 Our next speaker is one of our student speakers, Rebecca Caldwells with the University of Indiana, or Indiana University. She's been doing work with DELF3D, exploring sediment properties and its effects on deltaic morphology. Good morning, everyone. Well, she already told you who I am. My name is Rebecca. And the work that I'm going to be presenting today, I think, is a really good example of how we are utilizing these numerical models to start trying to get at some of the fundamental questions that we have about surface processes. So specifically, I'm doing some work using numerical modeling to explore the effect that grain size exerts on deltaic processes and morphology. Before I get started, I'd like to acknowledge my advisor, Doug Edmonds, who has worked extensively, not only on this research with me, but also on advising me. And I'd also like to acknowledge that this work has been partially funded by the NSF Frontiers in the Earth Systems Dynamics Delta Project, which, conveniently enough, Rudy Slingerland will be discussing in more detail following this talk. So traditionally, we think of delta morphology as controlled by the relative balance of rivers, waves, and tidal energy. And although this explains much of the morphologic variation that we observe in nature, it does not explain all of it. Take, for example, these three deltas, which we call river-dominated based on estimations of their marine-to-river power ratios. So these ratios mean they plot in the same location on that above diagram and should have similar morphologies. But instead, they actually look quite different. The Mississippi Delta has this bird's foot characteristic with a few channels that are elongate. The Masi Delta has a bifurcated channel network with a pretty rough shoreline. And the Goose Delta is semicircular with a large number of channels. So this additional morphologic variation that exists amongst river-dominated deltas suggests that there are additional variables controlling their morphology. Now, previous research has suggested that grain size may be an important factor. And interestingly, these three deltas have very different grain sizes, representing a fine, intermediate, and coarse grain sediment input, which leads us to ask if perhaps grain size is affecting their morphology. So this is the question that drives our research. And we aim to figure out exactly how grain size is affecting their morphology. Specifically, we're asking, how do changes in the incoming grain size distribution modify delta-building processes and produce morphological variation in the delta's channel network and its plan for morphology? So to answer these questions, we're numerically modeling delta growth in delt 3D, which is a physics-based morphodynamic model that simulates fluid flow and sediment transport. So here, you see the model setup in plan view, where bed elevation is represented by a range of colors. And you can see the initial channel cuts through an erodible beach, entering a standing body of water in a basin with a gentle offshore slope. To the northeast and west, we apply open boundaries with a constant water elevation. And in the basin, we're ignoring the effects of waves, tides, and buoyancy forces. And flow enters the domain through the initial channel from the south, carrying a constant water discharge and a sediment flux of approximately 0.04 meters cubed per second. And we vary that incoming grain distribution by the grain size distributions median and standard deviation. We start with a fine grain sediment input and vary the median grain size from silt to coarse sand. And then for each median grain size, we additionally vary the standard deviation from very well sorted to poorly sorted. And this results in 23 different modeled grain size distributions, shown here in parameter space. So I'm going to start off by showing you guys movies of delta evolution for three different deltas that plot in different locations in parameter space and represent a fine, an intermediate, and of course grain delta. So we'll start with a fine grain delta. Again, you're looking top down on the model setup, which shows the bed evolution through time as the delta is prograting northward into the basin. As it grows, we see that the channels bifurcate around mouthbars a few times. But as it continues growing, note that its dominant process seems to be channels that elongate via levy procreation, forming in a elongate delta shape. So we can contrast this with a coarser grain delta. As the delta grows, we see much more frequent channel bifurcation around mouthbars, which seems to be the dominant process controlling the delta's growth. And also I want to point out that as the mouthbars prograde, they form these local shoreline perturbations, which creates a delta with a highly rugose delta front. And we can contrast this further with an even coarser grain size delta. As the delta grows, the channels bifurcate around mouthbars. But as it continues growing, note that its growth seems to be dominated by a large number of channels that deliver sediment relatively evenly along the delta, creating a semicircular shape. All right, so here are the results of all 23 different model runs. In these results, we can observe that the delta morphology transitions as both the median and the standard deviation increase, which going left to right represents an overall increase in the dominant grain size constructing the delta. So these fine grain deltas seem to create elongate deltas with a few channels and pretty smooth shorelines. And then as grain size coarsens, we can observe that the delta morphology transitions into these semicircular shapes with a much larger number of channels. So this observation leads us to ask if we can quantify the variation and furthermore, can we explain exactly why this morphological variation occurs? So in order to quantify the morphologic variation, we've measured four different morphometric parameters on each delta. We measure the average topsec gradient, the number of channel mouths, delta front rugosity, and a bulk delta shape metric. So the delta front rugosity is simply a sinuosity index, where we take the total delta front length and normalize it, oh sorry, and it's normalized by a smooth delta front length, such that higher values indicate more rugos delta fronts. Now our bulk delta shape metric aims to quantify how semicircular versus elongate a delta is. So we simply take the ratio of the delta's shore parallel width to its length and we divide this value by two, such that a perfect semicircle is represented by a value of one and values less than one indicate a elongate plan forms that deviate from a semicircle. And here you see the results of all four morphometrics plotted against the grain size distributions D84, which is a value that we consider to be representative of the dominant grain size controlling the delta's growth. So you see that as grain size increases, both the average topsec gradient and the average number of channel mouths increase, showing that the courses grain deltas have steepest topsec gradients and the largest numbers of channel mouths. Delta front rugosity on the other hand has a somewhat parabolic relationship, though the data are scattered, but it shows that the intermediate grain deltas are creating the most rugose delta fronts. Finally, the bulk delta shape metric increases with increasing grain size, showing that coarse grain deltas are semicircular and fine grain deltas are elongate. So in order to explain this morphologic variation, we present a new process-based model for delta morphology. So this model is driven by the observation that we observe three fundamental processes constructing delta growth and that the prevalence of each process on the delta is set by its dominant grain size. So we observe that fine grain deltas are dominated by the process of channel elongation via levy procreation, but as grain size increases, the dominant process shifts to channel bifurcation around mouth bars on intermediate grain deltas. Finally, as grain size increases even further, we see that channels have a large number of highly mobile, or deltas have a high number of highly mobile channels, which are dominated by the process of channel vulsion. So our model suggests that it is the dominant process acting on a delta that dictates its morphology. So next, I'll step you through how each one of these three processes affects the delta shape. In order to determine which deltas are dominated by the process of levy elongation, we measure the percentage of channels on each delta that have an unstable turbulent jet, which is a criterion that is set by a channel mouth's width to depth ratio and its velocity. So we use this criterion because previous research shows that when sediment-laden turbulent jets exiting channel mouths are unstable, they meander, similar to the jet pictured here. This meandering increases their lateral diffusivity, which enhances levy elongation. So here I've plotted the percentage of channels on each delta that have an unstable turbulent jet against the dominant grain size, and we find that as grain size decreases along the x-axis, the smaller width to depth ratios of the channel mouths produce an increased occurrence of jet instability and a dominance of levy elongation. And interestingly, this dominance of levy elongation, which is now increasing along the x-axis, also relates to a decrease in the delta shape metric, showing us that the dominance of levy elongation on fine grain deltas produces elongate shapes. So how about the process of channel mobility? In order to quantify the observed channel mobility, we measure the average timescale that a channel remains in a given location, such that higher values indicate more stable channels and shorter channel timescales indicate more mobile channels. And here you can see that these channel life timescales, which we observed to be dominated by the process of channel evolution, here I've plotted them against the average grain size and we see that fine grain deltas have more stable channels, whereas coarser grain deltas have channel mouths with much shorter channel life timescales indicating they are more mobile. Additionally, we find that this dominance of channel evolution on coarse grain deltas creates deltas with the largest numbers of channel mouths. Here I've plotted the measured number of channel mouths against the measured channel life timescales, which shows that as channel life timescales get shorter, these deltas dominated by channel evolution create the larger number of channel mouths. And this is a relationship that occurs because when evulsions are frequent, they increase the occurrence of overbank flow, which outpaces channel annealing. So this allows the reoccupation of relic channel pathways increasing the number of channel mouths that are active at a given time. So finally, how does the process of mouthbar growth affect ultimorphology? So if you recall in those movies that I showed you earlier of delta evolution, when we have an increased occurrence of mouthbar procreation, we're creating local shoreline perturbations that seem to be increasing the delta front rugosity. But now in order for this process to dominate, mouthbar growth must outpace channel evolution because a channel needs to remain in a location long enough to actually construct a mouthbar before it evulces to a new location. So in order to test this idea, we calculate a mouthbar growth timescales, which we take as the ratio of a channel mouthbar's volume to its depositional sediment flux. And here I've plotted the percentage of channels that have river mouthbar growth timescales shorter than the evolution timescales for each delta against the dominant grain size. And this nonlinear relationship shows us that the intermediate grain sizes have the most channels, or produce deltas with the most channels dominated by river mouthbar growth. Finally, this dominance of mouthbar growth, which now increases along the x-axis, also relates to the highest measured delta front rugosities. So in conclusion, we present a new model for the effects that grain size exert on delta morphology. Our model shows that grain size controls delta morphology by shifting the balance of dominant process acting on the delta. Fine grain deltas have deep, narrow channels dominated by the process of levy elongation via unstable turbulent jets and bifurcating infrequently. This creates deltas with only a few channel mouths, smooth delta fronts, and elongate shapes. As grain size coarsens, we have wider channel mouths with more stable turbulent jets, which suppresses levy elongation and the coarser grains are deposited near shore favoring mouthbar growth. This leads to increased channel bifurcations and local shoreline perturbations, resulting in a delta that has a larger number of channel mouths, a high lever goes delta front, and a semi-circular shape. Finally, coarsest grain deltas increase their topsec gradients in order to create higher bedsheer stresses, which are necessary to transport those coarser grains. So these steeper gradients increase aggregation rates and evulsion frequencies, creating deltas with a large number of channels that evulse frequently, distributing sediment relatively evenly along the shoreline and creating the largest numbers of channel mouths, a relatively smoother delta front, and a semi-circular shape. Thank you. I was wondering, whether you also looked at the difference between the suspended and bed load. I mean, the coarser grains are definitely bed load and the really fine ones are definitely suspended load. So that would explain a similar type of, that would explain already the features that you received. Is that correct? Yeah, so that's a good point. He was asking about the differences between bed load and suspended load. Yes, so the coarser grain deltas do have higher percentages of bed load. And so we found that the dominant process that was affected by grain size has to do with its advection lengths or has largely to do with its advection lengths. And you could imagine that the finer grain deltas with more suspension, not only have smaller settling velocities, but I'm sorry, higher settling, smaller settling velocities, but they're also higher up in the water column. So they can be effected much further. And that will also increase the levy elongation that we see on fine grain deltas. I'm also thinking about the bed slope effect that in finer particles you, probably that's limited because everything is in suspension. Yeah, so we do account for the bed slope effect on bed load transport. I have not looked directly at how that would affect the deltas growth, but you could imagine that it would have very similar effects that Andrew was presenting in his previous presentation. That was very cool, thank you. Do you have the ability in Delft 3D to modulate sea level and see how that affects morphology and have you done any experiments with that, just casually? Yeah, so in these models, we are keeping it constant to just study the effect that grain size exerts. But funny you should mention that I'm actually just now starting to increase sea level to see how that's affecting the morphology but also to create more aggregational deltas which as my research shows may affect its morphology.