WSP05649

• File Number: 8220.101.10.D
• Description: Glen Canyon Dam/Lake Powell
• State: AZ
• Basin: Colorado Mainstem
• Date: 2/1/2000
• Author: Topping et al.
• Title: Colorado River Sediment Transport
• Water Supply Pro - Doc Type: Report/Study

TOPPING ET AL: COLORADO RIVER SEDIMENT TRANSPORT, 2

depth, a is the level (determined by the method of Wiberg and
Rubin [1989]) at which the reference concentration is calcu-
lated, p is the Rouse number, and /3 = 6.25 is a constant set by
the matching height of O. 2h. The Rouse number,

p = w.Jku.,

where w ~ is the settling velocity of sediment in size class m and
u. (the shear velocity) is set equal to YTblp for a planar bed.
On the basis of the work of Smith and McLean [1977] the lower
boundary condition for suspended sediment is

. ( T. - T")
(c",).=A"lIllCb'Y ~ '

where (c~). is the near-bed, time-averaged concentration of
suspended sediment in 6ize class m, A, is the fractional area of
the patches of fine sediment (i.e., sand and finer material) on
the bed, i m is the volumetric fraction of sediment size-class m
in the patches of fine sediment on the bed, cb = 0.65 is the
volumetric concentration of fine sediment in that portion of
the bed covered by fine sedimen~ "( is a constant set equal to
0.0045 (P. Wiberg, pemona! communication, 1989) when a is
determined by the method of Wiberg and Rubin [1989], and Ta
is the critical shear stress of the median size of the fine sedi-
ment on the bed calculaIed by the method of Wiberg and Smith
[1987]. To preclude the occurrence of physically unrealistic
high concentrations of suspended sedimen~ in the cases where
(c,). is predicted to be greater than 0.5 by (4), (c~). =
0.5A,im. Topping [1997] showed that (4), used in combinaIion
with the full suspended-sediment theory (i.e., including the
effects of both bed forms and density stratification) of Smith
and McLean [1977] and McLean [1992], is a good predictor of
both the mea6ured depth-integrated concentration and grain-
size distribution of suspended sediment in the flume experi-
ments of &nnedy [1961] and Guy el al. [1966] and is also a
good predictor of both the measured near-bed concentration
and grain-size distribution of suspended sediment in the Rio
PueTCO data of Nordin [1963].
As illustrated by McLean [1992], inclusion of the effects of
bed forms and density stratification decreases the suspended-
sediment concentration and grain size relalive to those pre-
dicted by the approach outlined above. By reducing the stress
on the bed, but maintaining a high degree of vertical mixing in
the interior of the flow, inclusion of the effect of bed forms can
decrease the concentration of suspended sediment by as much
as an order of magnitude and can decrease the depth-averaged
median size of the suspended sediment by as much as 20%. By
partially damping the turbulence and reducing the vertical
mixing in the flow, inclusion of the effect of density stratifica-
tion can decrease both the depth-averaged concentration and
median size of the suspended sediment by about 20%. Thus
the combined impact of these two effects on the predicted
magnitudes of the depth-averaged suspended-sediment con-
centration and grain size can be quite large. However, the
predicted change in suspended-sediment concentration and
grain size as a fwiction of a change in bed-sediment grain size
is similar (within 20%) regardless of whether or not these
effects are included. Therefore these two effects are excluded
for the sake of keeping the discussion below simple.
Solution of (2), (3), and (4) suggests that the grain-size
distribution of the fine sediment on the bed exerts a greater
control on the concentration of suspended sediment than does
the surface area of the patches of fine sediment on the bed.

567

(3)

The coupling between the grain-size distnbutlon of the fine
sediment on the bed and the concentration of suspended sed-
iment is strongly nonlinear, whereas the coupling between the
area of the patches of fine sediment on the bed is approxi-
mately linear (depending on how the patches are distributed
on the bed). Regardless of whether the fine sediment on the
bed is reiatively fine or coane, coarsening of the fine sediment
On the bed by a factor of two will produce a decrease in
suspended-sediment concentration of about an order of mag-
nitude (Figure 18a). In contras~ solution of (2), (3), and (4)
suggests that a factor of 2 decrease in the area of the patches
of fine sediment on the bed will produce a factor of 2 decrease
in suspended-sediment concentration.
A situation in which a cbange in the area of the patches of
fine sediment on the bed may be predicted to have a nonlinear
inftuence on the concentration of suspended sediment is when
the area of the patches gets small enough that the drag due to
protrusion of gravel through the fine sediment results in a
substantial reduction in the boundary shear stress (by the
mechanism proposed by Wiberg and Smith [1991] and Nelson el
al. [1991 D. When the diameter of the gravel on the bed is small
relative to the flow depIh (i.e., the median grain diameter is
less than 10% of the flow depth), this effect may be important
only when the patches of fine sediment cover less than 5% of
the bed [Topping, 1997). However, other mechanisms, for ex-
ample, enhanced near-bed turbulence because of the protru-
sion of gravel particles into the flow [Schmeeclcle, 1998], may
offset the effect of the gravel reducing the boundary shear
stress. In any case, because the median size of the gravel in the
pools of the Colorado River is less than several percent of the
flow depth and a 5% patch area is less than that observed in
pools by Anima el aI. [1998], this effect is probably not impor-
tant in the Colorado River in Marble and Grand Canyons.
In a given flow the grain-size distnbutlon of the suspended
sediment is tlghIly coupled 10 the grain-size distribution of the
fine sediment on the bed (Figure 18b) and is unaffected by
changes in only the area of the patches of fine sediment on the
bed. Changes in the area of the patches of fine sediment on the
bed, though probably accompanying the changes in the grain
size of the fine sediment on the bed, are neither necessary nor
suflicient to explain the observations made in the Colorado
River. During the 1996 flood experiment, the 1997 test flow,
following the 1983 LiIIle Colorado River flood, and following
the 1997 Paria River and ungaged tributaty floods, changes in
suspended-sand concentration were inversely related to
changes in the grain size of the suspended sand and the fine
sediment on the bed. In contrast, the area of the patches of fine
sediment on the bed did not change substantially from before
to after the 1996 flood experiment (Anima el aI., 1998].
By virtue of the physics in (2), (3), and (4), finer grain sizes
are more mobile than coarser grain sizes. This results in sys-
tematic coupled changes in sand grain size and transport in a
river with an intermittent and limited supply of sand [e,g.,
Bennett and Nordin, 1977]. Because of their lower setIling ve-
locities, the finer grain sizes of sand will be suspended higher
in the flow than the coarser sizes. Thus the finer grain sizes will
travel downstream at progressively higher velocities than the
coarser grain sizes. Therefore the finite quantity of sand tbat is
supplied to the Colorado River during a tributary flood will
travel downstream as an elongating sediment wave, with the
finest sizes (because of their lower settling velocities) traveling
the fastest (as observed in September 1998). Because the grain
size of this newly input sand (Dso - 0.11-0.15 mm) is typ-

(4)