Provided the data are available, the most accurate method of accounting for rainfall abstractions and developing a direct runoff (effective rainfall) hyetograph is to model abstractions and infiltration within each time step for a rainfall event. The process consists of subtracting the interception from the beginning of a gross rainfall hyeto-graph, subtracting infiltration from what remains after interception has been accounted for, and subtracting depression storage from what remains after both inter-ception and infiltration have been accounted for. This approach is physically based and is not limited to use with any particular storm duration or rainfall hyetograph shape. The procedure is illustrated in the following example.
Example 5.6 – Computing an Effective Rainfall Hyetograph. Develop a direct run-off (effective rainfall) hyetograph for a watershed with an initial loss (interception capacity) of 0.3 in., a depression storage capacity of 0.2 in., and Horton infiltration parameters of f0 = 1.5 in/hr, fc = 0.3 in/hr, and k = 0.04 min-1. The rainfall hyetograph, tabulated for both incremental depth and average intensity, is as follows:
Solution: The interception capacity of 0.3 in. is subtracted first. Because 0.24 in. of rainfall occurs during the first 10 minutes of the storm, all of that rainfall plus an additional 0.06 in. of the rainfall occurring in the second 10 minutes of the storm is lost to interception. The rainfall hyetograph after accounting for interception is given in column 3 in the following table.
The infiltration rate f(t) can be calculated and tabulated as a function of t using Equation 5.1, where t0 is the time at which rainwater first begins to infiltrate (t0= 10 min in this example, because rainfall prior to that time is lost to interception and hence is not available for infiltration).
Column 1 in the table below is the time since the beginning of rainfall, and column 2 is the time since the beginning of infiltration. Column 3 is the infiltration rate computed using Equation 5.1. Column 4 contains incremental infiltration depths for each 10-minute period during the storm. For example, the first value of F is computed as the average of the current and preceding infiltration rates multiplied by the time interval 't = 10 min = 1/6 hr or, 0.22 = [(1.50 + 1.10)/2]/6.
Subtraction of the infiltration depth in each time interval (column 3) from the corresponding rainfall depth remaining after interception (column 2) leads to the hyetograph in column 4 (any negative val-ues produced should be set equal to zero) below. Finally, subtraction of the depression storage capac-ity of 0.2 in. leads to the effective rainfall hyetograph in column 5. Column 6 shows the effective rainfall hyetograph converted to intensities.
The rainfall hyetograph and the effective rainfall hyetograph are illustrated in Figure 5.6.1 and Figure 5.6.2. Note that the effective rainfall intensities are less than the actual rainfall intensities. Note also that effective rainfall, and hence direct runoff, does not begin (in this example) until 20 minutes after the beginning of the storm.
Figure E5.6.1 Rainfall hyetograph for Example 5.6
(1) (2) (3) (4)
t (min) t – t0 (min) f(t) (in/hr) Incr. F (in.) 0
10 0 1.5
20 10 1.1 0.22
30 20 0.84 0.16
40 30 0.66 0.13
50 40 0.54 0.10
60 50 0.46 0.08
(1) (2) (3) (4) (5) (6)
t (min) P 0.3 (in.) Incr. F (in.) P (in.) Pe (in.) ie(in./hr)
010 0 0 0 0
10–20 0.4 0.22 0.18 0 0
20–30 1.17 0.16 1.01 0.99 5.94
30–40 0.58 0.13 0.45 0.45 2.70
40–50 0.35 0.10 0.25 0.25 1.50
50–60 0.17 0.08 0.09 0.09 0.54
Figure E5.6.2 Effective rainfall (runoff) hyetograph for Example 5.6
5.3 MEASURES OF BASIN RESPONSE TIME
The maximum amount of flow discharged from a watershed at its outlet is related to the amount of time required for the entire watershed to be contributing to the flow. In modeling stormwater conveyance systems, the basin outlet may be taken as the loca-tion of an inlet or some other point of interest in the system. It can take minutes, hours, or even days from the onset of a rainfall event for the water falling in some parts of a watershed to be contributing to flow at a point of interest.
Because some points in a watershed are hydraulically closer to the outlet point than others, flow originating from different locations in the watershed will have differing travel times to the outlet. The response time of a drainage basin is usually considered to be the largest of all possible travel times, although it is sometimes taken as an aver-age of all possible travel times. Estimates of peak runoff rates resulting from a rainfall event are quite sensitive to estimates of basin response time and vary inversely with them. That is, all else being equal, long response times are associated with small peak discharges and vice versa. Estimates of basin response time are also relevant to selec-tion of the computaselec-tional time step size 't used for runoff predicselec-tion, as discussed in Section 4.5 (page 91).
The first of two common measures of basin response time is the time of concentra-tion, denoted by tc. The most widely adopted definition of time of concentration is the time required for a drop of effective rainfall falling at the most hydraulically remote point in a drainage basin to reach the basin outlet. The most hydraulically remote point from the outlet is usually, but not always, the most geographically remote point in the drainage basin. The significance of the time of concentration is easily recog-nized when one realizes that it is the minimum amount of time that must elapse before all parts of the drainage basin contribute to the flow at the basin outlet.
The second measure of response time commonly used in runoff estimation is the basin lag time, denoted by tL. Often called simply the basin lag or lag time, this response time can be thought of as an approximate average of the possible travel times for runoff in a drainage basin. In practice, the basin lag is usually assumed to be the amount of time between the center of mass of a pulse of effective rainfall and the peak of the resultant direct runoff hydrograph (see Figure 5.7; tp denotes time of peak discharge). The basin lag time is often used when estimating a complete runoff hydrograph as opposed to merely the peak runoff rate.
Figure 5.7
Basin lag time