 Next keynote talk is from Sean Brown, who will be talking about the leaking models of the first scale process. Thank you very much and thank you to James for inviting me. It's a pleasure to be here. It's my first CSDMS workshop. I'm trying to learn a lot here. So, I'm going to talk about stuff that I do with my group back in Grenoble and also for the last semester or so I've been in Berkeley on sabbatical. And I will soon do at the GFZ in the EFC of Potsdam starting this September when I get a new job. The idea is to model what happens at the Earth's surface when it's uplifted mostly or sometimes it's being subsided due to tectonics mostly. And I'll talk a little bit about what the Earth is not that round, but I'll talk a little bit also about what we think happens at the Earth's surface directly due to motion in the Earth's mantle, the convection of the Earth's matter. But I'll start with some example of what we do in terms of understanding how landscapes at the Earth's surface, continental landscapes, are formed when the plate, tectonic plates, I'm sure you'll, I'm told here this is a very broad audience so I'll try to be as simple as I can. But you've heard about plate tectonics and the guys hitting each other. That creates a mountain or when they move apart that creates a basin. And the reason we have mountains and basins is because the crust, the continental crust in this case is actually thickened or thinned and biases as you, that causes the surface to move vertically. So when you uplift the Earth, like here in New Zealand, in the southern part of New Zealand, water moves at the surface and forms little streams and rivers. And that's what mostly incites the Earth. Glasses also work very hard in cutting through the continental crust, but here we'll focus on what happens in rivers. And we have this little equation there that we use all the time called the stream parallel that says the rate of incision in response to uplift U. It's proportional to K, a constant we really don't know what it is, times drainage area to some power who really don't know what it is. Melt it by the slope, the local slope to another power line, which we usually say is one, but it's mostly because it's convenient that we do that. A couple of years ago with Sean Willett, I developed this method to solve that equation and especially the right-hand side term here, which is kind of, even it looks very simple as a tough one, because it requires the calculated drainage area, which is an older and square potentially problem. And it also involves calculating S, which is the derivative of H with respect to X. So this makes this equation an abduction equation, which is really unstable. However, with this way we had to order nodes on the landscape when we solved this equation, building a stack, we're able to do this both computing the drainage area and solving the equation in an order N and fully implicit method. This is Sean there, where NP is the number of points and goes from a few thousands to a few millions here, and we have a perfectly linear scaling in the solution of the equation and also our manual is in fully implicit, so it allows us to use very large time steps. The other thing that happens on the same landscape in New Zealand is the side of the valley, it tends to react to that incision by the river and they fall, by gravity, sometimes by landslide, sometimes by soul creep, and we're not very clever in geomorphology, we say we have conservation of mass, we say that transport is proportional to slope, and we end up with something that looks like a diffusion equation. Greg here has been very good in trying to make a put in the KD and make it highly non-linear, but it always kind of end up being a diffusion equation. And we've had methods for a long time like this ADI method, or if KD is a constant, you can even use a spectral method to solve that equation, again, fully implicitly an order N. So this means that we can solve, you know, this is three model runs that I've put next to each other, where I increase the ratio between KD, the diffusion, KF, the Fruvian incision, but we can solve these now on, I'm usually said that little computer, but it's my ipad, I said that little computer, we can solve these very large problems in a matter of seconds, not even minutes. So it's extremely efficient, and it has actually led to many other things, many new things we can do with these models, which really help us to constrain not only uplift, this is what tectonicians or people working in tectonics are interested in, but also the geomorphology and the KF, the KDs, the N and the Ns. One way of doing this is using a full Bayesian approach to these numerical models where you take a landscape, I won't even tell you where it is from, and you try to reproduce that landscape or at least its characteristics. And the way we do this is by running a very large number of these models, hundreds of thousands of those, and we try to, and this is the hardest part, compare simulated models to the real landscape, which were not a simulated model, and we do that by varying the model parameters. The comparison is hard to make because we need to compare two things that will never look exactly the same, so we have to define some characteristic of the landscape that are constraining, that define the landscape, but that we can easily compare between landscapes. You can show that it is not a very well-posed problem because, you know, if we don't know much about K, the rate parameters, and we don't know much about you and the Earth, the uplift, so we need to use other type of data than just the landform, and we have a lot of geological data, typically sedimentary flux coming out of these landscapes as they erode away. So I'm just going to show you now an assimilation that we've done from a purely synthetic landscape, so I run one model, and I asked my method, this inversion method, this optimization method to recover that landscape, and all I'm doing is giving to that, my inversion method, the flux of sediment that comes off the four sides here, as well as the final shape of the landscape, something I could get from a natural case. And then I compare landscapes by simply looking at the histogram of elevation, slope, and curvature, or even drainage area in some cases, but not here. And so what you do is you run many models and you try by this Bayesian inversion method. Here we've used the neighborhood algorithm to do so. Not only the uplift history that I've put in this, which is kind of complex and I've moved it different paths through space and time, but also the erosion model parameters, the K, the N, and the N. And not surprisingly, it's not really surprising, but if you do enough, if you have a good inversion method, you recover the topography and its growth and its shape, you recover the uplift that you've put in in space and time, but maybe more interestingly, you also recover the value of the erosion parameters if you put in the landscape. So I don't have, because we are very actively working on this at the moment, we are trying to invert real landscapes, very scales from the whole of the South African plateau to a much smaller case like the San Gabriel mountains in California. And this is very promising.