Runoff Coefficients

Runoff coefficient is loosely defined as the ratio of runoff to rainfall, and is a function of watershed characteristics including land use, soil type, and slope of the watershed. The value of runoff coefficient ranges between 0.0 and 1.0. A value of 0.0 means that all of the rainfall is lost in the form of abstractions such as infiltration, interception, and evaporation and none of the rainfall is converted to runoff. The value of 1.0 implies that all the rainfall is converted to runoff and is discharged from the watershed. As an example, most of the rain that falls on impervious areas such as pavement and roof would be immediately converted to runoff. A value of C for such land uses is close to 1.0. Runoff coefficient values recommended by the American Society of Civil Engineers and Water Environment Federation for return periods not exceeding 10 years are given below for various land uses, soil types, and slope conditions.

For return periods that exceed 10 years, the runoff coefficient from the table should be multiplied by a frequency adjustment factor, Cf , given below.

For a subwatershed composed of multiple land uses, a composite runoff coefficient Cw should be determined by weighting C values of each of the land uses by their corresponding area according to Equation 35.

where Ci = runoff coefficient for individual land use in the subwatershed.

Ai = area of the individual land use in the subwatershed.

N = total number of land uses in the subwatershed.

Stormwater Runoff and the Rational Method from Innovyze H2OCalc for Reference

For storm sewer loading, the focus shifts to hydrologic analysis of excess precipitation and associated runoff. Common techniques for analysis include the rational method and unit hydrograph methods, as well as the use of more advanced hydrologic models.

For small drainage areas, peak runoff is commonly estimated by the rational method. This method is based on the principle that the maximum rate of runoff from a drainage basin occurs when all parts of the watershed contribute to flow and that rainfall is distributed uniformly over the catchment area. Since it neglects temporal and spatial variability in rainfall, and ignores flow routing in the watershed, collection system, and any storage facilities, the rational method should be used with caution only for applications where the assumptions of rational method are valid.

Rational Method from Innovyze H2OCalc for Reference

The rational formula is expressed as

where Qp = peak runoff rate (m3/s, ft3/s)

C = dimensionless runoff coefficient (see Table 3-9)

I = average rainfall intensity (mm/hr, in/hr) for a duration of the time of concentration (tc)

A = drainage area (km2, acres)

K = conversion constant (0.28 in SI, 1 in English)

The time of concentration tc used in the rational method is the time associated with the peak runoff from the watershed to the point of interest. Runoff from a watershed usually reaches a peak at the time when the entire watershed is contributing; in this case, the time of concentration is the time for a drop of water to flow from the remotest point in the watershed to the point of interest. Time of concentration, tc (min), for the basin area can be computed using one of the formulas listed in Table 3-10.

Table: Runoff Coefficients for 2 to 10 Year Return Periods

Source: Nicklow et al. (2006)

Table 3-10: Formulas for Computing Time of Concentration

Method	Formula
Kirpich (1940)	L = length of channel (ft) S = average watershed slope (ft/ft)
California Culverts Practice (1942)	L = length of the longest channel (mi) H = elevation difference between divide and outlet (ft)
Izzard (1946)	i = rainfall intensity (in/h) c = Retardance coefficient	Retardance factor, c, ranges from 0.007 for smooth pavement to 0.012 for concrete and to 0.06 for dense turf; product i times L should be < 500
Federal Aviation Administration (1970)	C = rational method runoff coefficient (see Table 3.9)
Kinematic wave	n = Manning’s roughness coefficient
SCS lag equation	CN = SCS runoff curve number (see Table 3.11)
SCS average velocity charts	V = average velocity (ft/s)
Yen and Chow (1983)	KY = Coefficient N = Overland texture factor (see Table 3.13)	KY ranges from 1.5 for light rain (i<0.8) to 1.1 for moderate rain (0.8<i<1.2), and to 0.7 for heavy rain (i>1.2)

Source: Nicklow et al. (2004)

Table 3-11: Runoff Curve Numbers for Urban Land Uses

Adapted from SCS (1985)

Table 3-12: Description of NRCS Soil Classifications

Adapted from SCS (1985)

Table 3-13: Overland Texture Factor N

Adapted from Yen and Chow (1983)