 So our next talk is going to be given by Katie Barnhart from CU Boulder. I'm going to do a quick town and slide check. There's a green thing below. How about now? I think you can get more together. That's brighter. Okay. Oh, it sounds like someone in the back. Okay. Katie's going to be telling us about testing landscape evolution models. Well, thank you and good morning. And I want to thank the organizing committee for inviting me to speak. And thank you, Allison, for a great introductory talk. I want to start by asking the question, how do we invert observations such as the photography shown here for information about geomorphic and tectonic processes. So obviously the topography contains information, the slope area and hip symmetric relationships of the fluvial terrain that we can see here on the side of the slide are clearly different from the glaciated landscape shown here. But does the topography of the fluvial terrain contain information about the correct decision of rock by rivers over geologic time? And what about the uncertainty in constraining tectonic processes from the shape of something like them? Of a fault scarf. So I'd like to ask the question under what conditions does the topography and other related quantities retain enough information to invert for these desired parameters? And when are we sort of lost and plagued by equitability? So in this talk, I'm going to start to approach some of these questions through the use of landscape evolution models. So after providing an overview of the development and use of landscape evolution models, I'm going to present two case studies. The first is an example of testing alternative models of landscape evolution in the context of a post-flatial environment. And we're going to look at how we can use the modern topography to infer what elements of model complexity are actually necessary to capture the dynamics of a particular place. And in the second example, I'm going to look at the synthetic experiment in which I attempt to invert for parameters used to create a synthetic truth with increasing levels of difficulty. So to begin, I want to describe the core elements of most landscape evolution models. These include a representation of topography, methods to create and route water, typically diffusion-like erosion and channel erosion and sometimes transport that depends on slope and drainage area. And additionally, many other processes may be represented like the generation of soil or vegetation. So landscape evolution models have been used for many applications, including developing insights into the evolution of specific field areas, creating testable predictions of landform development, demonstrating the consequences of our current theories for geomorphic processes and sparking our imagination through hypothetical scenarios. Somewhat like the example we were just discussing, what would the Olympic Mountains look like under different seismic scenarios. But coupling models of Earth surface processes and geodynamic processes totally changed the dynamics of the model system. If we want a couple Earth surface processes models with tectonic and geodynamic processes, we must first be able to create defensible models of Earth surface processes. I think there are quite a few challenges that we have in the development and application of landscape evolution models. These include things like defining and testing our geomorphic transport laws, the theories that we have for how rock is transformed into mobile material, and then moved by wind, water, and ice. I think we're also quite challenged in developing metrics or statistical abstractions that successfully differentiate small results that fit data and small results that do not. So in this first case study, I'm going to show you how we can use numerical inversion to determine the appropriate level of complexity for modeling the evolution of topography. Here, we're going to consider how we can use a suite of alternative landscape evolution models in the context of postglacial landscape evolution to ask the question, how much complexity in the model do we need to capture the dynamics of a field site? So the location of this work is in western upstate New York shown here by this red dot. And this site was glaciated until approximately 13,000 years ago at which point ice retreated northward. And the green, orange, and white domains of this terrain here indicate three important areas in this landscape . The white is shale bedrock. The orange is glacial till. And then the green is the fluvial network that's been incised into the till since the glaciation. And these two yellow icons here show the location of a nuclear waste reprocessing facility. So now we're going to zoom into this dashed law. And so here we have a shaded relief image of the site to photography. And work by colleagues in upstate New York determined the age of the most recent retreat in this, of ice retreat in this valley was about 13,000 years ago. And this work also characterized the details of the main stem river incision through C14 and OSL dating on terraces. So that's shown here. This plot shows the non-steady pattern of fluvial incision of our study watersheds outlet, which really serves as a boundary condition for the modeling that we did. So years before present are shown on the x-axis and elevation relative to the moderate angle shown on the y-axis. So as you can see, this waste site still marked by these yellow icons sits on a flat-lying fill plateau that's been incised by this nuclear network. And the location and timing of future erosion in this area is relevant to the decision made in the cleanup of the site. So we were tasked with making predictions of erosion 10,000 years before with sort of consideration of uncertainty from a variety of sources. And these included the structure of the landscape evolution models that we use, the estimation of the parameter values in each of these models, our understanding of past and future model boundary conditions related to climate and outlet down cutting. So before describing our study approach, I want to highlight a few of the characteristics of the site that are important for interpreting and thinking about the results. So we're going to zoom into this orange rectangle here and look at a map of slope. So here you can see the terrain colored by local slope and the location of the site is still marked by the yellow symbols. So as you can see the side channel slopes are nearly planar and approach 30 degrees. There are two major rock types in this watershed. So now we're looking at a slightly different view of the watershed on the outlet is here. The site is located still at these two icons. And here the topography is colored by the depth to bedrock such that blue means the bedrock is exposed at or very close to the surface and red means that bedrock is quite deep and the surface material is a clay rich glacial tail. So and up here we have a sort of a crappy Devonian shale. And so I don't we don't think you know beforehand there's necessarily an obvious reason to think any of either of these materials is more resistant to fluvial erosion. So with that context I want to sort of give you some information about our general approach. So our goal is to protect erosion with quantified uncertainties. And our first step was to develop a set of alternative erosion model. So I'm going to take a brief interlude from the approach and tell you about this set of models. So each model was created using the land lab modeling framework. All models were single variations on the simplest model which we call the basic model. So this basic model is a linear diffusion and stream power incision model. It's governing equation is shown here. And it has two free parameters. So we identified 12 additional elements of complexity that we thought might be important in better capturing our study sites. So these 12 elements of complexity fall into four main categories. Hill slope processing, channel processing, hydrology and climate and materials. And now show all of these 12 options. The default options those used by the basic model are shown in bold. So for an example one change we could make is to say well instead of using a linear tool for hill slope we could use a non-linear tool. So and sort of based on the steep planar hill slopes that we saw in the prior slide you might expect that a non-linear rule would really help. So when we have 12 choices like we do here, that's associated with 12 one element models in which we add one of these non-default options. So we have 66 two element models and 223 element models and so forth because of many thousand many element models. And that was just not feasible for us to do. So we looked at all 12 one element models. Most many of the 66 two element models based on which ones are actually possible to create as well as which ones might have sort of an interesting interaction. And that lent us 37 alternative models that we use in this work. So after developing this set of erosion models we needed to do a few other things before we could calibrate each of our models. We needed to reconstruct topography 13,000 years ago to find an objective function. This is our basis for comparing the observed topography and end of model run results. And so after doing a sensitivity analysis we calibrated each of those 37 models through a numerical inversion that identified which parameter values we should use for each model such that we minimized our objective function which is the thing I'll talk about a little bit in a moment. So after calibration was complete we ran the calibrated models in a validation watershed, selected the best performing models, and made our predictions. So right now in this talk I'm just going to focus on the lessons that we learned from calibration. Before showing you some of the results I want to tell you a little bit about the objective function that we used. So in this study the modern topography looks quite similar to the topography 13,000 years ago. So here on this panel I show the modern topography and this is our 13,000 year ago reconstruction. And so because we expect that our successfully calibrated models are going to create topography that is similar to the modern topography. Our objective function is based on just differencing the modern and end of model time topography. But we wanted to place more emphasis in our objective function on these channels incising the tilt plateau. And so we developed a weighting scheme which I show here in which the yellow colored areas the topographic difference there was weighted more heavily. So before showing you these results I want to step back and ask the question is this a good natural experiment? And I think it is. So one thing is that the initial conditions that we have are reasonably well constrained. And we also have well constrained boundary conditions. And in our modeling effort we very carefully designed the alternative models that we use that only one thing changed at a time. One thing that we don't have however is an intermediate benchmark or things that our models are trying to hit throughout the course of the time period. So here I'm going to show you some of the results. On the left here is the modern topography. And then on the right this is the calibrated version of the simplest basic model. So as you can see the model doesn't sufficiently in size in the lower part of the catchment. And it also over in sizes in this upper part of the watershed you can see some grid artifacts located here. And looking carefully at these in size channel slips you can see that they're not planar as these ones are. And I think many of these failings are to be expected. So I'm going to show you some of the results. I want to briefly discuss sort of our approach to interpretation. So we can expect that a more complicated model should best a simpler model in terms of having a lower objective function value. Because it typically you have more parameters and thus more degrees of freedom. So we can assess each calibrated model and ask the question, is it better? So if the answer is yes after we've accounted for the total number of parameters you can include that this new element of complexity has added to our ability to capture the dynamics of that particular system. And if the answer is no we can assess if the calibrated parameter values are trying to recapture the simpler version of the model. So for example if we had tried to add a threshold in the stream erosion and that threshold was calibrating to the zero we could say well we're being called that that threshold definitely does not add to our ability to capture the model as defined. So with this context I'm going to show you the three additional model elements that provided the most benefit to having a good model data fit. But before I do I want to ask you guys which one of these 12 elements of complexity do you think add the most? Don't be shy. Okay well we'll bedrock? Okay so we have bedrock and variability of climate. It turns out that in this particular case variability of climate never improved the results. However I do not think that is a statement that should be generalized. It's very specific. This site, this objective function and so forth. So it turned out that the most important difference is the differentiation between rock and till. And so you know some of you thought that this was an obvious addition. So here on the upper right we have the basic model which I showed before and the basic model with the rock and till units. And so what you can see is that now that we have the ability for different erodeability coefficients we're incising less in this upstream part of the catchment it was more in this lower part of the watershed. So the second biggest improvement was adding an erosion threshold. So as with what we saw before we have the modern topography and now the basic model with the rock and till units and now with an erosion threshold and so what I think you should see is that we're now able to incise a little bit more into the upper part of the watershed and there's a bigger differentiation here between being on the plateau surface and in the main channel. The final thing that made a big difference was the addition of a non-linear hill slope component. So here we have the modern, the rock and till unit and erosion threshold small that we were able to make elements of complexity. And just for reference these are the types of calibrated parameters that we came up with and so these are reasonable like we are ending up with a critical slope of about 20 degrees. But what did we learn from this calibration? That correctly capturing this landscape requires differentiating between lithologies using an erosion threshold and including the non-linear hill slopes. But before moving on to the next piece I want to ask the question are these improvements that we've made in adding elements of complexity linearly independent? That is to say is adding the erosion threshold and non-linear hill slope element the same as the sum of the effect of adding each of these independently? So to address this let's look carefully at each of these calibrated models. So here we have the basic model with rock and till units, the erosion, the modeling which we've just added the erosion threshold and as I said before you know this means that we're incising a little bit extra and that's part of the watershed. We're also having less erosion on the black toe than in the channels. But if you just add the non-linear hill slope model you end up making the exact same results as this one here in the parameter value for the critical slope ends up trying to calibrate to be such that you know you have linear sentiment slots. And it is only when you have both the erosion threshold and the non-linear hill slopes that the parameter is able to calibrate to a value such that you sort of create these linear hill slopes. And so our interpretation here is that without the erosion threshold smaller drainages in size too much lining off a large hill slope response too big. And so by limiting the channel incision with the threshold and we're able to have a more appropriate hill slope we can answer this question in this context the answer is no. So summarize, we can use numerical inversion to identify wet model element to improve model performance. I think this is a very exciting approach for testing our ideas in landscape evolution. I've showed that the effects are not necessarily independent and a point that I'd like to make that I think is that everything that I've said is really conditioned on the specific objective functions of the model and data and that's really the way that we communicate to a numerical inversion method like what we think is important. So I think you know exploring how our results change is that objective function is different it's of interesting things. So in the remaining time I want to tell you about a synthetic experiment in which I infer exploring geologic and tectonic parameters. So the last experiment really brings up a question to me which are what are the limits of inverting photography? And clearly there are limits. So if we have equifinality in the slope area relationship in the catchment limited and transport limited movial incision, it's not going to be easy or possible to say something about what the process is from that information in a steady case. And then this exercise I was really inspired by a lot of examples from literature. Things like this work by Taylor Paul and others thinking about the Long Valley profiles in a football of a normal fall understanding of whether or not the river transported in catchment limited. Things like work on the misogyny and salinity crisis inferring manful viscosity from lake bondable shorelines and the morphological dating of alt scarps. So I think we can consider that there are some number of model parameters that we would like to back out from photography. These might include the rank, the sensitivity of the process the timing of falting and so forth. And in reality we don't know what the actual answer is so it's very difficult to assess if the methods that we have are able to actually distinguish between alternative options. So in this experiment what I'm going to do is create a synthetic truth that's based on a known model with known parameter values. I'm going to test how well I can recover the true parameter values given to a plausible parameter range. Then I'm going to look at what happens when I add noise and use that to constrain our ability to use landscape evolution models to recover this desired information. So I did this in a model that I set up using the LandLab Modeling Framework and I used a hexagonal model grid with two process components, the stream power with alluvium conservation and entrainment component and an exponentially decaying generation of other transportable materials. And I used this space model because it's able to capture both the transport and detachment-limited behavior of movable incision through a parameter choice. So this model runs for 8 million years and then vertical faulting begins. This is a very simple fault in the context of a sort of pretend geodynamic part of the model. So I've set this model up to have two parameters. The faulting duration is between 0 and 4 million years corresponding to a highly transient system and a system that's long reached its steady state. And then I created a parameter which I'm calling the process parameter and it controls both the fraction of fine sediment that once detached is permanently detached and removed from the system as well as the production rate of the other component, a value of one is detachment-limited. And for each possible value of this process parameter I set the rock and sediment erotability such that the steady state slope area relationship is exactly the same. So here is an example of the long-profile evolution of the two end-member cases. On the left we have the transport-limited case, right the detachment-limited case defined as the profile of the largest channel in the model domain is 100,000 year time slices. And so we have elevation and normalized distance upstream here. And as you can see the transient response to two cases is very different. And the transport-limited case is the profile sequence everywhere whereas in the detachment-limited case it's the first one near the outlet. So these two animations show the end-members of our cases in slope area space. The x-axis is the log of drainage area and the y-axis is the log of slope. The black dots show all of the nodes that are faulted in the green dots here show just the nodes that are in the longest profile. So in this exercise I'm going to use an objective function that is based on this slope area relationship for the largest channel in the faulted domain. And so here is an example of say this is our synthetic truth and I'm going to compare that synthetic truth with a variety of candidates, parameters that see how well we can recover based on the slope area. So before showing you the results I want to introduce you to a plot that we're going to see a few times. So on the y-axis we have faulting duration on the x-axis we have the process parameter and the transport-limited over here and the detachment-limited over here. We're going to have a red star that marks the true parameter combination. And this color bar here shows the log of the objective function value. And that corresponds to goodness of fit to the synthetic truth. So this was calculated by running candidate model at every single point in this parameter space. So I want to orient you to the values of the objective function so you can see what they mean for the difference between candidate parameter sets. So this comparison has a log objective function value of negative 0.7 is a pretty bad fit. And these two have values of negative 2 and negative 3. So I think we can sort of calibrate our minds to saying that a good fit is sort of in the yellow and green colors. So what we're now going to do is look at some results. So this red star is going to show us the true parameter calibration. And so I'm going to reveal the colors back here and, you know, if we can perfectly recover the information about our system, which is a yellow blob right here near this red star. We end up seeing this. So we have yellow region that's extending here across this process parameter. And we also, we see some numerical striping in this area and I haven't fully figured out if that's related to the model or the objective. And so I think what this shows is in this, if we're using the slope area relationship as our objective function in this highly idealized case in which I use the exact same initial topography random speed as the initiation of the model that, you know, we wouldn't be able to necessarily tell where we are other than to say we're not detachment limited. But we wouldn't further the timing of the faulting reasonably well. So now I made this a little bit more complicated. I used a different random seed to generate the initial condition topography. And so this is what these results look like. As you can see, this has changed a bit the area of this yellow blob and we would still have uncertainty in the process parameter that we were trying to infer and there's a bit more uncertainty in the timing of faulting as shown by the sort of spreading out of these yellow and green colors. Let's make this one more step complicated. Here I've added normally distributed random noise the erodability coefficient for rock and sediment used by the base model. And I've added a different random field at every single time step. And so this is what it looks like now. As you can see, we'd now probably conclude that the process parameter is somewhere in the middle of transport limited and detachment limited. The truth is we got here much closer to transport limited and I think we still have some additional uncertainty in the timing of fault onset. So one thing that's interesting about doing these results to be different is the true parameter combination without here. The answer is that our ability to infer the parameters is very different. But here I think because the nature of the transient attachment limited slope area relationship is sort of so characteristic, even with the noise I've added in the erodability coefficient we have good constraint on both the timing and the process parameter. So in this exercise I hope I've convinced you of the utility of synthetic experiments to identify the limits of our ability to infer geomorphic and tectonically relevant parameters. And this is clearly a very simple example with a simple model and a simple objective function and other examples have been done by thinking about using more complicated objective functions like incorporating information from multiple drainage basins of different sizes as well as some of the logic data. But I think the point that I'd like to make is that synthetic exercises like this are really useful in providing us with information about when we can expect our data to retain information about the targets of inversion and when we can expect our data to retain information of inversion. And I think this can really be used to help us develop better methods for comparing models and data that we actually feel confident are going to hold up. So in summary, the beginning of the talk I provided a little bit of background related to the nature and use of landscape evolution models. And then we looked at a case study of what elements of complexity were necessary to be looked at a synthetic experiment in which we explored the limits of our ability to invert for topography for desired quantities of morphology. And so I think the approach I presented has a lot of promise but many challenges still remain. And so I'd like to conclude with some thoughts on how we can motivate future work with particular attention to work that requires coupling of surface and fluid dynamics. So first, the two examples that I showed are from highly transient systems and how must our methods be different when working steady versus and also many of the model structure choices and model coupling choices that we might do. And so that brings up the question when we are assessing, you know, is our model good enough? Our ability to calibrate the model good enough? How must that be different when we're dealing with both continuous and categorical choices? And finally I think the result of the natural experiment which I showed that the benefit of adding one additional process is not linearly additive but it shows how nonlinear actions can potentially mask the effect of an additive process. So if we just had added a nonlinear helpful out adding and you might conclude we don't need nonlinear this doesn't add anything. So, you know, this will only become more of a challenge when we're dealing with a couple models. How shall we approach addressing that? So with that I'm happy to take questions. We need it for the online So I have a question regarding tectonics in general. So because in your first case study I don't want to add another complexity to it but I think tectonics should be added because tectonics on the long-term scale is not only variable it might actually be differential across the landscape. So, for example, accounting for even though it's a post-glacial landscape you don't expect any kind of full trust spell tectonics but there is that element where you might have, for example, an isostatic rebound where you have that tectonic element. In the second case if you maybe in the future could consider variability in the faulting rate because that is over 10 million years you modeled that might vary as well. So a fault is not really at one rate in 10 million years. Of course it's an idealist model but I think that needs to be added. The tectonic element should be in a rigorous way. Yeah, so those are two really great points. So we spend a long time trying it all we'll be down tilting and so forth in the first case. We ended up concluding that the amount of data effect in this place on the 13,000 year time scale that we were modeling for was small enough that we weren't going to do it but I agree I think that you end up, this sort of leads into the second question which is that ultimately you know a lot about different processes that operate in the earth system I think there's a general question asked which is you know what do you do when you can't include them all? There are obviously problems with including them all. You may as in the words of Peter Molnar end up with something you just don't understand even more but you know I think you end up in a situation in which ultimately the approach that I like to think about is since you know that you're never going to actually be able to include every component so carefully adding components and understanding like okay well in this simple faulting exercise how different is my result if I include a more realistic faulting pattern which I have some distribution of timing faulting events and then I think the other thing that this really brings up is the question of you know important for what? You know we have there are established methods for assessing like if adding a piece of model complexity or changing parameter value impact assuming you're able to define what that thing is so you know a big question that all of this works brings up for me is what are our methods for model data comparison sensitive to the things that we want them to do and then you may have a situation in which you have the same model applying in two different contexts with two different targets and you know you decide you end up concluding that different things are important. Hi I encourage folks to introduce themselves when they talk and I wanted to follow on sorry a little bit with that question in a way in saying even the first example you have GIA in the area and as we're we're seeing from the microscope mental imaging that there may be more than just that as well and so tilting and regional tilting at isostatic scales of football but also at regional tilting and there are influences on some of the state revolutions that's something I guess it's evolving with I would say that the example that most closely comes to my mind when thinking about this is the way that we look at what study state is. It closely comes to my mind when thinking about this is work by someone like Andy Wicker who thought a lot about how post-Laurentide ice sheet demise and the sort of changes in the geography that gross geography that comes from the geodynamics influence the reorganization of river basins in the entire United States and Canada and with a main focus on Mississippi river drainage but I would say whether it's paid attention to or not is a patchy but I think one thing that both your questions bring up is that if there are main process components things like doing BIA right having tools that connect well with our surface processing models such that someone who is thinking about this question can include it or assess the question if I include it or not does it actually make a difference when does it make a difference what things do I want to think about this is Torsenbecker UT suppose when you look at landscape evolution there are certain players like the bedrock type and wherever we have a fault or not that are inherited or pretty much impossible to predict so those are important for certain sites to constrain but then on the other hand you have a set of processes that are hopefully universal and that would be nice to understand in a more general sense speaking about those you nicely highlighted the trade-offs between some of them and I just wonder in your case you were asking well I go from A to B and then you have these trade-offs and it's hard to tell if it's the limit in erodibility or the non-linearity that's more important in order to design your ideal experiment what would that be and what would the things be that you would be looking at to get at the process sort of constraints is it studying the amount of sediments when they were deposited the output of the system is it constraining the uplift rates and where would you invest most of the money if you had your ideal experiment to reduce those trade-offs any question at the end of the conference tomorrow I mean you must have some feeling from the models already you can keep track of the sediments and you go like oh it's non-linear it does that it's limited is this oh if I could only measure that then I could nail it down it's related to a point that needs 37 alternative models in which we made one or two or three changes at some level you'd like to think that we could use to figure out if we could exclude all the things we need the one thing we thought a lot about after having developed all of these sorts of things is okay we'll sort of modular Python package for creating and having different process models easy to swap you know a different component that does gluvial instance out for a different one and then you can just do that but like of things that we've created you know how what would we need to do to create one model that through parameter choice permitted us to capture the whole range from the from those 37 models and I think this ultimately got me thinking about sort of what happens when you have these continuous choices and the categorical choices in the modeling that you're doing and how do you modify your approach if you're really trying to invert for something that's you know beginning your things with this categorical but you'd really like to think of it as actually