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U "the unit hydrograph orcllT1ate for the Same pEOriod. : E' = the rainfall plus snowmelt excess For complex storms in which exce~.s occurs in more time tllan one period (the normal case), the resulting hydrograph can be determined by computing the individual hydrographs resulting 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 crdinate. A general equation for the total hydrograph ordinate for any period. i, is: Q "U,' E + U 2 . E + U .:: ,2 + ". + U , . E I , !l_ (IV-2) where: i= sequence number of excess Q " the hydrograph ordinate for period, i U,' " the unit hydrograph orclinates in order from 1 througll E the rainfall plus snowmelt excess in reverse order from i through ion n total number of unit Ilydrograph ord'nates or I, whichever is smaller. 2. UNIT HYDROGHAPH DERIVATION. A theoretically simple metllocl of deriving a unit hydrograph involves tile analysis of runoff resulting from isolated precipitation Itlat 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 individual ordinates of tha direct runoff hydrograpll are divided by the volume of d rect runoff. The resulting ordinates form a unit hydrograph for the specified duration 01 unit excess. The occurrence of floods resulting from single bursts of uniform precipitation rates are rare and, Itlerefore, the data required to develop unit hydrographs in the above 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 oj runoff from each burst. These Ilydrographs may tllen be used as runoff from independent storms for the development of unit hydro graphs in the manner described above. The result 01 the above derivation, or where unit Ilydrographs from different storms at the same location are derived, is a series of unit hydrographs with differences due to observation errors and other factors as describecl previously. For the cor1VEmience of dealing with only on'3 unit hydrograph, and to minimize any errors due to separation of the hydrographs in the above procedure, Itle unit hydrographs are normally averaged. All unit hydrographs to be averaged must have the same unit duration. whici1 may require converting to a common unit dura. iOI1. The averaging is usually done graphically to prevent reducing the peak incorrectly which is the likely result when an aritllmetic average Colorado Flood Hydrology Manual 7-37 a:w:r