Drainage Design Manual, Hydrology - Flood Control District of ...

Drainage Design Manual for Maricopa County
Hydrology: Unit Hydrograph Procedures
formly over the basin. Ultimate discharge (Q ult ), in cubic feet per second (cfs), can be calculated
from Equation (5.10):
645.33A
Q ult = -------------------
Δt
(5.10)
where:
A
Δt
= drainage area, in square miles, and
= duration of the 1 inch of rainfall excess, in hours.
S-graphs are developed by summing a continuous series of unit hydrographs, each lagged
behind the previous unit hydrograph by a time interval that is equal to the duration of rainfall
excess for the unit hydrograph (Δt). The resulting summation is a graphical distribution that
resembles an S-graph except that the discharge scale is accumulated discharge and the time
scale is in units of measured time. This graph is terminated when the accumulated discharge
equals Q ult which occurs at a time equal to the base time of the unit hydrograph less one duration
interval. The basin lag can be determined from this graph at the time at which the accumulated
discharge equals 50 percent of Q ult . This summation graph is then converted to a
dimensionless S-graph by dividing the discharge scale by Q ult and the time scale by lag.
In practice, S-graphs have generally been developed by reconstituting observed floods to define
a representative unit hydrograph and then converting this to an S-graph. Prior to the advent of
computerized models, such as HEC-1, flood reconstitution was a laborious task of rainfall and
hydrograph separation along with numerous manually calculated simulations to define the representative
unit hydrograph. Modern S-graph development generally relies on use of optimization
techniques, such as coded into HEC-1, to identify unit hydrograph parameters that best reproduce
the observed flood.
Although an S-graph is completely dimensionless and does not have a duration of rainfall excess
associated with it as does a unit hydrograph, its general shape and the magnitude of lag is influenced
by the distribution of rainfall over the watershed and the time distribution of the rainfall.
Therefore, the transposition of an S-graph from a gaged watershed to application in another
watershed must be done with consideration of both the physiographic characteristics of the
watersheds and the hydrologic characteristics of the rainfalls for the two watersheds.
5-22 August 15, 2013