The Soil Conservation Service (SCS) proposed a parametric Unit Hydrograph (UH) model. The model is based upon averages of UH derived from gaged rainfall and runoff for a large number of small agricultural watersheds throughout the US. SCS Technical Report 55 (1986) and the National Engineering Handbook (1971) describe the UH in detail.

Basic Concepts and Equations

The SCS unit hydrograph method makes use of a dimensionless, curvilinear unit hydrograph to route excess precipitation to the subbasin outlet.  This dimensionless, curvilinear unit hydrograph expresses discharge, q, as a ratio of the peak discharge, qp, for any time t, as a fraction of the time of rise, Tp.  Given the peak discharge and lag time for the duration of excess precipitation, all ordinates of the unit hydrograph can then be estimated.  The “standard” SCS curvilinear unit hydrograph contains 37.5-percent of the total runoff before Tp.  Tp can be related to the duration excess precipitation as:

1) T_p = \frac{t_r}{2}+t_p

in which tr = duration of excess precipitation (or computational time step) and tp = the basin lag which is defined as the time difference between the center of mass of excess precipitation and the peak of the unit hydrograph.  Furthermore, the peak discharge of the unit hydrograph, Qp [cubic feet / second] can be related to the watershed area, A [square miles], and Tp [hours] using the following relationship:

2) Q_p = \frac{PRF*A}{T_p}

where PRF is a constant which is usually termed the “peak rate factor”.  Given tp, Equation (33) can be solved to determine Tp.  Then, given a PRF, Equation 2 can be solved to find Qp.  The entire unit hydrograph can then be found from the dimensionless curvilinear form using multiplication.

The standard dimensionless SCS curvilinear unit hydrograph is created by setting the PRF equal to approximately 484.  However, the PRF constant has been shown to vary from about 600 in steep terrain to 100 or less in flat areas.  Various dimensionless unit hydrographs with predefined peak rate factors are presented in the NRCS National Engineering Handbook (2007).  A change in the peak rate factor causes a change in the percent of runoff occurring before Tp, which is typically not uniform across all watersheds because it depends on flow length, ground slope, and other properties of the watershed.  By changing PRF, alternate unit hydrographs can be computed for watersheds with varying topography and other conditions that effect runoff.

Required Parameters

Parameters that are required to utilize the SCS method within HEC-HMS include a PRF and a lag time [minutes].  Research has shown that tp can be related to the watershed time of concentration, Tc, using (Natural Resources Conservation Service, 1999):

3) t_p=0.6 * T_c

Estimating Parameters

The SCS UH lag can be estimated via calibration for gaged headwater subwatersheds.  Time of concentration is a quasi-physically based parameter that can be estimated as:

4) t_{c}=t_{\text {sheet}}+t_{\text {shallow}}+t_{\text {channel}}

where t_{sheet} = sum of travel time in sheet flow segments over the watershed land surface; t_{shallow} = sum of travel time in shallow flow segments, down streets, in gutters, or in shallow rills and rivulets; and t_{channel} = sum of travel time in channel segments. Identify open channels where cross section information is available. Obtain cross sections from field surveys, maps, or aerial photographs. For these channels, estimate velocity by Manning's equation:

5) V=\frac{C R^{2 / 3} S^{1 / 2}}{n}

where V = average velocity; R = the hydraulic radius (defined as the ratio of channel cross-section area to wetted perimeter); S = slope of the energy grade line (often approximated as channel bed slope); and C = conversion constant (1.00 for SI and 1.49 for foot-pound system.) Values of n, which is commonly known as Manning's roughness coefficient, can be estimated from textbook tables, such as that in Chaudhry (1993). Once velocity is thus estimated, channel travel time is computed as:

6) t_{\text {channel}}=\frac{L}{V}

where L = channel length. Sheet flow is flow over the watershed land surface, before water reaches a channel. Distances are short—on the order of 10-100 meters (30-300 feet). The SCS suggests that sheet-flow travel time can be estimated as:

7) t_{\text {sheet}}=\frac{0.007(N L)^{0.8}}{\left(P_{2}\right)^{0.5} S^{0.4}}

in which N = an overland-flow roughness coefficient; L = flow length; P_2 = 2-year, 24-hour rainfall depth, in inches; and S = slope of hydraulic grade line, which may be approximated by the land slope.  This estimate is based upon an approximate solution of the kinematic wave equations, which are described later in this chapter. The table below shows values of N for various surfaces. Sheet flow usually turns to shallow concentrated flow after 100 meters. The average velocity for shallow concentrated flow can be estimated as:

8) V=\left\{\begin{array}{ll}16.1345 \sqrt{S} & \text { for unpaved surface } \\ 20.3282 \sqrt{S} & \text { for paved surface }\end{array}\right\}

From this, the travel time can be estimated with Equation above.


Overland-flow roughness coefficients for sheet-flow modeling (USACE, 1998)

Surface Description

N

Smooth surfaces (concrete, asphalt, gravel, or bare soil)

0.011

Fallow (no residue)

0.05

Cultivated soils:


Residue cover <= 20%

0.06

Residue cover > 20%

0.17

Grass:


Short grass prairie

0.15

Dense grasses, including species such as weeping love grass, bluegrass, buffalo grass, blue grass, and native grass mixtures

0.24

Bermudagrass

0.41

Range

0.13

Woods 1


Light underbrush

0.40

Dense underbrush

0.80

Notes:
1 When selecting N, consider cover to a height of about 0.1 ft. This is the only part of the plant cover that will obstruct sheet flow.