 Hi, everyone. So I've been thinking about equilibrium, the Ganges Bromacutra and Magna Delta. I've done a handful of other projects here. But ultimately, everything's kind of inculminating towards the idea of what is the equilibrium elevation of the delta and how does that vary throughout the delta? So I'm going to talk to you a little bit about that today. But just for some overview, here we are looking down on the delta. We have the Ganges coming in from the west here and the Bromacutra from the north. And the Magna meets up right here south of Dhaka. But it's conveying about a billion tons of sediment total to the Bay of Bengal, about a third of that gets reworked into this extensive tidal network here. And that's predominantly where I focus my work. So zooming in on this tidal network, it's largely disconnected from the fluvial system, though you get fluvial input over here. But it's often been identified as one of the most at risk for sea level rise. Some recent work is showing that in the recent past, two to five millimeters per year is what's been experienced thus far. But there's been a growing body of literature showing that sediment is quite the resource here. All the way back to 2001, we see widespread. This is a high level study that said about a centimeter per year of elevation gain from sedimentation. More recently, we have these more point estimates that match that about a centimeter per year. As you get closer to the sediment source, the main river system, you get higher rates, about two centimeters per year. And here's a really interesting one that I focus on. There's a forthcoming allocation that I'm working on right now that focuses on that. But it's really high rates. We have about three centimeters per year there. And just a bit of a teaser, the way that sedimentation occurs, you have to have water on the platform that's bringing the sediment. So if the water is only changing a few millimeters per year, how are we getting centimeters of year of aggregation? And we think it's tied to tidal amplification, especially that one that was in orange in the northern extent there. It's likely due to the widening of the tide. So the highest tides are actually getting higher. So even those sea level, the relative water level, looks like it's moving a few millimeters. We're actually expanding the tidal range. The highest tide is getting higher, and it's actively occurring. My intuition on this was that tidal amplification would slow down over time because you can't amplify in perpetuity. But within the Ganges, there seems to be an ongoing reorganization on network that's creating this effect. And there's a recent paper that shows that this effect is continuing. This is adapted from one of their figures showing all of their amplification measurements aggregated together. So you can see that it's ongoing here. So I'm now starting to think about the long-term future stability of this delta and what's controlling this elevation. Ultimately, we think water level has got to be a part of that. And that manifests as relative sea level rise. So that's the subsidence plus any use of a static amount of sea level change. And we see that we expect maybe upwards of 100 centimeters across the delta by 2,100 as sea level rise really amplifies towards the end of the century. We have this ongoing tidal amplification piece that was identified. Changes in the sediment load. There's been a lot of work around this showing, hey, maybe the sediment load is going to increase from increased erosion and the catchment. But also, maybe it's going to decrease due to damming and human interventions. So there's a lot of uncertainty about what's going to happen over the long run with the elevation of this. So my question is, how is this going to impact the stability, the delta stability as a whole? I use simple models to ask this question. And here's what I mean by a simple model. Here's a stylized version of what my model is. I have a whole code basis on GitHub. I'll show a link for that at the end. But I can construct these tidal curves based on field data that we have. And I use a simple mass balance to estimate the aggregation per tidal cycle. So the top panel here, what it's showing is elevation. And the blue line is the tide. And the black line is a hypothetical platform. So as the tide goes above it, that's when you can have sedimentation. That's when you get sediment on the platform. You get aggregation elevation change. So I calculate that at every single tidal cycle. And we can look at the change in elevation through time. You can play with the tides. You can stretch them. You can increase sea level. You can increase the amount of sediment that's going into it, the amount of subsidence. But ultimately, it's a really simple model. And it's really just this mass balance here. The change in the land service is just the sediment plus the organic matter minus the negative terms, which is the compaction subsidence. And you can actually throw in sea level rise in here as well. But the way it's inherently in my model is as a tidal. But it is effectively a negative term because it's looking at the relative change to the platform. So anytime the platform is flooded as we get sedimentation, we call that the accommodation space. That's what the shaded blue here is. So the way I've been thinking about what the long-term elevation will be is this idea of equilibrium. And I'm calling it an equilibrium elevation. It's the long-term steady-state elevation for a given range of those conditions. So we can change all the different parameters and see what the elevation naturally tends to. So over the long run, the elevation is going to tend to something so that even if you have relative water level changes, if you're measuring it relative to the water, the elevation appears unchanged. So the things that control that, at least within our model, the way we inherently internalize this is looking at we use mean tidal range. And that should capture tidal amplification. Suspended sediment concentrations is going to capture some of the change in the sediment mode, and relative sealable rises capturing the relative water level change. It's important to note not only do those terms capture those points in yellow there, they capture the spatial variability across the delta 2. So what we're doing here is exploring the parameter space. We're looking at the response surface. As we change these things, what is the natural tendency? The elevation want to sit at of these platforms. So we're creating a choose your own adventure. You can look at your own specific conditions to determine what the natural elevation should be. And we decided on this range of values here for these three parameters. We think it captures much of what is going on in the delta, both now and hopefully in the future. And the way we equilibrate this model. So here I'm showing the top panel here is the elevation change. Blue line, and I realize this after the fact that we actually had these side by side, but I've changed blue not to be the tides anymore. It's now the platform. So keep in mind this is the platform elevation change through time. The dash line is mean sea level. So a flat line here, since we're doing elevation change, that's implying that sea level is increasing at a centimeter per year, which is on the high rate. But this is just one simulation that we ran. So if I run a platform evolution for 200 years, this is what slowly happens. It goes up and down and up and down. And the interesting bit, the up and down part is actually tied to an actual behavior that we see in the tides. There's an 18 year lunar cycle that seems to have some potential long term impacts for this stable surface. But in order to determine it's equilibrated or in equilibrium, we tried to minimize that difference until it was about under a half a millimeter. So at that point, it's equilibrated. And we choose 200 years here because it guaranteed the range of simulations we were running where it equilibrated by them. So there's a lot to work with here. I'm going to step through this slowly with you. So here's what the surface of the sequel of the elevation looks like. So we're exploring the parameter space here. This is a small multiples plot. What we're looking at here is we have three columns. And they represent highest astronomical tide, mean high water, and mean sea level. It's important to note that looking at just mean sea level tells you only one part about what the elevation of these platforms are because the highest tide is really impactful, especially if you're living there. So we look at all three of those. And along the y-axis of all these plots is the tidal range, and along the x-axis is the suspended sediment concentration. And as you move down through these slices, you're increasing the relative sea level rise. So starting up here at 2, all the way up to about a centimeter per year relative water change. So you might see things that I don't. Every time I look at this, I see something new. But things that stand out to me, this is something that really surprised me in terms of what the data showed me. Doesn't surprise me based on what I've seen in the field there. Much of the delta is quite stable. That is to say, small changes in these parameters result in not large changes in equilibrium elevation. But big things that jump out to me are these critical thresholds. There's a really strong, I call it a strong threshold here. But as soon as you get around a 0.1 grams per liter, you start to rapidly fall off in terms of re-equilibrium elevation. So that is really pronounced. It's partially pronounced in mean sea level here. But if you really look at the highest tide, you can really see the contours of that become steep and it falls off quickly. For mean tidal range, so if the tides are not, they're not swingy, they generally are more compressed. The highest tide isn't as high, so you don't have as much of a ability to exact sediment onto the platform. That might mean that you need more small inundations to maintain an equilibrium. And there seems to be somewhat of a weak threshold below two meters here for the tidal range. And the reason I think it's a weak, or it is important to note, is because as you increase sea level rise, you start to get into this range where the average tide, so this is the average high water, the average tide is flooding the platform, which has impacts if, say, you're living on this platform. So I think it's important to consider where the mean tidal range is as well. The big takeaway, one of the big, actually I think the biggest takeaway Delta's quite stable. Another big takeaway though here is that at really low suspended sediment and low tidal ranges, and you increase sea level above six millimeters, or relative sea level rise above six millimeters per year, you start to get into this zone where it becomes submerged always. There's no way to keep it in equilibrium above the lowest tide. So that's just one part of the story. The other part is what does this mean in terms of the dynamics on the platform? So the elevation is one thing, but in order to maintain that elevation, what does that mean in terms of the length of time that's being flooded, or how deeply it's being flooded? So we look at the same thing here. It's the same setup, relative sea level rise as you go down, and the same axes. And what jumps out to me here is the hydro period, which is the inundation time, is similar to mean high water. So it's being controlled somewhat by that. The depth is mirroring the highest astronomical tide here, and the threshold is very pronounced in both these, that SSE threshold here. And you can see that it quickly drops off below on both these cases. And it really, looking back at the previous plots, I didn't quite understand why this was triangular shape, but it becomes evident to me that these contours really get smushed down here within the hydro period, and they start to bend in that corner. And it's because you quickly get to a point where you're getting close to 12 and a half hours of inundation in a semi-diurnal system that's a full tidal cycle. So it's fully inundated always. So it turns out the hydro period's kind of controlling. So first order here, I wanted to step back. This is arm wavy, but I think it kind of gives me a sense for, can this model tell us something about the current configuration? So we can start thinking about the future configuration, the delta. And the way I'm thinking about that is as you move away, so here we are, the Ganges Brown Poocher of Magna River Mouth here carrying all this sediment out. As you move away, generally suspended sediment goes down and marginally tidal range goes up as you move away from it. The fluvial input kind of can suppress the tidal range, but also as you move west, the natural tidal range is higher. But I don't think it's quite, the numbers are a little fudged here at this point, but I think my intuition tells me that the tidal range is even higher though as you move inland from this tidal amplification. So suspended sediment tidal range inversely correlated as they move down the coast and then tidal range increases as you go in. So let's go back to this figure, equilibrium elevation. And let's think about, so that one dot that I told you, the orange one right here at the top, it's one area I thought about a lot. I would say that we're in the range of three to four meters for the average tidal range. And we have quite high sediment here because it's close to the fluvial system and it's receiving much of the input and it has the high tidal range and a lot of sediment. So if we are there, we're above two, we're around two, two and a half meters, which is exactly what we've seen in the field relative to the water level. So for the natural system, this is not considering the polders, which are an embanked system. We're looking at just these natural mangroves for right now. So if we're there, we have really high elevation. You can see it on the map here. And as we move west, there's been much conversation around, are these already experiencing drowning from sea level rise? That may be the case, but also this natural elevation seems to want to be lower. So if we go all our contours here relative to mean sea level and we go, let's approximate it as 0.1 grams per liter, we know it's less and we think it's three to four or maybe closer to three, you see that the elevation naturally wants to be lower relative to the eastern side here. So maybe what we currently see is expected, maybe there is ongoing drowning, but it's important to note, we do know that suspended sediment decreases as you move over here. And I pointed out there's a critical threshold around 0.1 grams per liter. So this area may, if it's not already, maybe critically close to that threshold. So just to summarize here, surprisingly, the delta surprisingly stable, even at these really high rates of sea level rise for much of the delta, but there are these critical thresholds of 0.1 grams per liter of suspended sediment. The low, small tidal range makes it more likely you're in a data more frequently, you're below mean high water. And present data, delta elevations roughly match our intuition and our understanding from this. And my code is available here and Python's open source, feel free to use it. I'm still in the middle of trying to actually publish it on PIP, but you can build it from source right now and play around. Is there a question for Chris? Do I call or you call? Yeah. There's a question back there. Looks like you're doing your CCMES fun run, Mark. That's very, very good. Chris, that was really wonderful. And I like to see that the tides have so much impact. But I'm wondering that part of the world also get impacted by less frequent, but large events like hurricanes or cyclones. I'm not sure how you call them there. We had just over the weekend, there was one slightly close to Myanmar, I think. But could it be that your orange dot is somewhat more land inward? So if such a large event occurs, it could erode some of the sediment that gets deposited closer to the coastline and maybe moves that lands inwards or less eroding at that orange dot. Could that also be a factor to consider or do you think the tides are really the driving force? Yeah, so I gave a talk on this AGU, the tidal amplification bit. It seems to be that the elevation is following tidal, ongoing tidal amplification. And we see this from Jeff Bommer and Carol Wilson's work on that site that the elevation gain there has been consistent over five years at least and probably longer, it's yearly that high. And you're right, storm surges is likely kind of remobilizing a lot of this, but I think the signal is so persistent that it's likely dominated by the tidal amplification.