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,. Journal 01 Geology LARGE FLOODS ON THE COLORADO RIVER 7 LI ~ largest floods from equivalent size u.s, water- sheds. The envelope curve of Costa (1987), which defines the limit of largest measured discharges compared to drainage area, indicates that for a drainage area the size of the Colorado River at Lees Ferry, the limiting discharge is about 43,000 m3sec-I, three times larger than the largest flood in the stratigraphic record at Axehandle Alcove. Flood Frequency Using the Gaged and Stratigraphic Records We combined the geologic record of flooding with the gaged record at Lees Ferry to evaluate flood frequency for the Colorado River by optimization of the parameters for a log-normal frequency distri- bution using m.rimum likelihood estimators Iflgure 5, table 21, This method efficiently com- bines stratigraphic evidence for ungaged floods with records of gaged floods to give estimates of the frequency of large floods IStedinger and Cohn 1986; Stedinger and Baker 1987; Stedinger et al. 19881, A further advantage is that categorical infor- mation on flood discharges can be used, such as the case for the stratigraphic record at Axehandle Alcove (and many historical and prehistorical rec- ords) where we interpret flows to have exceeded 20000 .. 'll888 eooo 7000 ., 6OClO ~ 5000 "'e 4000 ~ 3000 co .c 2000 ,~ 0 'S88 800 700 600 500 .. o AmuaI Peak 1lIsch8rg88 at 1MB Ferry (IS21-1962) .. Flood DeposI1s at at Axahandla Ak:ova O~ 90 70 50 30 10 1 0.1 0.01 Annual Excesdance Probability (percent) Figure 5. Log-normal frequency distribution and stan- dard errors for floods on the Colorado River near Lees Ferry based on maximum likelihood analysia of the com- bined gaged and stratigraphic records, The plotted dis- charges for the floods recorded by deposits in Axehandle Alcove are minimum ...timates, Plotting positions were assigned on the basis of Hirsch and Stedinger.(1987, Ap- pendix 3, a = 0.41, There is considerable uncertainty in the plotting positions for the largest flows of both series, known magnitudes, but are uncertain of their ac- tual discharges, A critical assumption in this analysis is that all floods above specified discharge thresholds are re- coJded in the stratigraphy; therefore, we have con- sidered only the ten floods that postdate, 2307- 2062 cal yr B,P, because, as described above, we infer that the stratigraphic record is complete for this time period, The discharge of each flood in the stratigraphic record was described as an open- ended range bounded below by the minimum dis- charge value derived from the stage-discharge rela- tion in figure 3, The largest flood, associated with the crevice deposits, was assigned a minimum value of 14,000 m3sec-1lf1gure 4), Because the top of the stratigraphic section be- came higher with each deposit, the discharge threshold required for allowing deposition of the next deposit increased after each recorded flood, To factor this in, the "recording threshold" was described as rising in a stepwise fashion as the flood deposits accumulated, with its height corre- sponding to the top of the last deposited unit. The date of each flood is not known, consequently, each of the ten floods was assumed to be evenly spaced during the 2307 yr length of record, This assumption does not introduce significant error into the long-term frequency analysis because the discharge threshold increased only by a small amount (about 10%1 over the 2307 yr record. Be- cause of this assumption, however, we cannot use this analysis to address possible changes in flood frequency during the period of record. Because ac- curate discharge thresholds are required for this type of analysis (knowing the exact discharge of a flood that exceeded a discharge threshold is not as critical as knowing the threshold discharge accu- rately), frequency analyses were also performed as- suming 25% uncertainty in the discharge thresh- olds {table 21, The gaged record used in the flood frequency analysis consisted of the annual peak discharges at Lees Ferry between 1921 and 1962 (figure 21, An- nual flood flows after 1962 have been artifically and substantially altered by closure of Glen Can- yon Dam, Annual peak discharges in the gaged rec- ord were considered precise values in all analyses, although as discussed above, there is an unknown uncertainty in the accuracy of the gaged peaks, The USGS estimate for the 1884 flood was not included as part of the gaged record because we infer that the 1884 flood is recorded in the stratigraphy at Axehandle Alcove, Used in this fashion, the stratigraphic record at Axehandle Alcove leads to improved estimates of t ,.;:: , (~ '.J> ., ~-'" ':'1 ~:'.: ' " . " I::~ ',.". ,~.' . ~ ;~ I ~-~ i\..:" 'it: '-..'.- ~ -l'; ::.-;-~ ,( .