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524 TOPPING ET AL: COLORADO RIVER SEDIMENT TRANSPORT. I the physical relationships that link. changes in suspended-sand concentration to changes in suspended-sand grain size. These relationships are based on the suspended-sediment theol)' re- viewed by Topping" al.(this issue] and hold true for all cases where suspended-load transport is the dominant transport mode of the sand on the bed (i.e., when the Rouse number of the median size of the sand on the bed is less than about 1). The relationships that link changes in suspended-sand con- centration and grain size are relatively straightforward when (1) the upstream supply of sand is in eqnilibrium with the flow conditions, (2) the upstream supply of sand becomes depleted while the ftmv is steady or increasing, and (3) the upstream supply of sand becomes enhanced while the flow is steady or decreasing. Given an upstream supply of sand that is in equi- librium with the flow conditions, sand in suspension will coarsen only when its concentration increases. In this case the coupled increase in suspended-sand concentration and grain size is caused by an increase in boundary shear stress associ- ated with an increase in ftmv. At steady or increasing flows, given a decreasing upstream supply of sand, the grain size of the sand in suspension will either increase or remain constant if the concentration of sand decreases. At steady or decreasing flows, given an increasing upstream supply of sediment, the grain size of the sand in suspension will either fine or remain constant if the concentration of sand increases. The relationships that link changes in suspended-sand amcen- tration and grain size are more complicated in flows that are decreasing while the sediment supply is being depleted and in flows that are increasing while the sediment supply is being en- hanced. This increase in complexity arises from the fact that under these conditions the rate at which the boundary shear stress changes can offset the influence of a change in the upstream supply of sand. For example, in decreasing flows, though the concentration of sand will always decrease when the upstream supply of sediment is depleted, the sand in suspension may actu- ally fine if the boundary shear stress deaeases quickly enough. Ukewise, in increasing flows, though the conoentration of sand will always increase when the upstream supply of sediment is enhanced, the sand in suspension may actually coarsen if the boundary shear stress increases quickly enough. In summary, regardless of how the flow changes, (1) a de- crease in suspended.sand concentration associated with either coarsening or no change in grain size always indicates sand depletion, (2) a decrease in suspended.sand concentration as- sociated with fining is inconclusive, (3) an increase in sand concentration associated with either fining or no change in grain size always indicates an increase in the upstream supply of sand, and (4) an increase in suspended-sand concentration associated with coarsening is inconclusive. In this analysis these four types of sand-supply events are referred to as (1) sand- depletion events, (2) decreasing-concentration inconclusive events, (3) sand-enhancement events, and (4) increasing- concentration inconclusive events, respectively. Determination of the relative seasonal importance of each of these four types of sand-supply events at the Grand Canyon and Lees Ferry gages was an eight-step process. First, the suspended-sand data from each gage were placed in the format of a time series. Second, these data were analyzed to determine how [he measured concentration and grain size of the sus. pended sand changed from sample to sample (Le., each pair of samples was assigned to one of the four defined types of sand- supply events). Third. so that this analysis would be consistent with the bed-elevation <lnalysis in Figure 6a, only those samples that were collected within 2 weeks of each other were used. Fourth, the time of each sand-supply event was calculated as the midpoint in time between the two samples. Fifth, the data were then segregated into the same 2-week bins used in the bed-elevation analysis. Sixth, each sand-supply event was then weighted by the measured suspended-sand load at the time of each event. This weighting was applied because the degree to which the upstream supply of sand gets depleted or enhanced depends strongly on the sand-transport rate. For example, sand-depletion events occurring when the sand-Iransport rate is low represent a smaller decrease in the upstream supply of sedimenl than those occurring when the sand-transport rate is high. Seventh, for each of the four types of sand-supply events in each 2-week bin, the load-weighted data were summed to determine the load-weighted occurrence of each type of sand- supply event. Finally, before the data in either differenl bins or at the Grand Canyon and Lees Ferry gages could be compared, a correction had to be made to remove the dependence of the load-weighted occurrences on the different total number of sand-supply events in each bin. Therefore, eighth, the "nor- malized load-weighted occurrence" of each type of sand-supply event was determined by dividing the load-weighted occur- rence of each type of event by the total number of the four types of sediment-supply events in each bin (Figures 6a and 6b). 5.4. Discussion of lb. Diff....nces in Coupled Changes in Suspended-Sand Concentration, Susp.nded-Sand Grain Size, Bed Grain Size, and Bed EI.vation in Grand and Glen Canyons In the average predam year the bed at the Grand Canyon and upper Lees Ferry cableways responded very differently during the annual snowmelt flood. The bed at the Grand Can- yon cableway would initially aggrade, while the bed at the upper Lees Ferry cableway would initially scour. FnUowing the initial portion of the snowmelt flood (but still during the rising limb), the response of the bed at the Grand Canyon cableway would reverse, and the bed at both cableways would scour. During the receding limb of the flood the bed at the Grand Canyon cableway would typically remain stable, whereas the bed at the upper Lees Ferry cableway would aggrade. The systematic response of the bed at the Grand Canyon cableway during floods was first recognized by Leopold and Maddock [1953], who related it to systematic changes in the upstream sediment supply and mean velocity during a ftood. This inter. pretation was essentially restated by Burldwm (1986], who an- alyzed time series of bed scour and mean velocity at the Grand Canyon and upper Lees Ferry cableways. The opposing initial responses of the bed at the two sites during floods was first documented by Colby [1964], who attributed this difference not to the mechanism proposed by Leopold and Maddock (1953] but rather to the control of reach geometry on the pattern of scour and fill during a flood. Colby [1964] indicated that sedi- ment concentrations were increasing at both the Grand Can- yon and Lees Ferry gages during the rising limb of the snow- melt flood but that the response of the bed at the two sires was the opposite. Colby [1964] demonstrated through flume exper- iments that, given only a difference in reach geometry, one reach will scour and one will fill given the same upstream supply of sediment. Using a conceptual model of sediment redistribution during high flows. Howard and Do/an [198 I], like Colby [1964[. suggested that the initial response of the bed at the Grand Canyon cableway was controlled by reach geometry [lfnward and Do/an, 1981, Figure 71 and that the initial scour