HYDRAULIC GEOMETRY OF GRAVEL-BED RIVERS Principal Investigator: John Pitlick  All The Important Work Done By: Erich Mueller Contact:  pitlick@spot.colorado.edu   erich.mueller@colorado.edu Geography Department Box 260 University of Colorado Boulder, CO  80309-0260 phone: 303-492-5906 Sponsor: US Forest Service Stream Systems Technology Center

Problem Statement: Rivers adjust their width, depth, and slope to maintain a balance between the water and sediment supplied from upstream, and that exported at the outlet.  However, in many river basins, human activities have altered the water and sediment supply, resulting in potential changes to stream channels and their natural functions.  The variability inherent in fluvial processes and sediment transport makes it difficult to assess the effects of these changes directly, and even with extensive field measurements, there is always a reasonable chance of obtaining ambiguous results.  This study seeks a potential solution to the sediment transport problem by relying on the principle of mass conservation (sediment continuity), and the assumption that rivers know what they are doing: they develop the necessary characteristics to carry the water and sediment supplied from the watershed, and they integrate these processes over periods of time.  It should be possible, therefore, to use the existing characteristics of a network of river channels to say something about the mass balance of sediment.  The section below provides background to the problem based on recent work on the hydraulic geometry of gravel-bed rivers (Parker, 1979; Pizzuto, 1992; Pitlick and Van Steeter, 1998; Pitlick and Cress, 2000), and the section after that describes field studies underway to address the problem.

Background: An important advance in our understanding of the link between channel geometry and bed load transport came in a series of papers by Gary Parker, published in the late 1970s.  Parker (1979) showed that gravel-bed rivers will adjust their bankfull width and depth to provide a shear stress, t, that is above the threshold for bed load transport, tc, but not so high as to cause bank erosion.  In contrast to threshold channel theory, this condition allows gravel-bed rivers to transport bed load, yet remain stable.  Expressed in terms of the dimensionless shear stress, t* = t [(rs - r) g D]-1, the theory predicts that gravel-bed rivers will set their bankfull width and depth to provide a t* that is slightly higher than the threshold for transport, t*c; for straight channels of uniform depth, Parker (1979) found that the cross section will adjust to provide a bankfull t* = 1.2 t*c.

Pizzuto (1992) used this result to formulate a theory for the downstream hydraulic geometry of gravel rivers.  This theory attempts to model the downstream movement of water and sediment through a drainage network, from first-order sources to the outlet of the basin.  Knowing the discharge, sediment load, and grain size at various points, the channel geometry is predicted by solving a set of equations for width, depth, slope and velocity.  The model did a good job of predicting the bankfull width and depth, but tended to underpredict changes in slope and grain size. Pizzuto (1992) concluded by suggesting that individual variables may adjust over different time scales, with the width and depth responding relatively rapidly in comparison to the slope.

One implication of Parkerís theory is that the bankfull t* of gravel-bed rivers should be constant downstream.  Results from our work on the Colorado River in western Colorado show that this is approximately true (Fig. 1).  Field measurements of bankfull depth, slope, and grain size taken at closely spaced intervals show that the bankfull t* of the Colorado River is essentially constant (0.049) over an order-of-magnitude range in the dimensionless bankfull discharge, Q*.

Figure 1. Dimensionless hydraulic geometry relations for the Colorado River;  B* is the dimensionless width, H* is the dimensionless depth, S is the slope, and t* is the dimensionless shear stress (data from Pitlick and Cress, 2000).
 

The consistency in bankfull t* values of the Colorado River suggests that this river has adjusted its hydraulic geometry to maintain roughly the same bedload-transport capacity from reach to reach.  There is clearly a connection between channel morphology and sediment transport.  The results imply that, all else being equal, the bed load transport rate per unit width is approximately constant downstream.  Of course, all else is rarely equal in gravel-bed rivers, thus simple statements about continuity may be difficult to verify in the field.  Assuming previous theoretical results are valid, direct application is limited by at least four problems: (1) the bankfull t* may not be representative of the full range of sediment-transporting flows; (2) accurate estimates of t* are difficult to obtain in rivers with coarse bed material and rough banks because of energy losses due to obstructions (form drag); (3) the critical Shields stress for gravel (0.03) may not be constant; and (4) the whole approach assumes that gravel-bed rivers transport at capacity, i.e. they are not supply limited.

The first three of these problems can be addressed with carefully planned and executed field studies (see below); the fourth issue of sediment supply is, arguably, more of a semantic or operational problem than a physical problem.  The notion that mountain streams are supply-limited arises because much of the time the material in transport is much finer than the material seen on the bed; calculations of bed load transport based on the surface particle size distribution give the impression that only high flows can mobilize this material, thus streams with coarse bed material could carry much more fine material, if only it were available.  This argument certainly applies to non-alluvial rivers, but alluvial rivers are free to form their channels and adjust their bed material characteristics to carry the supply, no matter how fine or coarse it is (see Parker, 1990).  The operational problem comes in being able to accurately measure or specify these characteristics at a given place or time, especially during high flow events.

Approach: Field work for this project is being conducted on Half Moon Creek, a moderately steep stream draining about 24 mi2 in the northern part of the Sawatch Range in central Colorado.  Measurements of channel geometry, slope, and surface and subsurface bed material have been made at more than 25 sites within the basin.  Measurements extend from 1st-order streams, down through the channel network to the basin outlet.  The data collection scheme emphasizes broad spatial coverage utilizing quick measurements at many sites rather than detailed measurements at a few sites.  Specific measurements include:

1. Bankfull hydraulic geometry: Three cross sections were measured at each site.  The purpose of measuring more than one cross section was to better define the average bankfull hydraulic geometry, and to examine the variability in channel geometry through the drainage network.  The slope of each reach was also surveyed.

2. Sediment Size: Surface particle sizes were measured at each site using the Wolman method.  Bulk samples of the subsurface sediment were taken at nearly all sites.  The purpose of obtaining both surface and subsurface sediment samples is to determine whether there are downstream trends in the ratio of surface-subsurface size fractions (e.g. D84 or D50) or the percentage of sand vs. gravel.

3. Velocity measurements were repeated throughout the snowmelt period at several of the sites.  The purpose of the velocity measurements is to address the issue of form drag (high roughness) in this steep stream.

Results: Erich Mueller (shown on the left) will present prelimnary results of this work at the fall meeting of the American Geophysical Union.

Parker, G., Hydraulic geometry of active gravel rivers, J. Hydraul. Eng., 105, 1185-1201, 1979.

Pitlick, J. and M.M. Van Steeter, Geomorphology and Endangered Fish Habitats of the Upper Colorado River 2: Linking Sediment Transport to Habitat Maintenance, Water Resour. Res., 34, 303-316, 1998.

Pitlick, J. and R. Cress, Longitudinal Trends in Channel Characteristics of the Colorado River and Implications for Food-Web Dynamics, U.S. Dept. Interior Fish and Wildlife Service Final Report, Grand Junction, Colorado, 2000.

Pizzuto, J.E., The morphology of graded gravel rivers: a network perspective, Geomorphology, 5, 457-474, 1992.