 Good morning, I'm happy to be here. I was asked to talk about scaling or, as I decided, scaling up marine sediment transport and specifically the challenge that I'm interested in as well as our many other people is how to go from the sort of some decades now that we've had of local events scale marine sediment transport studies and our understanding of those processes to time scales that are associated with morphologic evolution, human and land use impacts, climate change, stratiformation, and also larger spatial scales. So there are a number of possible approaches many of which have already been attempted by various people and some of which are conveniently represented by some of the clinics that are going on during this meeting. There's been a lot of work in enlarging spatial scales through models like ROMs and DELF 3D, increasing time steps with appropriate model adjustments. I think X-Beach is an example of a model that can do that, a variety of ways of running models for series events and then using those somehow to develop a distribution. One thing that's common to all of these approaches is that they all depend on explicit representations of the forcing conditions, the waves and the currents that drive this system. There's another class of approaches that are more I would say in general simpler time average representations which include advection or diffusion or advection diffusion type formulations and that's I'm going to focus on that today. Solving for equilibrium shelf profiles, Malcolm Sculling and Carl Friedrichs have done some work in that arena. Determining an effective storm like a representative or effective flood sometimes is done in hydrological systems. John Swenson has taken that approach or using more geometric models. Mike Stechler has taken that approach. I'm going to focus more on a diffusive type of representation and one of the reasons I did some work on this a while ago got a little bit stalled for several reasons not the least of which was availability of data to do what I wanted to do with it but then I was also struck by some recent work on the terrestrial side looking at hill slope diffusion and it's been thinking about that how to properly represent that. It's been an active area of research for a while but Greg Tucker, Tucker and Bradley just published a paper talking about the trouble with diffusion and FU Fufila, Georgia and colleagues also published a paper last year not local fluxes and hill slopes. Some of the conclusions from these papers is that GTL is geomorphic transport law. Most geomorphic transport laws are local like local diffusion, local linear diffusion but disturbances that induce transport can often produce large rate transport over large much larger distances than a local approximation can properly characterize. Both papers talk about connections between a non-local diffusion or that kind of approach and some of the non-linear diffusion work that has been done earlier by people like Josh Waring and others and they both point to promising alternatives to local diffusion approaches including Greg talks about particle based models and FU's paper talks about non-local transport models. So what I was hoping actually is by talking about this to this audience I can get some transport of ideas from the terrestrial to the marine environment. So in order to facilitate that I thought I'd start by drawing some contrast and similarities between hill slopes and shelves which are a shelf is in some sort of way kind of a hill slope on the margin and I'm doing this in part just to sort of cast the two problems so that if whatever intuition you might have about hill slope systems you might be able to think about how transferable it is to the marine environment. So in marine environments we have multi-directional versus primarily downslope transport so currents can drive transport in any direction. Rather than a slope driven system this is largely a flow driven system it's sensitive to depth but not especially to slope for the most part there's an important exception there that I'll mention. Sort of the equivalent of maybe a runoff event sort of a high-energy episodic event in this system would be storm driven waves interesting thing about waves is that they produce large stresses but they're inefficient at transporting mass so they they can get things moving but they can't take them anywhere. There are responsive currents which are the primary thing that actually affects material from place to another it's not especially responsive to storms and even to the degree that the surface currents might be currents at the near the better often decoupled from the currents at the surface. So in fact in many systems actually the wave environment the current environment are relatively uncorrelated and there's because of the combination of waves and currents and the difference in the stresses imparted by those. What we find is that when the wave velocities or wave stresses are much larger than those of the currents we can actually get near bed stratification at the top of the wave boundary layer that essentially caps the amount of material that can get into the water column. So it's not the case that the larger the wave event the more material necessarily that you you can't disproportionately put more material on suspension. There's some self-imposed limits on the system. In this case we have a river mouse which serve as point sources upstream point sources for sediment which are active during floods almost all the material delivered to the shelf comes from these. The floods that deliver the sediment and the waves that are able to mobilize the sediment may or may not be correlated with each other or synchronous in time. Sediment availability on the shelf despite the lack of vegetation and large expounces of open sediment is for the most part supply limited owing to consolidation of the fine-grained sediment and to prevalence of small-scale bed forms that limit the active layer depths even in the sandier part of the system. And then there are these there are occasional gravity flows that are slope sensitive there they can occur when you have a large input of fresh sediment and waves at the same time that can trap a lot of sediment in the wave boundary layer and that can actually move under the force of gravity we call this wave-supported gravity flows Carl Friedrichs and Malcolm Scully have worked a lot on that problem so that's a process that would not be amenable to a diffusive type representation. So one thing that we can't get away from when we think about marine environments is that we have three basic sources of fluid motion that all have to be counted for waves that control the timing of transport through most of the certainly most of the shelf and many other even shallower systems currents that control the direction and the vertical distribution of flux and tides which are an ever-present source of variance and turbulent mixing in these systems. All of those actually let me just sorry back up and just this is just an illustration some measurements from Northern California. These are low frequency currents and their direction hourly currents showing tides bottom wave velocities showing sort of wave events. These are the shear velocities due to the waves in blue and the currents in yellow and the resuspension. You can see very clearly that the resuspension events are highly correlated with the wave events and then all of those combined to affect the magnitude of the flux. The flux is shown here in red and there are definitely times when you have waves putting material on suspension but you don't have the currents aren't very high and therefore you don't have very much flux and there are times when the currents are large but there's very little material in suspension and therefore you don't have flux. You really need both and there's no way to get around them. As I said the volume and suspension is limited to a relatively thin layer of active material near the bed surface. It's on the order of generally of millimeters and we're able to do pretty good job representing these processes on the short time scale with a variety of models. Actually up here there's some the lighter color are calculated concentrations and the red and the gray are measured values and in general we do reason we can do reasonably well. So the question is how can we combine say all those things the waves occurrence and the tides into something that's like a diffusivity and it's important to capture all of those effects. We're going to expect that the diffusivity is going to be a function of depth because of the depth dependence of the wave energy at the seabed. One of the reasons I've been interested in this is because when you try to characterize say the sediment transport potential in a marine environment it's a little hard because it depends on the wave environment and the current environment and the sediment environment. One of the things that intrigues me about the diffusivity idea is that maybe it's like a single number that you can use to kind of represent all those things together but we need to be a combine that with some sort of an effective flux to get the whole picture. Okay so the way that I approached this was kind of a standard random walk type approach. I did this for sites where I had a long record at least a decade long record of wave conditions and here for example in Northern California this just shows the probability of the wave velocities or stresses at the seabed exceeding certain thresholds but basically the top of these bars is the threshold of motion and this is as a function of depth so in shallow depths 20 meters that succeeded about 90% of the time but when you're out past 100 meters it's very solid and then also at least a year's worth of currents. So what I did was I just picked two week long sections random sections of currents took out the mean and then said that a particle moves with the current at that time as long as a randomly chosen value from the probability distribution of waves at that depth says that that the threshold would be exceeded and so as the as the particle progresses a long shelf it doesn't change in depth obviously but as it goes across the shelf then it becomes less and less likely to move. So just as an example I started 500 particles initially at a depth of 60 meters allowed them to move for a period of 14 days and these are the kind of distributions that I get so you know it looks kind of like the standard thing that you'd expect for a diffusive system relatively at least in the Kraschhoff case relatively good approximation to Gaussian distribution you'd see that there's a tendency especially in the long shelf for them to be peaked or higher kurtosis that you'd expect from a random from a regular normal distribution presumably due to the distribution of the currents. If you do this across the shelf for different water depths we do get a decrease in the standard deviation of those distributions which is related to the diffusivity like we'd expect and some kind of patterns of variation in the shapes of the distributions which you know might merit some more attention. So I did this for a few sites just to see kind of how what it can tell us about the difference between sites. So this is the eel shelf in northern California it's a relatively energetic site on a California margin this is at 60 meters kind of mid-shelf and 90 meters on the outer part of the shelf and then compared to a site in southern California a Palsverde shelf near Los Angeles this is a fairly sheltered area the wave environment's not nearly as energetic and you can see much smaller so these are the diffusivities calculated from the standard deviations more than an order of magnitude smaller at the same water depth and comparing the eel shelf to the Russian River shelf which is about 300 kilometers to the south again a much smaller here about a six times smaller value of the diffusivity so you could ask the question why are those numbers even meaningful and in a rare bit of fortune it happens that there is a period of time when there are measurements of waves and currents available for both the eel shelf and the Russian River shelf so these are based on time series this is showing currents the filtered currents to show kind of the lower frequency direction and magnitudes the wave velocities at the bottom concentrations 30 centimeters above the bottom and then the calculated flexes so one of the interesting things that we can do in this case is we can sort of parse apart how important different contributions are to the total flux so the total flux on the eel shelf is about four and a half times larger than the total flux on the Russian River shelf for this exact same period of time about 55 to 60 percent of that is actually due to differences in tidal conditions 15 to 20 percent due to differences in subtitle currents 15 to 20 percent due to differences in waves and 5 to 10 percent due to differences in the sediment conditions so basically 60 70 to 80 percent due to effects of currents and and a smaller contribution due to effects of waves maybe not surprising I mean these aren't that far apart in the wave environment that you can see there's a lot of correlation in the waves at the two sides it's just that the waves are a little smaller at the Russian River site well so how does that compare with the diffusivities so what I did was I took the measurement the values or the runs that I had already done for the eel shelf and the Russian River shelf these are 90 meters and I swapped the currents so I have the waves on the eel shelf with the Russian River currents and the waves on the Russian River with the eel river currents and what I find is that if I do that the diffusivities are reduced actually in both cases by about a factor of four so there's a total of about a factor of six difference in the diffusivities that means about two-thirds of that difference can be accounted for by the waves by the currents which is actually very similar to what I got from that specific representation so I think that there's some sense in these that is the you know in a relative sense anyway it's telling us something meaningful about how things are varying across this at different points along the shelf and also across the shelf we could also think about effects of grain size obviously finer sediment that's what I've been showing you which is primarily what's in suspension there will have much larger travel distances in there for diffusivities and if you go to find very fine sand or even medium sand so that's just the diffusivity if we want to actually talk about the effects on the morphology then that has to be applied to some sort of concentration gradient to get a flux and then the divergence of that flux would will give us erosion and deposition what I've done is to have the diffusion act on essentially the sediment available in active layer that's either controlled by wave ripples and their transport rate in shallow water shallower water where the sediments are sandy or by the consolidation state of the bed in deeper water where the beds are muddy and we have only a certain amount of sediment that would be available at any given stress so what I did is I took a representation kind of a typical representation of what actually let me just back up and say that both of these things the thickness of both of these layers depends on the excess shear stress the difference between the stress applied by the flow and the critical shear stress for the sediment so taking a reasonable cross shelf range of values for that to get a variation active layer depth I applied the diffusion to it I started with a initial linear slope and I get something like this I mean the shape is reasonable that here the rates are very high and essentially what happens is that because there is a lot of the diffusivity is high in the shallow parts of the system it's very easy to move all the sediment that's available and that gets moved over you know transport it down slope deposits somewhere so you have a high erosion rate here and essentially the mac the size of that the magnitude of that erosion is going to be completely determined by how much sediments available so if I have you know a layer like this it's only three millimeters deep in the shell part of the system I can easily remove all that material and then what happens next just depends on how long it takes for that to to reset or to go back to its initial sort of configuration that we started with so we can think of that as like a recovery time that first simulation I was letting that reset every two weeks obviously the less often I allow that to happen the slower this process occurs well it kind of obvious major weakness in this approach because we don't really know very well what those reset times are but it also actually highlights kind of a more fundamental problem which is that that those active layer thicknesses and the frequency at which these events happen and the reset times are all tied to that way of environment wave and current environment that I was using to calculate the diffusivities to begin with so so that's like just to me and this is kind of I think Greg Tucker's message in his paper is that rather than sort of go through this step of calculating diffusivities and then calculating changes in morphology maybe it'd be better to just like have the random walks move mass around and just do it that way and and then have everything kind of all part of the same set of conditions so that's that would be one one thing obviously to to think about and be interested in sort of experience of people working in terrestrial systems on doing that kind of taking that kind of approach one thing we could build into that which wouldn't be too hard I think would be a trigger for some sort of cross shelf advection by way of supported gravity flow so you might be able to fold everything into one big picture where we have occasional during flood events with highways give the capacity to get these very turbid layers that can move under gravity and otherwise we have a more diffusive type transport system another possible next step would be to even apart from the morphology just to think about what the diffusivity says about transport potential that requires spatial wave current and tidal time series and that's kind of where I got stuck before to actually getting good tidal time series but you can ask some interesting questions about the spatial variations in that and also how those affect sediment redistribution on the shelf there are a lot of spatial data available for example NOAA has an operational wave model that gives it can give a spatial wave fields that's what I'm showing here this is the forecast actually for Monday you can see on the west coast a lot of variation and wave activity we could use something like Ron's probably to get the currents and the core of engineers at certain model at least for the US to get the tides at this point and and we can also think about sort of either in the particle base model or in the diffusive morphologic change model effects of textural variations flood deposition you can put in a pulse of sediment look at the redistribution of that effects of consolidation times and all those on the plexus and in order for the person to talk about geostatistics I just want to say it's not that that's never entered our realm so I worked on a project with Chris Sherwood and some other people in Southern California where we actually use geostatistics to try to get some detailed information about erodibility on the bed in many cases it may be our knowledge of the bed that's going to be the ultimate limitation in our ability to predict morphologic change so this is kind of one interesting possibility for a way to get denser information and well okay so there are a lot of ways you could approach this problem I think this idea of diffusivity or set or particle base model seems to have some offer some interesting opportunities still somewhat limited by the shortness of available forcing records and we still need to know more about the small-scale processes in order to be able to really think about these larger-scale issues thanks you still have time for a question I'm from University of Maryland just a simple question I'm curious what is the mechanism for the recovery of the actively thickness so that you have to reset them periodically what is resetting it yeah well I'm you know that's a good some combination of probably flow-driven small-scale particle motion plus wave pumping biological activity you know I on some time scale we know that you go from that sort of over consolidated condition back to kind of a more normal consolidation state but exactly how that happens at least I don't know in detail okay thank you so I'm more familiar with the land surface and not submarine so I apologize if this sounds really simple but I do from when looking at surface process models and we have the same problem although we have a lot of equations we still don't really know the details as you know and but we still want to apply them to understand how landscape have evolved right and so one of the things that we do is we just kind of assume these limited models work and then try and constrain things so I'm wondering if you could take the same approach and your problem because you showed the example where okay you have this you just assume this diffusion model right and then you have to have this resupply of sediment in order to get kind of the right shelf configuration if I understood correctly so can you turn that on its head and say well that tells us something about that we have to be getting supplied enough sediment in order to get a nice shelf configuration or could you is the is the problem such that you could tweak your diffusivity so that you would get a nice shelf configuration regardless of how much said and how often you were refeeding that active layer I don't know if that yeah I understand and I you know I know that like if he's done some work where she's backed out of the morphology kind of what the effective non-local diffusion would have to be in order to produce that and I that's an interesting possibility but one thing we don't know yet for example is what the balance of diffusive and invective transport is and you can also develop those shapes as Carl Malcolm have shown from this gravity driven kind of flow process so we might be over interpreting if we were to take the morphologies that we have and then assume that those were formed by these more diffusive processes we don't actually know but it's still something we hope to be able to address or what the balance of the more effective processes and more diffusive processes are and then and then if you really talk about longer time scales and you have sea level kind of confounding everything a little bit so thank you