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recent debris flows was determined easily by comparison with previous surveys of the debris fan. In other cases, the surfaces of historical debris-flow deposits were projected over the reworked debris fan, and photographic evidence was used to identify boulders or terraces that had not been eroded or buried by subsequent debris flows. Boulders visible in historical photographs that were covered by later debris flows but not moved by subsequent Colorado River floods provided minimum thicknesses for the deposits. We could not estimate the accuracy of the estimated thicknesses. In some cases, the volumes of historic debris flows were estimated by projection of remnant deposits over reworked debris fans (Webb and others, 1999b). Deposits were surveyed to estimate the slope on remnant deposits, and surveying of both sides of the Colorado River allowed projection over water. Volumes of debris flows Debris flow volumes vary considerably when plotted as a function of drainage area (fig. 13). Lacking sufficient data to describe a magnitude- frequency relation for all tributaries (we have debris-flow magnitude-frequelcy relation for only one tributary, Prospect Canyon; Webb and others, 1999b), we assumed that, like large streamflow 1S0 ~ Ql .~ 100 E ~ '5 G; D E i 50 o o floods (Enze1 and others, 1993), the volume of sediment delivered by debris flows is a function of drainage area and its upper limit can be described by an enveloping curve of the form: ViA) = a' Ab, (10) where V = total debris-flow volume (m3), A = drainage area of tributary (krn2), and a and b are empirical coefficients. We defined the enveloping curve usiog the highest five points in figure 12 and fitting a power function using least-squares regression (fig. 13). We also determined an average volume by fitting a power function to the scattered data (fig. 13). We then estimated maximum and average debris flow volumes using [he envelope curve and the average regression respectively. The volume of sediment transported to the river is also related to storm type but is only weakly related to the peak discharges of debris flows (Melis and others, 1994). Particle-Size Distributions of Debris Flows To account for boulder-size par1icles (larger than -8 4>), accurate determination of the par1icle- size distributions using weight-based determin- ations (e.g., sieve analysis) are problematic because Range in Frequency Factor, F 2 3 4 5 Figure 12. Distribution of debris-flow frequency factors (F) for 736 ungaged tributaries in Grand Canyon. DEBRIS-FLOW SEDIMENT YIELD 29