The unit hydrograph is a hydrograph that results from rainfall excess occurring at a uniform rate and uniformly distributed in a specified time period. It is based on several assumptions.
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The rainfall excess is uniformly distributed over the watershed.
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The unit hydrograph reflects all basin characteristics to the degree that the runoff rate is simply proportional to the runoff volume for a given rainfall excess.
A full discussion on the unit hydrograph is outside the scope of this manual, however, StormShed3G™ does use a unit hydrograph in computing runoff, so a discussion as to the shape of the hydrograph is of interest. Generally, the unit hydrograph has an empirical shape that was originally drawn not computed. It wasn’t until 1966 (DeCoursey) and 1970 (Haan) that dimensionless hydrograph equations were developed. The form that is used by this program[1] is:
where
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q(t) is the hydrograph ordinate at any time t
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qp is the peak flow rate (iph)
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tp is the time to peak (hrs)
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K is a parameter defined by the equation
where
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V is the runoff voluem
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e is the base of the natural logarithms
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represents the gamma function
The relationship between K and qptp/V can be approximated by:
The SCS dimensionless unit hydrograph corresponds with a K of 3.77.
StormShed3G™ also supports the use of unit hydrograph files. The default file is “scsduh.uh” located in the RAC subdirectory. It contains the standard SCS Unit Hydrograph values. When computing runoff hydrographs StormShed3G™ allows for the specification of a peaking factor (default is 484) defined as:
Where
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qp is the peak Flow of the unit hydrograph
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A is area in square miles
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tp is the time to peak in hours
The time to peak factor is defined as:
Where
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tL is the basin lag in hours
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D is the duration of the rainfall excess
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D is should be from one fifth to one third the time to peak
Note that the basin lag is simply 0.6 times the time of concentration.
The time to peak factor is the range that the SCS recommends for the Duration and is generally within the range of 3 to 5. The time to peak is a function of the computed lag and Duration.
[1] Material adapted from Design Hydrology and Sedimentology for Small Catchments, Haan, Barfield, Hayes, Academic Press, 1994