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<br />from the runoff for each event. With regression <br />analysis, we determined relations between peak <br />discharge and the total sediment yield for each <br />event (table 9). The relation of sediment yield to <br />peak discharge took the form: <br /> <br />Qe = a . Q/, (5) <br /> <br />where Qe = sediment yield in Mg/event, Qp = peak <br />flood discharge in m3 Is, and a and b are regression <br />coefficients. The R2 values ranged from 0.76 to <br />0.82, indicating a high degree of relation between <br />peak discharge and sediment yield per event (table <br />9). <br />In order to reduce the potential overestimation <br />of Grand Canyon sediment yields, we elected to use <br />the sediment yield-peak discharge relation that <br />produced the smallest sediment yield: Moenkopi <br />Wash # I. Of the five Black Mesa drainages, <br />Moenkopi Wash #1 is also most similar to the <br />average Grand Canyon tributary in terms of <br />drainage area. <br /> <br />Calculations of sediment yield <br /> <br />We linked flood-frequency discharge estimates <br />to sediment yield using <br /> <br />Q, = [I )(QIO) + 2 '.!(Q5) + 5 '1(Q})] 110, (6) <br /> <br />where Q, is sediment yield in Mglyear, Q, is the <br />peak discharge of the I year flood in m3/s, andJ(Q,) <br />is a regression equation relating peak discharge to <br />sediment yield in Mg/event (Qe)' With this relation, <br />we make the key assumption that total sediment <br />yield per decade from a tributary can be <br />approximated by the sum of sediment loads from <br />one 10-year, two 5-year, and five 2-year floods. <br />Using the regional-regression equations of <br />Thomas and others (1997) to estimate flood <br />frequency, we calculated the annual sediment yield <br />of all 768 tributaries in Grand Canyon for both the <br />Bright Angel Creek and Moenkopi Wash #1 <br />sediment-yield peak-discharge regression relations <br />(table 9). As expected, sediment yield estimates <br />based on the Bright Angel Creek data are two <br />orders of magnitude smaller than those based on the <br />Renard (1972) equation and regional data (fig. 8). <br />Although Grand Canyon sediment yield may be <br />somewhat smaller than estimates based on regional <br />data, a difference of two orders of magnitude <br /> <br />suggests that the Bright Angel data is not <br />representative of Grand Canyon tributaries. <br /> <br /> 10' <br />i 10' <br />:!1 10' <br />. <br />" <br />. <br />. <br />E <br />~ 10' <br /> 10 <br /> <br /> <br />.' <br /> <br />. Brighl Angel Creek <br />o Moenkopi Wash .1 <br />-0._193,,'00 <br />- - - Renard (1972) EQuation <br /> <br />10.4 <br />10.) , 0.' <br /> <br />'0' <br /> <br />10' <br /> <br />10' <br /> <br />10' <br /> <br />10' <br /> <br />DraInage AraB (knt) <br /> <br />Figure 8. Streamflow sediment-yield estimates for 768 <br />Grand Canyon tributaries caiculated using the regional <br />flood-frequency estimates of Thomas and others (1997) <br />and sediment-rating data from Bright Angel Creek and <br />Moenkopi Wash #1 compared to the data regression <br />equation and the Renard (1972) equation. <br /> <br />Estimates derived from the Moenkopi Wash #1 <br />relations exceeded estimates based on regional data <br />and the Renard (1972) equation (fig. 8). Although <br />we would expect estimates based on Black Mesa <br />data to exceed actual Grand Canyon values, we do <br />not expect them to exceed regional values in <br />general. This overestimation likely results from the <br />wide geographic extent of Thomas and others's <br />(1997) flood regions. For example, only to of 109 <br />gage stations used in the region 8 regressions are in <br />Arizona; most of region 8 is southeastern Utah as <br />well as parts of northwestern New Mexico and <br />southwestern Colorado. In contrast, the flood- <br />frequency regressions of Roeske (1978), although <br />calculated with shorter gage records and fewer <br />initial basin variables, use Arizona data exclusively <br />and contain the same independent variables of <br />drainage area and mean basin elevation used by <br />Thomas and others (1997). Using the Roeske <br />(1978) relations to calculate tributary streamflow <br />sediment yield produced results similar to those <br />derived from the Renard (1972) equation and the <br />regional data regression equation (fig. 9). Again, <br />the estimates based on the Bright Angel data are <br />two orders of magnitude smaller than estimates <br />based on regional data. Based on the above <br /> <br />18 Sediment Delivery by Ung.ged Tributaries of the Colorado River In Grand Canyon <br />