,000 permanent residents, including a large seasonal population. And this is not during a hurricane. This is not during like a particularly large storm. This is high tide in 2015 during a king tide. And so during this king tide, I'll just let this run run back a little bit. During this king tide, Highway 80 flooded and this is the only overland connection between Tybee Island and the city of Savannah where most medical services, emergency services are located for Chatham County where Tybee Island is located, right? And so ultimately, you know, the story here, which is sort of the motivation for my talk today is that when Highway 80 was extended to Tybee Island in the 1930s, sea level here was about a foot lower than it is today, right? So it made sense to build the highway at the elevation that it was built. And as sea level has been rising globally, but in particular on the east coast of the United States at something like 50% higher than the global mean rate, you know, this has become these engineering decisions that were made over a century ago have become problems. And so ultimately the context here is, you know, ice sheets are melting and this is contributing to global sea level rise, glaciers in mountainous regions are also melting and sea water is expanding due to ocean warming, right? So all of these different processes which you can see here on the left. So this is sort of our community consensus projection of sea level rise over the next few centuries from the recent IPCCS rock report. And so you can see sort of the combined sea level projection on the bottom in the big figure under a high emission scenario in red and under a low emission scenario in blue. And then you can see the contributions from the loss of mountain glaciers, the Antarctic ice sheet and the Greenland ice sheet. And there are two things that I really wanna point out here is that 2100 is sort of a special time in our sea level projections, not only because it's a nice round base 10 number that we usually project to, but also for sea level projections, it tends to be when emission scenarios diverge, that is to say when the fruits of our current actions start to become most apparent and when uncertainty really starts to grow quickly, right? And so as you're going forward into the future, what you see is that the uncertainty and this is our current community consensus of uncertainty is by no means a complete accounting of uncertainty and that's partly what I'm gonna be talking about today is accounting for the complete uncertainty and sea level projections, but the magnitude of uncertainty, right? So the spread of these bars is approximately equal to the signal of uncertainty, right there of the same order of magnitude, right? We know that sea level is going to be rising globally on average varies a lot regionally, but the amount by which it will be rising is really where there's a lot of uncertainty going into the future. And so why is there so much uncertainty? Well, there's a variety of reasons, which ultimately come back to many things within sort of the field of glaciology and ice sheet modeling that we still don't understand just to go back here for a second. The last thing I wanna point out is that most of this uncertainty in the projections, especially after you get past 2100 is coming from your ice sheet projections. So the Greenland ice sheet mass loss and Antarctic ice sheet mass loss that you see here on the left, right? So ultimately, post 2100 sea level projections are so uncertain due to lack of understanding of various processes in our ice sheet systems. One is how the climate forces the ice sheet system, but also how the climate responds to changes in ice sheets. So here's an example on the left of from a recent ice sheet model intercomparison project ISMIP, which is a part of the sort of CMIP model intercomparison project for climate models. And you can just see the each color, you don't really need to look at the fine details here. Each color is a different climate model that is used to force ice sheet models, right? And so the top is surface mass balance. That is basically the net balance of how much snow is being added on the surface of ice sheets. And at the bottom is basal melt where the ocean comes into contact with in this case, the Antarctic ice sheet, right? So there's a really wide range basically in how ice sheet projections are seeing the climate. Also within ice sheet projections, within ice sheet models, there are many under resolved multi-scale processes. So an example on the top is sort of the, this is a few meters of interface. This is from a direct numerical simulation of the boundary layer beneath an ice shelf where it comes into contact with the ocean, right? And so you basically have, you have a dissolving boundary, right, that is compositionally different from the ocean that it's in contact with. And then you have complex currents flowing across it. And so calculating the heat and salinity flux through this boundary layer is an incredibly difficult problem. And observations tend to indicate that the current parameterizations that we use can be wrong by up to an order of magnitude. And the bottom is an example of a very high fidelity model of iceberg calving at the edge of an ice sheet. And this is something that's also not resolved in our ice sheet models that we're using for projections. And then finally, of course, issue in a lot of geosciences but particularly a problem in glaciology is data sparsity. We really don't have very much data before we start, we turned on satellites, right? In the 1970s and 1980s. And this is in particular a problem because ice sheets respond to climate change on time scales of at least the decades but really more like centuries, right? And so we've only been observing a small snapshot of time. We've only been observing ice sheets during a small snapshot of time during which they've been changing. And this is a problem because then we have a problem calibrating our models to observe or to reproduce the sort of observed ice sheet sensitivity to climate change. So all of these contribute to producing this uncertainty. But in particular, what I wanna talk about here and just short few slide vignette is that there's an intrinsic problem of growing uncertainty in ice sheet projections. And ultimately it comes down to the fact that the Antarctic ice sheet and parts of the Greenland ice sheet are susceptible to something called the marine ice sheet instability. You haven't heard of the marine ice sheet instability before it in sort of summary comes from the fact that large parts of our large ice sheets, Greenland and Antarctica are resting below sea level. So what this is is a map of the elevation if you took all the ice off of Antarctica, right? So people who haven't seen this before are often surprised because Antarctica is actually an archipelago at least at its current elevation and the ice sheet sort of combines all of these islands together to what we see on the surface, right? But the issue here is that basically in the blue areas are areas that are below modern sea level. And as the ice sheet retreats, the ice sheet remains in contact with the ocean. And in particular, the speed of ice flow speeds up as ice retreats into deeper and deeper water, right? So an example here is on the left area of Antarctica that we call West Antarctica. You can see there's this area where the base of the ice sheet goes from being maybe 500 meters below sea level to something like close to two kilometers below sea level. And so as ice sheet models project the ice sheet retreat into that deeper and deeper water, the ice flow speeds up and you have an accelerating and irreversible retreat. And so when models simulate this, the issue is that this instability leads to sort of an intrinsic growth and uncertainty. And this is something that's known from dynamical systems theory. We had a paper a few years ago in PNAS using some methods from statistical physics to show in sort of a mathematical model and then in a more complete model, the fact that any ice sheet model that simulates this instability, this marine ice sheet instability, if you have many ensemble members, so here's just a sort of a toy schematic example on the right. You have many ensemble members either that have parameter uncertainty or that have uncertainty in the climate forcing. There is intrinsically going to be a growth in the uncertainty and a skewing in the distribution of uncertainty towards worst case scenarios, right? And the skewing ultimately comes from sort of the nature of nonlinearities and ice sheet dynamics that I won't get into in here. But the point is that when we look at ice sheet model projections, so here's just two more examples that the one that I showed before was sort of an aggregation of many different projections, but here's two sort of well-sighted projections for Antarctic ice sheet evolution and contribution to sea level rise over the next few centuries. And you can see the same growth and uncertainty and also skewing towards higher sea level contribution. And ultimately this is a problem because if you wanna build something on the coast, right? And you're trying to make allowances for future sea level rise and you're very risk averse, right? You're going to build to try to be let's say at like the 1% or even higher level of potential inundation. That is to say you want to avoid inundation in the future as much as possible. Let's say if you're building a nuclear power plant or some other piece of critical infrastructure on the coast. And so this long tail that intrinsically comes into our projections it's always gonna come into our projections because of the nature of ice sheet dynamics makes adaptation costs rise very, very quickly, right? And so this is an intrinsic problem. I'm not talking about solving it. What I'm talking, what I'm talking about today is how do we quantify this better? So the particular issue that we're tackling in my group is how to quantify the uncertainty due to the inherent noisiness of climate, right? And currently this is something that's not done in ice sheet model projections that contribute to sea level projections, right? So if you look at the ocean around ice sheet so here's one example from Greenland on the left or if you look at the atmosphere over ice sheets so here's another example from the Greenland ice sheet of ice core record of accumulation what you see is that the climate is noisy, right? Basically the temperature and the snowfall that the ice sheet is seeing in the ocean and in the atmosphere are constantly fluctuating, right? And that's because we live in a complex fluid system that is chaotic. And, you know, Klaus Hasselman, he recognized this 50 years ago and two years ago received the Nobel Prize in physics along with another climate scientist particularly for his role in elucidating the importance of this very internal variability of the climate system. And actually in his original paper about this in the 1970s, he talked about how the slowly responding components of the climate system such as ice sheets, right? Act as integrators of this random input. So he really, he identified this problem in the 1970s particularly for ice sheets and then we spent 50 years not incorporating this variability in climate into our ice sheet model projections. So what we've done with funding from the Heising-Simons Foundation at NSF along with collaborators from Dartmouth and Caltech is to build the first large scale stochastic ice sheet model and in particular what we've done is we've taken an existing ice sheet model that's widely used in the community, ISSM and we have basically architected, re-architected part of the core of the model to be able to internally generate noise and then apply it to any field in the model, right? And then we've had various project members working on incorporating and developing realistic stochastic parameterizations for the surface mass balance that is the snow accumulation and surface melt on the top of the ice sheet, ocean melt, iceberg calving and some glacial hydrology and here are some of the many cast of collaborators particularly I wanna point out Vincent Verjantz who's the lead model developer for this project, post-doc in my group, Liz Ulti who's now a professor at Middlebury but who has worked on the SMB component of the model and Amina Ambaloran who's a PhD student of mine who's working on stochastic cabin. So we have a number of papers about this the sort of core model code was described in a GMD paper last year and now we've had a few other papers recently released and that are kind of coming out now. I'm just gonna highlight a few of the things that we've done in this problem. So this is Liz Ulti's work. So we have actually quite good regional, validated climate models that are used to do high resolution projections over ice sheets. The problem is you can't easily run those 100 or 1,000 times in order to produce different realizations of variability. So what Liz has done is using some sparse penalized methods to basically capture spatial variability and temporal variability of snowfall and surface melt on the surface of the Greenland ice sheet has developed a stochastic model for surface mass balance variability. And this is a paper, there's a pre-printed GMD that you can currently find online. Quickly, another paper that just came out from Vincent Verjean's does the same thing except for ocean forcing. Now, in the case of ocean forcing, we do not have high resolution regional models of ocean variability around the Greenland ice sheet. But we've had to be a little bit more clever in basically taking course models and downscaling them or extrapolating them from their sort of course on the continental shelf where their last grid point is right up to the front of the ice sheet, which is where the ice sheet actually sees the ocean. And so we've developed this, Vincent developed this extrapolation technique and also a bias correction technique that takes all available observations around Greenland and uses it to bias correct. So an example here is the red is what a sort of cement class ocean model would say for ocean forcing near a glacier in Greenland. The black dots are what observations say and then our method produces the blue and the yellow lines here for varying realizations of ocean forcing of the Greenland ice sheet or of this particular glacier in this example. And then finally, here's an example of sort of when you actually turn the model on this stochastic ice sheet model and start running it. I'm an example of an ensemble from a kind of relatively idealized simulation. So this is 500 years of model runs. We have a hundred ensemble members here. Those are the blue lines. And then we're basically on the Y axis we're looking at the change in ice mass. So this is with no trend in climate forcing. One of the very interesting things that we found that as soon as you turn on this model it starts drifting, right? And that's not something that if you had that sort of deterministic version of this model with no stochastic forcing, it would not do that drift, right? The black dash line is the deterministic run here, right? So this is a phenomenon that is well known in stochastic modeling community known as noise induced drift. You can come from a variety of different processes but basically we've identified and we're currently writing a paper about how the fact that there are these instabilities that I talked about before inherent in ice sheet dynamics produces the possibility of noise induced bifurcations also known as noise induced tipping. Also there's non-linearities within the system that filter symmetric noise and make it asymmetric and cause this drift. And basically what this means is that if you are running a deterministic ice sheet model it is going to be intrinsically biased because it does not include this noise induced drift which occurs in reality. So this is one of the nice things about when you build these new modeling systems all of a sudden you learn about some of the things that that kind of you've been doing wrong for a while. Okay, so some takeaway messages from this part and then I'm going to do a very brief illusion to just another modeling system that hydrologists might be interested in. Sea level rise after 2100 becomes increasingly uncertain and skewed and this is something that we expect as a fundamental mathematical property of ice sheet instabilities or in any system in any modeled system that has an instability. Ice sheets they're slow integrators of fast climate and glaciological variability and this makes them ideal for stochastic approaches as Hasselman originally identified and as which we've been implementing now in a model over the last few years. So these stochastic models are ultimately useful because not only can they tell us how much sea level rise we can expect in the future that is the uncertainty in our future projections. But it actually allows us to tackle a different problem which is unsolved in the ice sheet modeling community which is the attribution problem. If you currently look in the IPCC report there are low to medium confidence statements that humans have caused the change that we've observed or the ice loss that we've observed in the Greenland and the Antarctic ice sheets over the last few decades. And this is like a major issue because there's starting to be litigation over the sort of who is responsible for sea level rise and ice sheets are a major contributor to sea level rise. The models like this will finally allow us to tackle this question robustly. And then finally, I just wanna plug this other project if I was talking in six months I probably would have talked about this because hydrologists love this stuff. But this is a NASA funded project that is led by a former postdoc of mine, Sammy Buzzard who's now a lecturer at Cardiff and a PhD student, Danny Grau. This is called Monarchs, it is a tortured acronym but it is basically, it is a 3D hydrology model. It's portable to Python native. It's parallelized for water flow on the surface of ice sheets. So for those of you who haven't worked on this problem before, you have a liquid that is dissolving into the material that it is made of, the solid form, the material that it is made out of. So it's actually a very interesting problem in sort of percolation physics and hydrology and boundary layer issues. And so here's just an example of sort of an early result from that. So thank you very much. Happy to take questions or talk over lunch. Thank you, Alex. Are there any questions? We have time for one question. We see a question over there. Sorry, Mike. So you were showing that the stochastic models were giving results that were sort of worse than the deterministic models where the sea level rise is higher. And you also said that we don't have enough data to really test what's happening over a long kind of decadal time scale. So how do you know if your worst predictions are right? Yes. So when you say worse, I think you're saying that not in terms of accuracy, but in terms of like producing more sea level rise. Yeah. Yeah. Skewed towards, I call it worst case scenarios. Yes. So how do we know that's a tricky problem and it's actually the subject of another project that we're just spinning up. This is part of a career grant that was just funded for my group. The issue is data simulation there. And right now the way that most ice sheet models incorporate information about the past is that they undergo what's called snapshot initialization which is basically they are initialized at one point in time with observations, right? And that is usually in the last 30 years because that's when we have the best observations. And the issue there is that because ice sheets change on such long time scales that if there is a transient in ice sheet change, like for example, when you initialize your ice sheet model, let's say in the year 2000 or 2010, which is when we initialize most of our future projections, if there was a sort of transient tendency in the ice sheet, which there was for the Greenland and in the Antarctic ice sheets over the last 30 years, then you're basically assuming that the model starts at a steady state, typically assuming that the model starts at a steady state. And so what you need is you need transient data simulation methods in order to capture that sort of tendency in the real system by assimilating observations at many different points in time, even before the satellite era. And so that is something that the community is currently grappling with but it's something that our models don't all universally deal with right now. So the answer is sort of a work in progress.