20 Total Load Part 2 PDF

Preview

Summary

Download 20 Total Load Part 2 PDF

Description

CEE 474 Sediment Transport Lecture 20 – Total Load 2 Introduction From the number of formulas we have introduced and their relative spread in predicted sediment transport rates, it should be clear to see that estimating the sediment transport at a particular location is very difficult to do! In fact, if we are interested in total load, it is practically impossible to predict based on local hydraulics and bed material because of the material in the wash load. Furthermore, most of our formulas for sediment transport depend in some way on the shear stress. However, actually obtaining an accurate and representative estimate of the shear stress can be quite difficult! Consider the conditions that our systems often exist in: fully turbulent, unsteady, and nonuniform. This means that shear stress is highly variable in both space and time! Even if we are able to monitor a section or reach of a river and estimate some average shear stress, consider that our sediment transport formulas are often nonlinear functions of shear stress. Many of them take the form qt = func (τ0 )α or qt = func(τ0 − τc )α , where α is some power generally greater than one. So, they are power-laws of some kind. Even if we can accurately estimate some timeaveraged shear stress, the power of an average does not equal the average of a power! Additionally small errors in estimated τ0 or τc values could produce large errors in qt ! Sediment Rating Curves Sometimes what we end up doing is measuring sediment transport rates for a range of flow rates and relate them using a sediment rating curve. You may be familar with discharge rating curves. This is essentially what is done at USGS stream gaging stations. Scientists use field measurements to relate water surface elevations to a volumetric flowrates. Then as we monitor the changes in water surface elevation we can predict what the volumetric flowrate is based on the relationship. That relationship is the discharge rating curve. A sediment rating curve is similar, except now we are relating sediment discharge to flow characteristics (usually either depth or water discharge). Sediment rating curves most often are determined for sediment discharge as a function of water discharge. Qt = aQb where Qt is the total sediment discharge, Q is the total water discharge, and a and b are constants fit to field measurements. Sometimes sediment rating curves are created for bedload and suspended load separately, or, depending on the system, sometimes only one or the other is necessary. Sediment rating curves can be an extremely powerful tool! Consider a case where you have a sediment rating curve and 25 years of flow data. You can estimate the amount of sediment transported at each time step using the rating curve. By integrating the time-series of estimated sediment discharge you can predict the 25-year sediment yield at that location! Be careful, though! Sediment rating curves can shift rapidly over time. In some situations, measurements must be collected on a more regular basis to update the sediment rating curve. Some1 of 2

CEE 474 Sediment Transport

Lecture 20 – Total Load 2

times finer temporal resolution is necessary to capture the transport during rapidly varying flow conditions or at morphologically active sites. In the absence of field measurements, sometimes sediment transport formulas are used to estimate a rating curve. Often we are interested in sediment transport rates at very high water discharges, when it is not practical or safe to make measurements. So we also sometimes combine measurements and calibrated transport formulas to create a rating curve that covers the range of discharges we are interested in. We can also create a concentration rating curve by dividing the above equation by water discharge. Qt = C = aQb−1 Q Effective Discharge One of the uses of a sediment rating curve is the determination of the so-called “effective discharge”. The concept goes back to M. Gordon Wolman and Luna B. Leopold (1960), who hypothesized that for alluvial rivers, there was a certain water discharge that controlled the channel shape. This channel-forming discharge, the effective discharge, is defined as the flowrate at which the maximum work is performed (in terms of sediment transport). Low discharges occur very frequently, but transport little to no sediment. High discharges, on the other hand, have the capacity to transport high sediment rates, but occur infrequently. Wolman and Leopold defined the sediment yield density, which is the product of the flowrate frequency curve and the sediment rating curve.

The discharge that corresponds to the maximum sediment yield density is the effective discharge. Leopold and Wolman argued that the effective discharge was equal in magnitude to the bankfull discharge. However, many studies since then have shown that for some rivers there are significant differences in effective and bankful discharges. While the effective discharge is still a common concept and a geomorphically important discharge, it is generally accepted that the form and shape of alluvial channels is the product of a range of discharges and no single recurrence interval can be considered to be representative of a particular river or site. 2 of 2...