A unit hydrograph is a direct runoff hydrograph resulting from a rainfall excess (or effective rainfall) of unit depth. The unit depth is 1 centimeter (cm) in the metric unit system and 1 inch (in.) in the customary U.S. system. It is assumed that the rainfall excess is generated uniformly over the watershed area at a constant rate for an effective duration.
We usually abbreviate a unit hydrograph as UH, and use a subscript indicating the effective duration of the rainfall excess. For instance, the direct runoff hydrograph produced by a rainfall excess that has an effective duration of 2 hours (hr) and constant intensity of 1/2 in./hr is denoted by UH2. Note that the depth of the rainfall excess is (1/2)(2) = 1 inch.
We can obtain a unit hydrograph for a watershed from simultaneous rainfall and runoff records. In the absence of such records we can use a synthetic unit hydrograph approach. Various synthetic unit hydrograph methods are available. The widely used Soil Conservation Service (SCS) unit hydrograph is adopted here as an example. In this approach, the unit hydrograph is determined based on the size of the watershed and the time of concentration. The time of concentration is defined as the time it takes for runoff to reach the watershed outlet from the hydrologically most remote point in the watershed. The time of concentration is a function of the size of the watershed. However, for a given size, the time of concentration is shorter in steeper watersheds and in urban watersheds where runoff takes place over paved surfaces and in gutters and pipes.
Notation and Units for SCS Unit Hydrograph Procedure
The figure below shows the elements of a unit hydrograph where
Qu = discharge per inch or per cm of rainfall excess (cfs/in. or m3/s/cm).
Qup = peak discharge per inch of rainfall excess (cfs/in. or m3/s/cm).
t = time (hrs).
tp = time of occurrence of the peak discharge (hrs).
We determine the time of the peak unit hydrograph discharge as
where tR = effective unit hydrograph duration in hours and TC = time of concentration in hours.
In the U.S. unit system the peak unit hydrograph discharge is calculated by using
where A = watershed area in square miles.
In the metric system, the watershed area A is in square kilometers, and the unit hydrograph peak discharge is calculated by using
Then, we can use the table below to calculate the unit hydrograph for either unit system. For selected time t values we first calculate t/tp. Then we determine the corresponding Qu/Qup value from the table. Multiplying this value by Qup will yield Qp at the selected t. Linear interpolation between the tabulated values is allowed in the use of this table.