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As an example, suppose an estimate of Q25 was required for an ungaged basin with a effective drainage area of 8.25 mi'. As indicated in table 4, equa- tion 17 should be used, the resultant estimate of Q25 being 3,950 ft3 Is. Flood Volumes The relationship between peak discharge and flood volume was studied using both recorded and synthetic flood data. The analysis of recorded data produced equation 1. while the analysis of synthetic data produced three relations of which equation 4 was judged to provide the best results. Both equations 1 and 4 are quite similar. However, because the synthetic data base is (1) much broader with respect to number and size of floods, and (2) a better estimate of the magni- tude of rare floods (such as QIOO as previously discussed), equation 4 will pro- bably provide the best overall estimates of flood volume from peak discharge for small ungaged basins in the study area. This relationship is given in table 4 and is app licable to pea k discharges less than about 13,000 ft3 s. For examp Ie, the volume for a 3 ,950-ft' Is peak discharge, previously determined to be Q25 for an 8.25 mi' basin, is estimated using equation 4 to be 285 acre-ft. Synthetic Hydrograp h Methods thus far have been discussed by which the magnitude and volume of floods can be estimated for small ungaged watersheds in the Arkansas River basin in Colorado. These flood characteristics can be further used to develop a com- plete synthetic hydrograph as described by Commons (1942). The dimensionless hydrograph developed by Commons was refined for small watersheds in Wyoming by Craig (1970). This refined hydrograph, called the composite mean dimension- less hydrograph, has a volume of 970 square units, a rise time of 12 time units. and a time base of 70 time units, The dimensionless time and discharge units of the synthetic hydrographs are given in table 5, which also shows an example calculation of the synthetic hydro- graph for Q25 (peak discharge, 3,950 ft's; flood volume, 285 acre-ft) on an 8.25 mi' basin. The equations necessary for computing the discharge and time constants are giv!,!n in table 4. As shown in footnote 2 of table 4, the flow and time constants for this example are calculated using these equations to be 65.8 ft'/s per discharge unit and 3.24 min per time unit, respectively. The general shape of the resulting hydrograph, shown in figure 7, compares favorably with an observed 3,300-ft'/s flood that occurred September 13, 1976, at station 07099250, also an 8.25-mi' basin; this flood would have a recurrence interval of about 20 years. Comparisons with other observed flood hydrographs also indicat- ed this technique provides satisfactory results. I I I I Accuracy and limitations The statistical accuracy of the equations developed in this preliminary analy- sis of the rainfall-runoff data for the Arkansas River basin is indicated by the standard errors of estimate (S ) and correlation coefficients (R) shown in table 4. e 26