Stormwater Calculations - Mathematics and Statistics for the Environment - page 775

TABLE 25.4
Rational Equation Frequency Factors

Frequency Factor c f Storm Return Frequency

1.0 10 yr or less

1.1 25 yr

1.1 50 yr

1.25 100 yr

Q = C × C f × I × A (25.2)

The C f values are listed in Table 25.4. The product of C f × C should not exceed 1.0.

25.6.2 m odiFied r ational m ethod
The modified rational method is a variation of the rational method, developed mainly for the sizing
of detention facilities in urban areas. The modified rational method is applied similarly to the ratio-
nal method except that it utilizes a fixed rainfall duration. The selected rainfall duration depends
on the requirements of the user. For example, the designer might perform an iterative calculation to
determine the rainfall duration, which produces the maximum storage volume requirement when
sizing a detention basin.

25.6.2.1 Assumptions
The modified rational method is based on the following assumptions:

1. All of the assumptions used with the rational method apply. The most significant difference is
that the time of concentration for the modified rational method is equal to the rainfall inten-
sity averaging period rather than the actual storm duration. This assumption means that any
rainfall, or any runoff generated by the rainfall, that occurs before or after the rainfall aver-
aging period is unaccounted for. Thus, when used as a basin sizing procedure, the modified
rational method may seriously underestimate the required storage volume (Walesh, 1989).

2. The runoff hydrograph for a watershed can be approximated as triangular or trapezoidal in
shape. This assumption implies a linear relationship between peak discharge and time for
any and all watersheds.

25.6.2.2 Limitations
All of the limitations listed for the rational method apply to the modified rational method. The key
difference is the assumed shape of the resulting runoff hydrograph. The rational method produces
a triangular shaped hydrograph, which then modified can generate triangular or trapezoidal hydro-
graphs for a given watershed, as shown in Figure 25.6.

25.6.2.3 Design Parameters
The equation Q = C × I × A (rational equation) is used to calculate the peak discharge for all three
hydrographs shown in Figure 25.6. Notice that the only difference between the rational method and
the modified rational method is the incorporation of the storm duration ( d ) into the modified ratio-
nal method to generate a volume of runoff in addition to the peak discharge. The rational method
generates the peak discharge that occurs when the entire watershed is contributing to the peak (at a
time t = t c ) and ignores the effects of a storm which lasts longer than time t . The modified rational
method, however, considers storms with a longer duration than the watershed t c , which may have a