 to step on the cables. Hi everybody, very honored to be here. Thank you to the organizers for inviting me. This is my first systems meeting, so I'm very excited and only a little intimidated. So I'm here to talk about some work I did as part of my PhD project at UT Austin, using some reduced complexity modeling to understand material transport in river deltas. So I wanna thank my co-authors here as well as some collaborators at Caltech as well as UT and JPL for funding this work. With that, I'll get into the presentation. So we're gonna be talking about river deltas, which are these very interesting and dynamic landscapes that I'm sure many of you are familiar with. And one of the central features of deltas that I wanna underscore is that the way that these systems build land and function depends on how flows of water sediment and other materials get distributed and partitioned around these landscapes and between channels and wells. So in general, water is the driving force for the transport of these materials, obviously, which gets at this idea of hydrological connectivity being a very important feature of these landscapes. So delivering these materials into the wetlands and places where these materials are depositing and building these systems. And thanks to advancements in tools like hydrodynamic models and advanced field methods like ADCPs, our ability to constrain water transport and connectivity in deltas continues to improve, especially in this wax lake system down here on the bottom right, which I'll be talking about a lot today. But I want to talk about something a little different than water, because I think that even though we're understanding the water transport a little better, I think there's some interesting dynamics that could be happening with other materials that we're maybe not capturing with these water dynamics. So the main thing that I wanna talk about today is that unlike water, most of these other things that are transporting into deltas that we're interested in have some positive or negative buoyancy in water and tend to concentrate either near the surface or near the bed. So due to this balance of sort of turbulent mixing and settling, you end up with these vertically stratified concentration profiles that leads to this non-uniform shape that you see here. So this is something that's typical of sediment where you have most of the sediment concentrated near the bed. And this is true of other materials too. So we could think about, for example, plastics or microplastics that might be buoyant, might be negatively buoyant. And so they could concentrate near the surface or sort of somewhere in between. And so the question I wanna ask with this presentation is how does particle buoyancy affect the patterns of transport that we see, especially in these deltaic systems? And one big reason that I think that this matters, I'm gonna demonstrate with this sort of simplified schematic. And so you can imagine that if we're looking at something flowing downstream in a river delta where there's kind of a central channel, and then there's some amount of exchange into these nearby wetlands where water's flowing over these sort of intertidal levees. If we imagine that there's sort of three different distinct populations and materials that are concentrated in different locations of the water profile. Some near the surface, some near the bed and perhaps something in between. You can imagine that if something is sort of floating on the surface that these populations are gonna find it much easier to spill over into these nearby intertidal wetlands or islands because it's much easier to overtop these sort of topographic features in the landscape. Meanwhile, things that are sort of heavy in the water column and are not only flowing downstream but also sort of pulled more so by gravity, they're also sliding downhill. And so you're gonna find higher concentrations sort of near the thaw wag of these channels. And so just due to this sort of differential topographic steering that you would expect based on these things being in different locations, we think that this could affect the transport pathways of these different materials. And that's what we sort of want to investigate today. But this is a little difficult to model in a generalized way. So we have models for most of these things that we're interested in in these landscapes. And we could be talking about a wide variety of things that could be interesting in depositional landscapes like a Delta, we could talk about surfactants, so mineral or biogenic oils, many biotic elements like floating vegetation, fish larva, seeds, things that are often floating, perhaps we're interested in ice or woods or plastics which wood and plastics could be heavy or they could be floating. It depends on the attributes of that material as well as a variety of sediments that could be sort of well mixed into the water or sinking at the bottom. And we have a lot of models for different components of this state space, but due to a bunch of model differences it becomes a little hard to compare those transport patterns in a generalized way between different models because there's a lot of model assumptions that are built in that make it difficult to compare things to each other. So we are actually gonna take some inspiration from a reduced complexity model that many of you will be familiar with called Delta RCM. This is a morphodynamic model that is able to build these very realistic deltaic systems just through a simple few parameters that just by changing a single parameter you can change the way water, mud or sand are routed in these systems. And so we're gonna take inspiration from this and we're gonna build this out into this Python package called Dorado that me and my co-authors helped develop which is a Python package for simulating passive particle transport in shallow water flows. So basically this model is a stochastic reduced complexity Lagrangian model it's for particle transport and it uses the same transport rules as Delta RCM. It's a stochastic model, it's a Markovian model and it's kind of an agent-based approach. And the way that this model works is that just by changing a few routing parameters gamma and theta and theta is gonna be of interest in this presentation. We can change the extent of this topographic steering effect that I described before. And this is a grid-based model. So these particles are basically walking downstream in a D8 fashion and the routing weights to each of the cells that it can be routed to depend on first the hydrodynamic information that you're pulling from some more sophisticated or higher fidelity model like a hydrodynamic model. And then there's a stochastic element that chooses the weights of the cells according to a couple of different features. And I'm gonna talk a bit about theta because that's the one of interest today. And the way theta works is that when a particle is stepping into a downstream cell you can imagine that if we have a theta of zero then the routing weights are not affected by the depth of these receiving cells. So any cell that is sort of in the downstream vector is equally likely. Whereas if you have a theta of, for example, one then this routing weight is linearly proportional to depth. So we are routing sort of in proportion to how much room there is in those cells which is a more applicable assumption for something like water. Whereas if we have an even higher theta such as a theta of two then this dependence on depth is non-linear. So it's not only routing downstream in proportion to depth but also potentially sliding downhill or adding in this extra element that you would expect for something more like sediment. And that's the way that Delta RCM uses this parameter is that water is routed with a theta of one and sediments are routed with a higher theta. So just by changing the simple parameter we can actually extend this to a pretty wide range of different materials that we might be interested in. And that's what we tried to do with our work for this. So we're focusing again on the Wax Lake and a Chafalaya Delta system in coastal Louisiana. So this is a smaller distributary of the Mississippi River. And we built out this sort of suite of simulations that varied a few things that we wanted to investigate. Two of these things are environmental conditions. So by changing the discharge between low and high and changing the tides between kind of a steady scenario and an unsteady scenario we can see how these transport patterns are changing for some different environmental conditions. And then we tried a sort of range of sort of pseudo materials that we're interested in by changing this theta parameter between a range of zero and one. And the idea is that hypothetically speaking we should be able to approximate the transport pathways of a bunch of different kinds of things just by changing this simple parameter. Obviously this is very simplified physics so we're not using the most sophisticated high physics model. But we can compare these things directly to each other by using this approach because we're simply changing one consistent thing between all of them so the model is staying the same. And the metrics that we're going to be using to compare this transport one of the specific frameworks that I want to specifically touch on is this idea of a nourishment area. So this is a sort of downstream equivalent of the catchment area that you might be more familiar with in more upstream hydrological application. And the idea is that in a Delta system the nourishment area is the region of space that's nourished by material from some given location. And so we're specifically looking at sort of a global picture of nourishment in these Delta. So just from the Apex we're seeding these materials and we're watching how they propagate and over the entire time span of our simulation and over all of the particles that we're seeding we basically for every location in our Delta we're seeing how many times that location was visited by some material and we're quantifying that over the whole range of our simulation and then normalizing it into zero to one. So basically we end up with this picture that shows in the darker colors places that received a significant amount of material from that injection site. And then for it kind of fades sort of into this background gray in places that were rarely if ever visited by these particles. And what's cool about this is that for each simulation that we do we can compute this nourishment area again and again for every environmental condition that we're looking at every pseudo material with this data parameter. So here I'm showing six examples and you can see just kind of looking at these in a qualitative sense that this picture is changing. So there are some very interesting trends that you can kind of visualize and see by simply changing one or more of these different variables that we're looking at. Or we can perhaps change scenarios again and look at how this picture is changing between these. But the interesting thing that I wanna really touch on is that because this is a quantitative approach that actually quantifies this magnitude of nourishment in each of these scenarios we can directly stack these on top of each other and take differences to see which regions are relatively speaking receiving more material in different circumstances. And so here's a particular example of that where we're looking at how the nourishment is changing by a function of discharge. So if we change the discharge from low to high for these particular three pseudo materials with this data parameter we're seeing how these nourishment patterns changed in each of these scenarios. So places that are shown in blue are places that we're receiving a greater relative nourishment when the discharge was high whereas places that are shown in red we're receiving a greater relative nourishment at a low discharge. And if you're familiar with Delta's you would not be surprised to see that we're seeing blue inside of these inter-distributary islands. So islands receive more flow when it's flooding that intuitively makes sense. And you can look at the same picture as a function of tides. So if we turn on and off tides we can look at the same difference map. So again tides when we increase this mixing in the system we're seeing more material flushed back into these islands so we're getting more of this exchange with these wetlands that we're very interested in. And there's a lot of interesting things to pull out of this picture. But one specific one that I wanted to point out is that you can see that as we move from left to right on this slide we're generally seeing less colors. And that's one interesting finding that we found is that it appears that patterns of buoyant material transport seem to be much more sensitive to these environmental changes than at higher Thetas. So I thought that was an interesting finding. It's maybe not super surprising but it's very interesting to be able to quantify that. We can also look for some given environmental condition if we change this Theta parameter how that nourishment changes relative to what we would expect for water. And so each of these four maps that I'm showing here are taking the difference between the nourishment of water and the nourishment of this other material that we're looking at. So places that are shown in brown are places where we're seeing sort of a relative enrichment of that material. You can think of this sort of like a concentration. So places that are brown are higher concentration of those materials relative to what's entering the Delta upstream and places that are blue are places with lower concentration. So you can see sort of where we expect more of these materials in these Deltas. So one last way that I wanted to quantify these differences is I mentioned that in the Wax Lake we're very interested in this idea of hydrological connectivity between the channels and the islands. And so I basically constructed sort of a pseudo ADCP water budget approach where I drew these radial transects at different distances downstream from the apex. And I wanted to see just in bulk what amount of material is exiting out of the channels versus out of the islands in the Wax Lake. And so I'll start with actually I'll go ahead to this one. So for some particular environmental conditions if we look at the total amount of water that is exiting out of the islands versus out of the channels focusing on these downstream plots that are showing this downstream transect. We see that the total flux of water that's exiting the Delta through islands rather than out of channels is about 25 to 40% which is a very typical number based on the field estimates that have been done in the Wax Lake. So how does this number change if we change theta if we look at a different material? So here we're looking at sort of floating materials things that tend to be more concentrated near the surface. And we can see that this number actually increases to 60 to 65% so significantly more material is exiting out of the islands than out of the channels. It's actually preferentially much harder to stay in the channel the entire way down the transported downstream. Meanwhile, if we look at something that's sinking something more like sediment we're seeing a much lower fraction of material exiting out of the islands down to 10 to 15%. And that's not to say this 10 to 15% is not a relatively speaking large flux of material like obviously these islands are being built from the sediment that's making it into them but compared to the amount of water that's entering them it's a very different magnitude which I think is interesting from the perspective of using water as a proxy for where these other things are going. I'm not gonna belabor the point of this too much in pursuit of time but we wanted to get a little more specific I've been talking this whole time about this theta parameter which is sort of a model specific abstract concept of what kind of material we might be looking at. And so I wanted to tie this back into a more like physical parameter that you could use to say where you are in the state space instead of just a theta of one or two or whatever what are we actually talking about when we're looking at each of these maps? So I constructed this little toy model where we imagine some material is routing from cell A into either cell B or C depending on some preference based on the changing topography in each of these cells. And if we imagine that we have some concentration profile and we fill in some other details about the simplified model we can sort of derive what flux of material we might expect into each of these downstream cells and going back to the definition that we used in the routing weights in Dorado we can sort of tie these sediment fluxes into what these different routing weights are in the model based on the theta parameter that we've been using. And if that was way too fast and not easy to follow the point of this is that we were able to derive essentially this plot that I'm showing here on the left which is now showing what the theta parameter looks like for a range of different Rouse numbers or suspension numbers including the sort of negatively buoyant sinking materials as well as the positively buoyant floating materials all in one plot. And what's cool about this is that we can go to field data and we can look and see what kinds of materials tend to occupy different parts of this plot. And so we can fill in some details and say, okay, this particular theta is appropriate for flocculated mud and this one is for sand certain plastics tend to fall in this surface load range. And so you can actually work backwards from this and say, if I have some material that I'm interested in in these fluvial systems, you can use this to say what theta should I be using if I wanted to approximate these transport patterns. And so I'll get into a few conclusions and to drive home those conclusions I wanted to show one last figure. And what I'm showing here is the choice of theta that led to the maximal nourishment in each location in the system. So places that are blue are places that were maximally nourished by a sort of floating material whereas the yellow colors are places that are maximally nourished by a sinking material. And what I think is interesting is that going back to the very definition of how the model is implementing these routing weights this is a local parameter. It's locally changing the preference for routing into each of these downstream cells and just using this local vertical stratification combined with this sort of differential topographic steering we see that this is sufficient to create these emergent system scale sort of hydraulic sorting of materials in space. So looking at this delta on the right we're not modeling deposition, this is a passive model but you can imagine that if we were modeling deposition that we would be seeing very different deposits in these different types of things that are routing in the system which is interesting that these systems are being built by these materials that are routing through them and that paints a very interesting picture I think of how these are getting sorted. Likewise, we saw that these external drivers like discharge and sediments or discharge and tides as well as some other parameters like wind and waves did not affect all of these nourishment patterns equally floating materials were more affected by these changes in environmental conditions than other materials were. And so these external flows of energy into the delta seem to be able to reinforce these spatial gradients between these sort of geomorphic constituents. So floating vegetation and seeds are being routed to somewhere different than a lot of sediment. And I think that has interesting ecogeomorphic implications. I wanted to emphasize the Dorado's fully open source it's compatible with any 2D hydrodynamic flow fields that you might have access to. So if this is something you're interested in using in your landscape, it should be pretty easy to copy and paste this entire approach to whatever system or model you happen to be using. And I really like that it's able to quantitatively compare this partitioning and connectivity between materials in a unified way. Obviously this is a very simplified approach. So we're leaving out a lot of interesting physics for each individual material. But the weakness of that is also a strength because we know that we're comparing things like to like which I think is a very fun and interesting approach. So with that, I will call it, that's all. Questions for Kyle or hold on for the mic. Really great presentation, Kyle. I appreciated it. My question is, is there a pathway to linking this model with morphodynamic models, like to translating this information into morphodynamics? Absolutely. Thank you and that's a very good question. I think that there is, and I think it's one of the more interesting things that I would like to see worked on is adding in that depositional component. And I know that I'm talking mostly about the sorting that you see when you simply have just a passive particle that has this differential sorting effect that I'm showing here. But when you add in the depositional picture and potentially materials that transport at a different speed than water, there's a whole other realm of processes that could be influencing where things are ending up in space. And I think that would be a very interesting second layer on top of this. Now that we understand this a little bit better, I think we can build up more and more sorting processes from there. One other question from Chris. That was super cool talk. I really like, and I'd like the way you're quantifying the value of theta depending on the Brause equation, I kind of think. But one component of that is that that will change with the local shear velocity, right? So can your model change theta on the fly place by place as things are going on? Right, so it cannot, and that is definitely a weakness. So going back to this plot that I showed here, the fact that these aren't just one line, but actually a couple of different lines is this spread is due to the weakness of that assumption being sort of a global single parameter in space. So we're making an assumption that that doesn't change too much in space, which based on the spread of these plots from each other is not a considerable amount of variability given the other modeling assumptions we're making. So it doesn't seem like it's maybe the biggest source of uncertainty, but it isn't actually a perfectly global parameter. So that is true.