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34 - to PITLICK AND CRESS: DOWNSTREAM CHANGES IN CHANNEL GEOMETRY <br />Figure 10. Downstream trends in the bank-full dimensionless shear stress of the Colorado River. <br />Symbols are the same as in Figure 7. <br />higher. Both data sets support the hypothesis that Tb is <br />independent of Q*, and the average values of Tb are <br />identical (0.049). This last result has interesting implications <br />for bed load transport. Typical transport equations express <br />the dimensionless unit bed load transport rate, qb, as a <br />function of the excess shear stress, T* - T,, raised to a <br />power >1. The results above imply that if Tb is constant, <br />then qb is also constant (assuming that T*, does not also <br />vary). By definition, the volumetric bed load transport rate <br />per unit width is qb = qb RgD3/2, and the total transport <br />rate is Qb = Bqb. Combining these relations, we get Qb = <br />Bqb RgD3/c, or more generally, Qb a BD312. Thus, if q*b 1 <br />indeed constant, then the downstream change in total bed <br />load transport depends on the change in B relative to the <br />change in D3 2. Our data show that the grain size decreases <br />more rapidly than the width increases (Table 3), suggesting <br />that the total volume of bed load carried by the Colorado <br />River is decreasing downstream. This interpretation is <br />supported to a limited extent by the comparison of surface <br />and subsurface sediment (Figure 6), which shows a pro- <br />gressive coarsening of the surface layer downstream. The <br />surface layer regulates the transport of different sizes, and <br />for particular combinations of discharge, slope and sediment <br />supply, the surface texture may become finer or coarser <br />downstream [Parker, 1990]. The development of a static <br />armor downstream of a dam represents the extreme case of <br />supply limitation, while the absence of a surface layer may <br />indicate high sediment supply [Lisle and Madej, 1992]. The <br />Colorado River lies somewhere in the middle of this <br />spectrum, with hillslopes and ephemeral tributaries main- <br />taining the supply of coarse material, but apparently at rates <br />that diminish downstream. <br />6. Conclusions <br />type. In contrast to the trends observed in many other rivers, <br />the bank-full width of the Colorado River increases slowly <br />downstream in comparison to the bank-full depth. The <br />differences in bank-full width and depth appear to be driven <br />by competing effects of slope and grain size. In comparison <br />to other rivers, the slope of the Colorado River decreases <br />more rapidly downstream, whereas the grain size decreases <br />more slowly. Continuity requires that the river form a deeper <br />104 103 <br />r ?.. ? <br />B. <br />• <br />103 + * 10 <br />M • ` B- = 39.3()'`0.32 H* <br />H- = 0.070_1-0.53 <br />102 101 <br />S S = 0.780"-0.50 100 <br />v <br />10-3 cr:,: c <br />10'1 <br />• <br />• <br />[3o] The segment of the Colorado River examined in this <br />study exhibits morphologic characteristics that are, in some <br />aspects, very different from other gravel bed rivers, but in <br />other aspects quite similar. We find, for example, that <br />channel properties (bank-full width, depth, slope and bed <br />material size) change systematically downstream, and that <br />transitions in reach type caused by local changes in bedrock <br />geology often have little effect on overall trends. Partitioning <br />of cross section data from alluvial and quasi-alluvial reaches <br />shows that downstrcam relations for bank-full width and <br />bank-full depth cannot be distinguished on the basis of reach <br />10-41 0.049 <br />1° ( 10-2 <br />105 106 107 <br />Q* <br />T* <br />Figure 11. Downstream hydraulic geometry relations for <br />dimensionless width B*, depth H*, slope S, and Shields <br />stress T*.