The concept of the unit hydrograph was introduced to the hydrologic community by Sherman (1932). The basic theory rests on the assumption that the runoff response of a drainage basin to an effective rainfall input is linear; that is, it may be described by a linear differential equation. Practically speaking, this means that the concepts of pro-portionality and superposition can be applied. For example, the direct runoff volume and discharge rates resulting from 2 in. of effective rainfall in a given time interval are four times as great as those caused by 0.5 in. of effective rainfall in the same amount of time. It also means that the total amount of time for the basin to respond to each of these rainfall depths is the same. Consequently, the base length of each of the direct runoff hydrographs is the same.
The unit hydrograph approach to runoff estimation is a spatially lumped approach, meaning that it assumes that no spatial variability exists in the effective rainfall input into a drainage basin. In cases where the effective rainfall input varies from one loca-tion to another within a basin, the unit hydrograph approach requires the subdivision of the basin into smaller subbasins, with routing of the runoff from each subbasin to obtain the integrated basin response.
Figure 5.10
Hydrograph development process
Visualizing and Developing Unit Hydrographs. By definition, the 't-hour (or 't-minute) unit hydrograph of a drainage basin is the direct runoff hydrograph produced by 1 in. (or 1 cm in the case of SI units) of effective rainfall (runoff) falling uniformly in time and space over the drainage basin during a duration 't time units. By conservation of mass, the volume of direct runoff produced (repre-sented by the area under a graph of the unit hydrograph) must be equal to 1 in. (or 1 cm) of runoff (effective rainfall) times the drainage basin area (see Figure 5.11). It may be observed from this definition that the unit hydrographs for two drainage basins must be different from one another, because the basin areas (as well as other factors) are different.
Figure 5.12 helps to demonstrate the principles of a unit hydrograph. A sprinkler sys-tem distributes water uniformly over an entire drainage area. Constant rainfall is mod-eled by using the sprinklers to apply a constant rate of water until exactly one inch of direct runoff (effective precipitation) is generated, at which time the sprinklers are turned off. The duration of time required for the sprinklers to generate the required depth of effective precipitation is shown as 't. A stream gauge is placed on the down-stream end of the contributing drainage area to record the runoff hydrograph resulting from the 1 in. (or 1 cm) of runoff. The recorded hydrograph represents the unit hydrograph generated for the drainage area.
For a given drainage basin, there are an infinite number of durations over which 1 in.
of direct runoff (effective rainfall) could be generated depending on the intensity of the rainfall being applied to the area. For instance, 1 in. of runoff could occur over 't = 30 minutes, over 't = 1 hour, or over some other time interval. Thus, for any given drainage basin, one could speak of its 30-minute unit hydrograph, its 1-hour unit hydrograph, or its unit hydrograph of any other duration. Note that the
duration't
Figure 5.11
Unit hydrograph resulting from 1 in. of effective rainfall (runoff) over time 't
Figure 5.12
Visualizing the unit hydrograph concept
associated with a unit hydrograph is the duration over which the 1 in. (or 1 cm) of effective rainfall occurs and not the duration over which the corresponding runoff drains from the area.
Two basic categories of unit hydrographs exist: (1) unit hydrographs for gauged watersheds and (2) synthetic unit hydrographs (described in the next section). When
concurrent rainfall and runoff records are available for a drainage basin, methods of deconvolution (separation) may be applied to estimate a unit hydrograph for the basin on the basis of those records (Singh, 1988). More commonly, rainfall and runoff records for a drainage basin do not exist, and one must resort to synthesis of a unit hydrograph based on information that can be gathered about the basin. Extensive lit-erature exists on various ways to calculate synthetic unit hydrographs, including pro-cedures proposed by Clark, Snyder, and Singh (Snyder, 1938; Singh, 1988). This text provides an introduction to the development of synthetic unit hydrographs by apply-ing the NRCS (SCS) method.
NRCS (SCS) Synthetic Unit Hydrographs. The NRCS (SCS) analyzed a large number of unit hydrographs derived from rainfall and runoff records for a wide range of basins and basin locations and developed the average dimensionless unit hydrograph shown in Figure 5.13 (Snider, 1972). The times on the horizontal axis are expressed in terms of the ratio of time to time of peak discharge (t/tp), and the dis-charges on the vertical axis are expressed in terms of the ratio of discharge to peak discharge (Q/Qp). Table 5.15 lists the dimensionless unit hydrograph ordinates.
Figure 5.13
NRCS (SCS) dimensionless unit hydrograph (from Snider, 1972)
Application of the dimensionless unit hydrograph involves estimating the lag time tL of the drainage basin. The lag time can be estimated by relating it to an estimate of the time of concentration, or it can be estimated directly (see Section 5.3). The time to peak of the synthetic unit hydrograph of duration 't is then computed as
(5.26) The NRCS recommends that 't be equal to 0.133tc, or equal to 0.222tL (Snider, 1972). A small variation from this value is acceptable. The 't chosen for the develop-ment of the synthetic unit hydrograph must be consistent with the 't chosen for devel-opment of the design storm and effective rainfall hyetographs (see Section 4.5, page
p 2 L
t 't t
91).
The peak discharge Qp for the synthetic unit hydrograph is calculated as
(5.27)
where Qp = peak discharge (cfs, m3/s)
Cf = conversion factor (645.33 U.S., 2.778 SI)
K = 0.75 [a constant based on geometric shape of dimensionless unit hydrograph (Snider, 1972)]
Q = runoff depth for unit hydrograph calculation (1 in. U.S., 1 cm SI) A = the drainage basin area (mi2, km2)
tp = the time to peak (hr) Simplifying yields
(for U.S. units) (5.28)
or
Table 5.15 Ordinates of the NRCS (SCS) dimensionless unit hydrograph (from Snider, 1972)
(for SI units) (5.29)
The coefficients 484 and 2.08 appearing in the numerators of Equation 5.28 and Equation 5.29 include a unit conversion factor and are average values for many drain-age basins. These values may be reduced to about 300 and 1.29, respectively, for flat or swampy basins, or increased to about 600 and 2.58, respectively, for steep or mountainous basins. Care should be taken when changing this coefficient, as the base length and/or shape of the synthetic unit hydrograph must also be changed to ensure that it represents a volume of water equivalent to 1 in. or 1 cm of effective rainfall over the drainage basin area.
After tp and Qp are estimated using Equation 5.26 and Equation 5.27, the desired syn-thetic unit hydrograph may be graphed or tabulated using the dimensionless unit hydrograph shown in Figure 5.13 and Table 5.15.
Example 5.12 – Developing an NRCS (SCS) Synthetic Unit Hydrograph. Develop a synthetic unit hydrograph for a 1.5-mi2 drainage basin in Memphis, Tennessee, having a time of concentration of 90 min. Assume that the basin slopes are moderate so that the factor 484 can be applied in computing Qp.
Employing the guidelines given above for estimation of 't, its value should be about 0.133tc = 0.133(90) = 12 min
A duration of 't = 10 min is selected, and the synthetic unit hydrograph will be a 10-min unit hydrograph. The basin lag is estimated as
tL = 0.6tc = 54 min
Using Equation 5.26, the time to peak of the synthetic unit hydrograph is tp = (10/2) + 54 = 59 min = 0.98 hr
The peak discharge is estimated using Equation 5.28 as Qp = 484(1.5)/0.98 = 740 cfs
Ordinates of the synthetic unit hydrograph are tabulated in Table 5.16 and plotted in Figure 5.12.1.
The first column of the table is the time t, in minutes, and is tabulated in 't = 10 min intervals. The second column is the dimensionless time ratio t/tp, where tp = 59 min. The third column is the dimen-sionless discharge ratio, and is determined using the dimendimen-sionless time ratio and interpolation from Table 5.15. The fourth and last column contains the ordinates of the 10-min unit hydrograph, which are computed as the products of the dimensionless discharge ratios and Qp = 740 cfs.
Table 5.16 SCS (NRCS) synthetic unit hydrograph computations for Example 5.12
(1) (2) (3) (4)
Figure E5.12.1 Synthetic unit hydrograph for Example 5.12