Stormwater Calculations - Mathematics and Statistics for the Environment - page 771

or determine the runoff hydrograph for the direct runoff from the watershed. A hydrograph shows
the volume of runoff as the area beneath the curve, and the time-variation of the discharge rate. If
the purpose of a hydrologic study is to measure the impact of various developments on the drainage
network within a watershed or to design flood control structures, then a hydrograph is needed. If the
purpose of a study is to design a roadway culvert or other simple drainage improvement, then only
the peak rate of flow is needed. Therefore, the purpose of a given study will dictate the methodology
that should be used. Note that procedures such as the rational method and TR-55 graphical peak
discharge method do not generate a runoff hydrograph; however, the TR-55 tabular method and the
modified rational method do generate runoff hydrographs.

25.6 CALCULATION METHODS
Because they require different types of input and generate different types of results, environmental
engineers responsible for stormwater design should be familiar with the different methods for calcu-
lating runoff from a watershed. The methods covered here are the rational method, modified ratio-
nal method, and various TR-55 methods (estimating runoff, graphical peak discharge, and tabular
hydrograph). Note that many computer programs are available that develop these methodologies,
utilizing the rainfall-runoff relationship described previously. Many of these programs also route
the runoff hydrograph through a stormwater management facility, calculating the peak rate of dis-
charge and a discharge hydrograph. Examples provided later utilize TR-20 , Project Formulation:
Hydrology (USSCS, 1982). Other readily available computer programs also utilize SCS methods.
The accuracy of the computer model is based on the accuracy of the input that is typically generated
through the rational or SCS methodologies covered here. Again, the engineer should be familiar
with all of the methods covered here because any one may be appropriate for the specific site on the
watershed being modeled.

Note: All of the methods presented below make assumptions and have limitations on the accuracy.
Simply put, however, when these methods are used correctly, they will all provide a reason-
able estimate of the peak rate of runoff from a drainage area or watershed.

Key Point: For small storm events (<2 inches rainfall) TR-55 tends to underestimate the runoff, while
it has been shown to be fairly accurate for larger storm events. Similarly, the rational formula has
been found to be fairly accurate on smaller homogeneous watersheds, while tending to lose accuracy
in the larger more complex watersheds. The following discussion provides further explanation of
these methods, including assumptions, limitations, and information needed for the analysis.

25.6.1 r ational m ethod
The rational method was devised for determining the peak discharges from drainage areas. Though
frequently criticized for its simplistic approach, this same simplicity has made the rational method
one of the most widely used techniques today. The rational formula estimates the peak rate of runoff
at any location in a drainage area as a function of the runoff coefficient, , mean rainfall intensity, and
drainage area. The rational formula is expressed as

Q = C × I × A (25.1)

where
Q = Maximum rate of runoff (cfs).
C = Dimensionless runoff coefficient, dependent upon land use.
I = Design rainfall intensity, in inches per hour, for a duration equal to the time of concentra-
tion of the watershed.
A = Drainage area (ac).