 So our final speaker for this afternoon is Ajay LeMay, who is the winner of the 2013 Student Modeler Award and will give us a short presentation on vector-based approach of bank material tracking. All right, thank you very much for the invitation, the opportunity to speak today. I was trying to think of a suitable transition from the last talk, but I decided I'll just go for it. So I've been working on a method for taking our knowledge about meandering rivers and playing it forward over geologic timescales, working on a method to essentially improve predictions for taking channel migration and seeing how that plays out in the landscape and in developing sedimentary deposits. The lateral movement of channels is a fundamental geologic process that ties into many broader themes in earth surface science. For example, if we look at to bedrock river valleys, in some cases the channel migration might be very muted, but in other locations it's very common to find strapped terraces that are preserved in the landscape. These terraces formed by valley widening that's carried out by channels and the formation of different terrace levels is often conceptually linked to changes in climate and tectonics that affect entire watersheds. If we shift to depositional settings, the migration of channels combined with agridation is a fundamental control on the architecture of sedimentary deposits. That's true on earth, but also on Mars. We're very commonly fluvial deposits are one of our key constraints in the past climate of that planet. To understand meandering in its evolution, its impacts in the landscape, we also need to be able to understand how these meanders interact with bank properties elsewhere in the landscape. To get a sense of this, we can take a quick tour of some different river valleys across North America, one of which is not like the others. So we can see that the Colorado River in Texas as well as the San Juan River in Utah, even though these are in very different environments, have the common characteristic that the channel has essentially a gently varying sinuosity across the landscape. The Colorado River in Texas is migrating through poorly consolidated valley fields, whereas the San Juan River is carving into much more resistant bedrock. But in both of these landscapes, bank strength is relatively constant, and so it doesn't impart a strong influence on the channel form. However, the Beaver River in Alberta, Canada, shows a very distinct form, where we have some hints of regular meandering in the middle of the valley, but where the channel meets the edges of the valley, we have this very strong deflection of the channel migration. So in the context of numerical modeling, tracking bank material properties is really a key phenomenon that we want to be able to incorporate. Existing approaches to tracking bank materials in landscapes commonly use grids, so I'll quickly step through how that works. If the channel banks are represented at a given moment using vectors, the actual channel extent in the landscape is very commonly mapped onto a static grid to give some memory of where the channel has been. If we then have the channel evolve forward in time, as we see over here, the channel shifts from the location in the solid line over to the location in the dashed line. We can see that certain parts of the landscape are updated as having been newly eroded by the channel, and those are highlighted there in red. So what we can see is because this mapping of the channel is done in a discreet fashion, there's a discontinuous mapping of the erosion carried out by the channel. Now this is a detail that turns out to have cascading consequences as we look in terms of time-evolving scenarios. So we can see that here where we look at two simulations that track bank strength and landscape, that have an evolving channel that starts with the same geometry in both cases. And the way bank strength evolves is that the channel is eroding bedrock as to pausing sediment behind it. And that sediment is highlighted in gray. So what we can see is that for these cases that have two different grid resolutions, they essentially result in a different memory of bank strength that's imparted in the landscape. And that then feeds back to cause different trajectories for the channel. So we can see in these these two map views that even though they start with the same initial channel geometry, our channels have gone off in very different directions entirely because of this grid scale. To understand how this works, we can zoom into the scale of an individual grid cell. And what we find is that the necessary grid resolution we need to overcome this resolution dependence depends on the rate at which the channel is moving. So very simply if we consider an individual grid cell and right at the margin of it, we have a channel, channel boundary. If that boundary moves just a small amount or some fraction of that grid cell width in a time step, then the cell is not going to record, it's not going to record that increment of channel migration. However, if the increment of channel migration is substantially larger, then the cell can record that amount of channel migration. Of course, this distance that the channel moves in that time step is going to be equal to the lateral erosion rate times the time step. And so if we had complete freedom to choose an arbitrary the large time step, we could always get into a regime where our cells could be large enough or that it could be small enough that the channel migration would always overlap an entire cell. Very often, however, there are physical reasons that we would want to fix that time step. In the case of channels, that time step would very often be linked to some relevant timescale morphologic change, which we might consider to be the bankful recurrence interval of flood. So given that we want to fix the time step, that means that as the lateral erosion rate of our channel is decreasing, we need an increasingly smaller and smaller cell width in order to overcome this resolution issue. Now in many landscapes, the channel may be migrating fast enough that this resolution issue doesn't become a problem. But in bedrock river valleys, where lateral erosion rates are commonly on the order of a centimeter per year or less, and in valleys where we're considering spatial scales that may be several tens of kilometers of river length, this eventually requires a very dense network of small measurements, which can impart a very high memory cost, perhaps even on the order of terabytes, depending on how you implement it. So to overcome this challenge, we developed a framework that essentially uses the channel geometry instantaneously, records that, and uses that information instead of a grid to keep track of where the channel has been in the landscape. And so that's shown here, where the channel position at different time steps is colored with different colors, and the instantaneous or the current position of the channel is shown in white. Now the key point is that the footprint of the channel here in this landscape, rather than being mapped onto the grid, is recorded using these connected set of nodes which actually define the channel boundaries. And in so doing, we can use a lot less memory to represent the same information of where the channel has been. So in slightly more detail, the channel geometry is archived as vector data or sets of collected nodes at each time step. So that vector data includes longitudinal profile of the channel, its map to the extent, and also its cross-section. And then this vector data is used to reconstruct arbitrary bank material properties such as grain size or elevation that are set by channel scour and sedimentation. This history of bank properties is then used to scale channel migration rates. So as an example, if we take an arbitrary meandering model, which defines where our channel is, we can look along the channel banks at different locations and query for the locations of sediment and bedrock that exist in this landscape. So I'll give a quick example of how this approach opens up some new opportunities, especially for looking at landscapes at a very high contrast and bank strength, which is very common in bedrock river valleys. So the map you were looking at here on the left shows the channel, active channel in white, and the different colors correspond to the effective fraction of bedrock or sediment that's exposed in the channel banks. So the blues correspond to all sediment and as we go to the margins of the valley where the channel is deforming, it's hitting up against all bedrock walls. Now cross-section runs from the top to the bottom of this model domain and is shown on the right. And so we can see the contact between sediment and bedrock in this landscape and also channel right over there on the margin. So as we advance in time, the channel is going to dance back and forth across this model domain. Okay, looks like there's a problem with the movie. So anyway, so I'll have this on my laptop for the rest of the week. But what I can point out, at least just from the starting point, is if we do let this run forward in time, the channel, we can reproduce many of the features of bedrock river valleys just with accounting for an evolving bank strength in the landscape, even without other perturbations in the channel behavior that might be driven by changes in vertical incision rates. I think it's not uploaded. In any event, a result I can show you is that the memory use, compare the memory use that would be involved in a simulation that would, in an equivalent simulation that would use a grid-based approach versus the present approach. So to track the bank strength with a grid that had a resolution sufficient to track one centimeter per year, channel erosion in bedrock, would take on the order of essentially terabyte to represent this landscape. And for the simulation here, which is equivalent to bedrock river valley evolution on the timescale of several tens of thousands of years, we can do, we can track the bank material properties relatively efficiently with only about 15 megabytes of data use in this case. So to conclude, bank material properties can strongly influence river meandering. A vector-based approach to bank material tracking makes simulations tractable, particularly when we have cases of very high contrasts in bank strength. And another example, which I didn't have time to include here, is that this framework is also flexible to incorporate simple simulations of building sedimentary deposits and to depositing sediment on floodplains. And so it's potentially a type of framework that could be flexible to many different environments. Thank you. This kind of problem also would seem to be very suitable for level set methods, for example. Is that a popular approach for doing these kinds of simulations? I have seen it in some related work. But in general, there hasn't been, at least in models that are treating meander evolution over geologic timescales, I think there hasn't been a lot of attention to the detailed representation of boundaries, and particularly right at the channel in bank boundary. I was thinking, especially when you have topological changes, so reconnections of loops and so on, then it would probably be nice if that would be taken care of automatically in your simulation, right? Yes, I think it would. One advantage, I think, of one particular advantage of keeping track of the channel extents from different time steps is that you can record, essentially, I think it boils down to whether we need to record a boundary only instantaneously, or if we need to record the position of boundaries at different portions in time. And at least in some of these bedrock landscapes, or when we're thinking about floodplain meander belt evolution, I think very commonly we want to represent, keep track of boundaries at different points in time, because they can tell us about topographic breaks that we want to record. Are the properties similarly vectorized, or are you essentially having, sorry, are the bedrock and bank properties vectorized, or are you kind of pulling a raster onto a set of vectors which represent the channel margins? So these properties are reconstructed essentially entirely from the channel geometry. So, for example, in the case of a bedrock river valley, in the conceptual model, the channel would migrate and essentially erode a bedrock surface and deposit sediment behind it. And so if we know where the channel was, if we know where the channel's been at different portions of time, and what elevation it's pointing off the surface to, then at any where the channel's been, you can analytically solve for what the elevation would be. So it's really a process of reconstructing properties such as elevation or grain size, as long as there's simple mathematical formulation for what they should be.