 Okay, so I have limited time, so I'll just start quickly. So as you can see that I'm working on a delta formation. I'm trying to model a delta with channel networks and what I would call it a 2.5 dimension because it's not averaged. So just in case the title doesn't say it all, I put this, my favorite animation from my model results on the left. As you can see that this domain is four kilometers in this direction and six kilometers in the vertical direction. And the inlet channel is about 300 meters wide and the number of nodes in this model are 80 times 120. So what I wanna point out is that as you can see that the channels are migrating and it has bifurcations and it has evulsions. And you can see the slope switching, which I think makes sense. And also another interesting feature I wanna point out that you can see this meander channel is growing and then cut off itself, which wasn't I expected. So I call it reduced complexity model, which is actually all types of modeling are reduced complexity because you cannot capture all the details in the nature. Depending on how you simplify all the processes in the nature, you have different degrees of modeling. And so as Michael mentioned yesterday that there is no free lunch. I would like to add to that that it's not only not free, but also how much you pay for the lunch doesn't necessarily determine that how tasty your lunch is. So there's a linear, no, actually it's not linear relation that how much money you pay and how tasty your lunch is. Definitely across the origin, which means not free, but it doesn't mean that it goes linear actually as you try to put as much details as possible in the model, it might just blow up and doesn't give what you want. So that's why I put this dunker here saying that you never know what's gonna happen. So the question is to decide which model you wanna use, you have to have this question in your mind that what is your purpose? So since I'm working on deltas, let's talk about deltas. This is picture of Wax Lake Delta, can we model it? What are the processes you need to include to grow something like this? If you go from the basics, you have to model individual particles jumping around carried by water or even a fish can do something to it, right? But that's too complicated. So the highest level of complexity I can imagine now is something for some, look at this small picture here. It's a topo scan of the outdoor stream lab in Seville where I'm from. And you can see this individual gravels in this about two meters wide outdoor channels. So there's a group at the lab trying to use the large eddy simulation and the DNS to try to model the secondary flow in the enders. Imagine you want to apply this for a whole delta. For each individual meander, about a meter scale, one minute in real time, real lifetime, it took I think weeks, I think at least days to run it. Imagine you want to apply this for a whole delta for thousands of years, hundreds of kilometers. So that's not something that we can handle now, maybe in a few years, this development of computation. On the other side of delta modeling, that if you just want to capture that the overall growth of delta, then you have this type of modeling by... And also this type of geometric model that's trying to just capture a diffusive profile in the cross-average framework. And that's a good job to predict the land growth like in this project for the restoration of this delta. So what might model fit into this spectrum of all types of deltas? So this is just one picture. I think it's easier to talk about it if I have pictures. So first, as I mentioned, I want 2.5 dimensions. So I don't want something just a plan view. I don't want just a cross-section. I want to have topography in three-dimensional, although it's depth-average for the water. And also I want the channels to form by themselves to above the bifurcate. I don't want to give rules saying that you have to bifurcate here or above here. So it's self-organized. And what else? I think it's good for now. So for the following part of the talk... I'm not going to talk about the detailed individual formulas and rules I use because I have a poster in the afternoon so you can ask all types of questions you want for the hardcore modelers. What I'm talking about here is the development of this model, the history, the ideas where they come from. I think it might be more inspiring and a few results with the future goals. So this individual project is still going on. I'm still trying to develop it. It started this spring just half a year ago. So the jumpstart was a model that... when I was working with Bonn by the realm. So we had this idea about this two-particle random work model that just saying that trying to model a delta, you have two types of things that you can transport into the system. One is water, the other is sediment. So what do they do? So the water just build up these paths for things to be transported. And sediment, they deposit and block and occupy space so that water can have only limited paths to go through. So this computation process, if you put it in a simple code, saying that water particles can travel only through water. Land particles or sediment particles can travel by boats and it's a higher chance to travel by water. You have this dendritic pattern by the end. It looks really fuzzy. So what I did to modify this prototype is by saying that, well, you just count the main direction of transport particles in the system. If you have this dead end because you have things in and out, then it's kind of cancel out. So you get rid of them by giving a threshold to remove things that are not actively flowing. Then you have this nice structure with several active channels at the same time. And it's a little bit more tricky than you have this dendritic pattern. And that's the first step of this model. And another one, they have different patterns, this kind of self-randomness. So next, I want to add ways to the channel. If it's only one node wide, it's flat, it doesn't have topography in it. So the first step is to add ways to the channel. So the way I do it is to get a flow field. Since I'm counting the particles, why not I just use these water particles for calculation of flow? Actually, all these ideas are in the final model. So I started with a simple test that I have this active channel here and I sent everything from left to right, this water particle. Now it's only water. And because of this randomness, you have several nodes with more visits of water and some of them are less visited. And those less visited, I just erase them, changing them into land. So you can imagine that in this way I'm just removing but not adding, so the channel will get narrower and narrower, right? But it naturally doesn't happen like that. The channel, water tends to go to the deeper region and kind of concentrated by depths. But at the same time, we have the diffusive process because it cannot be too deep, too sharp, because it collapse. So I use a diffuser saying that if concentrating too much, it expands by one node. So you have this pattern here and you can see this kind of, this is one run and different time step, you can see this migration. Another run, similar. So I try to put these two together and try to build a delta, but two problems came up. So the first one is, you can see this channel elongating itself but it doesn't see that there's a shorter path to ocean. The other one is, well, I send too much sediment and it blocks water and water doesn't know where to go. So one simple, one easiest way to do this is to, I need a global guide for the water to know where to go. Well, my thought was that's a free surface because it's flat, it doesn't know the basic direction. So if you have the free surface or slope, any kind of potential thing, then you can bring this idea of where to go. So, okay, forget about it. Okay, so this slide contains all the rules that you need for this model. So this is the one I have. You have a basin, constant depth, a tunnel coming from the left and the way that I calculate the flow field and the sediment transport is by doing random walk. So you send out water particles, do the random walk, and decide the flow field. But one thing I want to mention, it's important is that this random walk is not complete, random is directed. So you have two sets of rules, give you the probability of all the eight directions. One is guided by the free surface. The farmer is here. You don't need to know the details. It's on poster. And the other one is I bring in inertia by saying that if the water has been going this direction, then the particle will prefer to follow where it has been going. And then I calculate the free surface also in a random walkway. I don't have time for details. The sediment transport is really fuzzy now. It's very simple just by saying sediment particles are carried by water. That's this random walk in the field along the stream line and deposit when the flow is really slow and erode when the flow is fast. And I also have this diffusive process just to avoid over-deepening of channels. Okay, so to test the results, first we have to use up intuition that before we do some detailed statistics, just by looking with our eyes we can tell a lot of things. And also the flow solve is really simplified. For sure it's going to give trouble at what we lose from a simplified flow solve. It's even not hydrodynamic equations. It just rules guide random walks. And the randomness and the parameters. So this is one animation. Or as you can see that these are caused by some numerical problems but it doesn't affect. You can see the channels bifurcate and migrate and build up different loops and evolves. So just to do a basic check. Really sorry that I'm running over time. Just to check if the model works well you can test some basic variables. Just look at the free surface if it makes sense and check the topography if it makes sense and the flow vectors if they make sense and they look okay. And also the randomness. I'm sending particles, right? So does it affect how many particles I'm sending? Because it's very important. If you send a lot it's going to be slow. The code is going to be slow. But I wanted to keep it within, actually this model run takes just one hour in MATLAB it's less than 1,000 lines of code that I wrote each line of them. This is 10 times difference of particles from the left to the right. And you can see that you don't see a significant difference. And if you want to say that okay you have bifurcations here but this one is a little bit different but I'll show you that this randomness can generate exactly the same run but run different times. When you send up the same number of particles one run, another run, another run they look satisfactorily the same. And then I tested a few parameters just last slide. Changing the flow number because this model is a very sensitive flow number the basic assumption is that it's valid when the flow number is low. So this high flow number actually changes that by varying the basin depth from 5 meters in this case to this case of 2 meters and then this is 10 meters deep. So they look different. So if the flow number is really a problem then I use 2 meters deep basin with the same flow number as 5 meters and 5 meters deep with the same flow number 5 meters deep basin and actually they start approaching each other and also I test the coefficient of sediment transport on, okay so just one point here is that this model is sensitive to how you transport the sediment by saying that if it's dumped sorry I'll talk about details in the posters and I tried to recall stratigraphy also and the next will be improve this model with more details and that's not the wrong but I guess it just doesn't matter. One way, the last point I want to make is that the flexible structure of this model can take impose from high resolution models to be components and objects integrated in this framework and I think that's all oops, that's too much details thanks