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6 rIM E, O'CONNOR ET AL, have been deposited after 520-280 cal yr B,p,ISam- pie GX-I6012; table I}, consistent with our inter- pretation that G 1 was left by the flood of 1884, Neotoma fecal pellets and plant fragments from the crevice deposits above the stratigraphic section at Axehandle Alcove yielded an age of 1517-1187 cal yr B,P, for the largest flood in the 4500 yr record, An additional sample of Neotoma fecal pelletS (GX-16024) from high crevice deposits across . the river from Axehandle Alcove yielded a similar date of 1595-1179 cal yr B,P" strengthening the conclu- sion that there was one extremely large flood 1600 to 1200 years ago, Discharge Bstimlllion. The highest elevation of each flood deposit gives a minimum estimate for the peak stage of the flood that emplaced it, We developed a stage-discharge relation for Axehandle Alcove by calculating energy-balanced water sur- face proBles for a wide range of discharges (figures 3 and 4), The water surface proBles were calculated by the step-backwater method (Chow 1959; Hydro- logic Engineering Center 1985, O'Connor and Webb 19881 for 11 surveyed and four interpolated cross sections for a 1,2 km reach encompassing the site. Because the top of each deposit provides only a minimum estimate of the peak flood stage, this stage-dischllrge relation (figure 3}likely provides minimum estimates for discharges of correspond- ing flood deposits, Because these minimum discharge values are used in the following flood frequency analysis, some discussion of their accuracy is pertinent. Un- certainty in discharge estimates derived from the step-backwater method as applied here arises pri- marily from uncertainties in 11) downstream flow conditions and their effect on the local water- surface proBle, 121 values of energy loss coeffi- cients; 131 the channel geometry at times of peak flow stages, and (4) the depth of water above each deposit as it was emplaced, For Axehandle Alcove, sensitivity tests indicate that the maximum com- bined uncertainty resulting from 1 and 2 is about ~ 25% considering reasonable limits for the un- known parameters. Uncertainty in the channel ge- ometry is probably the most important consider- ation, especially uncertainties in channel bottom elevation, We have used the present (1990) channel bottom for our step-backwater calculations, There is no evidence of long-term channel change at the site (based on inspection of matched photographs of the reach taken in 1890 and 1991-1992), Chan- nel scour during floods is probably a larger source of error, Several meters of bed lowering coincident with flooding have been documented at both the Lees Ferry (Burkham 1986) and Grand Canyon (Leopold and Maddock 1953) gages, This effect can be large; 3 m of channel bottom lowering (similar to what has been observed at the Grand Canyon gage) at peak stage would increase the discharges 'lSsociated with the elevations of the flood deposits at Axehandle Alcove by 20-300/., The likelihood of such scour during large flows, combined with the requirement that the peak flood stages were higher than the resultant deposits, leads us to be- lieve discharge estimates assigned to the flood de- posits should be considered minimum discharge estimates, The discharge values assigned to flood deposits (on the basis of the stage-discharge rela- tion in figure 3) are overestimates only in the un- likely circumstance that energy-loss coefficients are significantly underestimated and channel scour is minim.! at peak stage and there is little or no water above the sediment deposited by the flow, The maximum possible discharge overestimation, on the basis of the above discussion, is about 25 % , It is far more likely, however, that the discharge value assigned to each individual flood deposit un- derestimates the magnitude of the flow that depos- ited it, The potential underestimation is large, de- pending primarily on the depth of water above the deposit left by the flow, and the amount of channel scour at the time of highest stage, Assuming that the stage-discharge relation of figure 3 does not overestimate peak discharges as- sociated with corresponding flood deposits, the 15 floods preserved in the stratigraphic record that post-date 4518-4239 cal yr B,P, all had discharges that exceeded 5700 m!sec - I, The ten floods since 2307-2062 cal yr B,P, (probably including the flood that emplaced the crevice deposits) had discharges larger than 6875 m!sec-I. On the basis of the strati- graphic continuity between flood deposits and the conformable contscts in the upper part of the two measured sections, we infer that the stratigraphy subsequent to 2307-2062 cal yr B,P. records all floods that overtopped the section, It is likely that all floods are not recorded in the lower part of the section where deposition occurred under more en- ergetic, and locally erosive, conditions, The high- est G 1 deposits indicate that the most recent flood in the stratigraphic record had a discharge of at least 8800 m!sec -1, This estimate is similar to the USGS estimate of =8500 m!sec-I for the 1884 flood at Lees Ferry, The elevation of the highest crevice deposits requires a discharge of greater than 14,000 m3sec-I, A discharge of 14,000 m3sec-1 surpasses the 1921 flow by more than a factor of two, and is 1.65 times larger than the historic flow of 1884, Nevertheless, it is substantially less than the