- [Voiceover] Okay, that brings us to the last point, is is that, the last step, is is that bankfull flow is a good thing to know. Cause you can, you know, the river channels, and the rock record are preserving the actual bankfull, or approximation I should say, of the bankfull dimensions of that river. And so what would that river have carried under bankfull conditions? You don't know what it would have carried under low flow conditions or extreme floods, but you know what it would have carried under conditions where the channel was bankfull. And that's a good number to have, and that's a good thing to know, and you can get things like drainage area out of that, and you can get how much sediment moved during the big bankfull floods, but if you really want to calculate how much sediment that river would have moved over the course of hundreds to thousands of years, or a collection of rivers in your section would have moved over millions of years. In other words, the scales would work at the rock record, you have to be able to convert the bankfull flow to the mean annual flow of that river. In other words, not just how much sediment, the rate at which that river would have moved sediment during a flood, but how much sediment would it have moved over the course of a year? Well, this is where I go into confession time, because when I first did this project, and I was over working in Egypt, and I realized I need to come up with a project, and we're measuring all these channels and stuff, you know why don't I just do a basic paleohydrology estimate of these channels, it's been done a thousand times. I'll just go back and look up the numbers and run them, and I'll get some estimates, and this will be a pretty simple paper. And then I got back and realized, you know, yes, people talk about doing that all the time, but no one had ever actually done it. And the pieces were lying all over the place, and there were people who had approached these questions, like Parker, who I owe a big thanks to for his e-book which talked about several of these processes, but no one had ever gone to the steps of actually doing it. In other words, taking an ancient channel and estimating how much sediment it would have moved at bankfull flow, water, yes, but not sediment. Well the problem is then, is that, the information to do that was there, it was just scattered through the literature and the equations are around, and people have thought about them. But when you get down to the question of how you turn a bankfull flow into a mean annual flow, in other words, a rate of sediment during the time the channel is flowing at bankfull to an estimate of the total amount of sediment it would move over the course of the year, no one had ever touched it. And the reason is because it, well if no one has tried to do the calculation of sediments of the ancient at bankfull, they've certainly not tried to transfer it to the ancient. And if you work in geomorphology in the modern, well you'd never do that, because that estimate is going to be extremely course, and those rivers are operating. So, you can actually monitor them over the year and figure out how much sediment they're actually moving. So it would be like trying to figure out mineralogy of a rock based on its sphericity. Why would you do that? If you can see the sphericity, you know the mineralogy. So, never been done there either. So what I had to do was come up with a proxy equation for this, which is a first of the kind, and it's very course so here's the way we did it. Is rivers have an effective bankfull discharge. Which is the bankfull discharge at which they move most of their sediment. That's going to be roughly the bankfull discharge, not exactly, but they're close in most river systems. So all rivers, the bankfull discharge, is approximately the effective discharge, and it's about one point five year recurrence example. So the bankfull flow that is responsible for moving most of the sediment in the year, and it comes about every year and a half for the average river. Bear in mind no two rivers alike. There's a lot of range here, but for the average, generic river, that tends to be about the number. So the next question is how much total sediment does the river move over the course of the bankfull flow. So for an average river, it'll move close to half the sediment it moves during the year during the bankfull flow. And the bankfull flow will run for about a week and a half. So what that means then is that for a course of a year, a bankfull flow on average, for a bankfull flow duration for a year is roughly a week, and it'll move close to half the sediment that's going to move in that year during that flow. That means then that we have two variables we can play with, and here's our equation. So the Qmas, in other words the total amount of sediment that the river moves over the course of the year, is equal to the bankfull discharge, how much sediment is moving during the bankfull, times the amount of time the bankfull flow is running, which is about a week, for a given year, and B the inverse the proportion of the sediment it moves over the course of the year. So if it moves half the sediment over the course of the year in the bankfull flow, then that means that number is two. You have to multiply the bankfull flow times two to come up with the mean annual flow again. That said, that's our rough estimate of how we're going to turn bankfull flow into mean annual flow. Okay, now let's run that then for the Bahariya Oasis, and essentially that means that when I run all of my numbers my sediment supply rate to the fulcrum is somewhere between 160,000 to about 600,000 cubic meters per year. And the accumulation rate, in other words, if I take the isopach, which I have of the Bahariya Formation out in here, and the deposits down dip of my fulcrum, okay so from my fulcrum out, and I calculate up from isopachs how much sediment is actually there it's only between about, it only works out to about 72,000 to about 144,000 a year. In other words, there's about three times, these rivers are carrying at least three times as much sediment than is actually accumulating in my base. So that gives me a very important, that tells me something important, it tells me my sink is about a third the sediment that should have been coming out of the source. My sink leaks, in other words the sediment is moving on someplace else is what that would tell me. Okay, that said, here's the important point then. Error sources and volume/mass balance, this is what they call a tornado diagram. It's an estimate of your errors, there are some massive errors in this calculation, and I don't claim that we've got this one down to where it's perfect yet either, by far. Most of your errors are small, like channel thickness in the field you might miss the actual channel depth by a quarter if you ill-quarter it, that's easy enough. Mean dune height is a number you need from the cross edge, you might miss that one by a quarter. Compaction correction of your channel fills, cause if your trying to say here's my story thickness, well, how much of that compacted versus the real original depth of the channels, you could miss by about a factor of one there, and so the actual calculations of the numbers in here are only good to about a factor of two to three. So essentially, even if you got everything right, the numbers, the calculations themselves, only are good to about a factor of three. So if you said the number was two, it could be six, but it's probably two or three. Then the big one, the two biggest error sources are here. One is we estimate a channel width. If we only have the vertical thickness, we have to estimate width, and we could be way off there, by about a factor of four, cause there's a lot of variability in channel depth versus width. So that aspect ratio of channel depth that we estimated, versus how wide the channel was, it could be a fourth that or four times that. We don't know. The the other one of course is this one, that's the big one, is all that voodoo I did about saying the average bankfull channel rolls by, the bankfull flood comes by every year and a half, and it moves about half the sediment that the river moves, well that's true for the average river. But no river is average, and rivers in terms of those two numbers range by order of magnitude. So that's our biggest source of error by far in this. So again, this fulcrum test as it stands right now, and as the state-of-the-art, is pretty much like all the other ones in that it gives you a very ballpark figure as to how much sediment that those rivers that you're looking at in the rock record would have moved. Right now we're using some very generic numbers for this to try to get at it, and so an order of magnitude is as close as it really gets. But that is the state-of-the-art at the moment. Now that said, there are a couple things you can do to improve that. First off, as far as width, we're used to looking at seismic data. We quantify width of channels all the time, and so if you have some 3D seismic to go with your cores, you might actually be able to measure the real width of those channels and not have to worry about that factor of four error in estimation of channel width. You can see the width and the depth. That can greatly improve that source of error. The other thing of course is, is that we've just started with this, and at this point we have gotten to the place where we are only beginning to address channel types. If you know more about your channels than just they're channels, and you know the climate, you know the thickness, and all that good stuff, you might be able to get those numbers for bankfull discharge in mean, and the amount of sediment carried down to a more precise number. So that's actually where our research is right now. I've got students looking at trying to refine those numbers to get this more accurate. One source of error though, is also multiple channels from the source to the sink, how many channels were actually working at once? That's where you have to be just a good geologist. You're simply looking to say how many trunk systems are actually moving through this system. And so that said if you miss-estimate that, well you're estimating the amount that's going to move down one channel, if there were two of them, and you only assumed there's one, well you've missed it by half, and so if there's two, if you assumed there were two channels at the same time and there was only one, well you've got twice as much as you should. So looking at your draining system, and making an estimate of what is truly the trunk channels, and what is their size, and how many values, or systems are actually feeding this, is a very critical piece of information to have. So you see it in the modern, you have to figure it out in the ancient, that's basic geology. The other thing is the statistical sampling machine that is the rock record. You're capturing channel bankfulls. You want to look at a lot of them. Let's hope that the rock record is actually getting a good representation, and preserving a good representation of the channels that actually would have been draining from the source at the sink, and that you sampled them properly. Welcome to the world of statistics, your numbers are only as good as the sample that the rock record gave you, and the sampling procedure that you made to come up with these numbers. In the end though, Fulcrum test is a valid way to estimate source-to-sink flux with common data sets. It's still rich with errors though, and limitations, and at some point we might be able to get to a factor of three as we sharpen it with more robust data sets. Right now we're to order magnitude. It's a good method to couple with other methods though. So the more methods that you apply into this system, the better.