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U" = the unit hydrograph ordinate for the same period, i , . E = the rainfall plus snowmelt excess For complex storms in which excess occurs in more time than one period (the normal case), the resuiting hydrograph can be determined by computing the individual hydrographs resuiting from the various excess periods in their proper time sequence and adding the individual components. The individual components need not be tabulated separately, but accumulatively multiplied until all excess periods have been used, to obtain a total hydrograph ordinate. A general equation for the total hydrograph ordinate for any period, i, is: Q. = U , . E + U 2 ' E", + U 'j . E '.2 +'" + U , . E" I I 1-' I-n.. (IV-2) where: i = sequence ('lumber of excess Q" = the hydrograph ordinate for period, i U,' = the unit hydrograph ordinates in order from 1 through E = the rainfall plus snowmelt excess in reverse order from i through ion n = total number of unit hydrograph ordinates or i, whichever is smaller. 2. UNIT HYDROGRAPH DERIVATION. A theoretically simple method of deriving a unit hydrograph involves the analysis of runoff resulting from isolated precipitation that produces reasonably uniform excess rates for a period approximately equal to the desired unit duration. Base flow is separated from the direct runoff, and the individulll ordinates of the direct runoff hydrograph are divided by the volume of direct runoff. ,-he resuiting ordinates form a unit hydrograph for the spec~ied duration of unit excess. The occurrence of floods resuiting from single bursts of uniform precipitation rates are rare and, therefore, the data required to develop unit hydrographs in the abeve manner seldom exists. However, if individual bursts of rain in the storm result in well-defined peaks, it is sometimes possible to separate the hydrographs produced for the various bursts by estimating the recession of runoff from each burst. These hydrographs may then be used as runoff from independent storms for the development of unit hydrographs in the manner described above. The resuit of the above derivation, or where unit hydrographs from different storms at the same location are derived, is a series of unil hydrographs with differences due to observation errors and other factors as described previously. For the convenience of dealing with only one unit hydrograph, and to minimize any errors due to separation of the hydrographs in the abeve procedure, the unit hydrographs are normally averaged. All unil hydrographs to be averaged must have the same unit duration, which may require converting to a common unit duration. The averaging is usually done graphically to prevent reducing the peak incorrectly which is the likely resuit when an arilhmetic average Colorado Flood Hydrology Manual 7-3i/ ffi4CT