Stormwater Runoff and the Rational Method in Innovyze H2OCalc

 

Stormwater Runoff and the Rational  Method

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

The rational formula is expressed as

                                                                                                                             

where  Q_p          =         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 (t_c)

                  A         =          drainage area (km², acres)

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

The time of concentration t_c 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, t_c (min), for the basin area can be computed using one of the formulas listed in Table 3-10.

 

Table 3-9: Runoff Coefficients for 2 to 10 Year Return Periods

Description of drainage area			Runoff coefficient
Business	Downtown		0.70-0.95
	Neighborhood		0.50-0.70
Residential	Single-family		0.30-0.50
	Multi-unit detached		0.40-0.60
	Multi-unit attached		0.60-0.75
Suburban			0.25-0.40
Apartment dwelling			0.50-0.70
Industrial	Light		0.50-0.80
	Heavy		0.60-0.90
Parks and cemeteries			0.10-0.25
Railroad yards			0.20-0.35
Unimproved areas			0.10-0.30
Pavement	Asphalt		0.70-0.95
	Concrete		0.80-0.95
	Brick		0.75-0.85
Roofs			0.75-0.95
Lawns	Sandy soils	Flat (2%)	0.05-0.10
		Average (2-7%)	0.10-0.15
		Steep (≥7%)	0.15-0.20
	Heavy soils	Flat (2%)	0.13-0.17
		Average (2-7%)	0.18-0.22
		Steep (≥7%)	0.25-0.35

         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

Land use description	Soil Group
	A	B	C	D
Lawns, open spaces, parks, golf courses:
Good condition: grass cover on 75% or more area	39	61	74	80
Fair condition: grass cover on 50% to 75% of area	49	69	79	84
Poor condition: grass cover on 50% or less of area	68	79	86	89
Paved parking lots, roofs, driveways, etc	98	98	98	98
Streets and roads:
Paved with curbs and storm sewers	98	98	98	98
Gravel	76	85	89	91
Dirt	72	82	87	89
Paved with open ditches	83	89	92	93
Commercial and business areas (85% impervious)	89	92	94	95
Industrial districts (72% impervious)	81	88	91	93
Row houses, town houses and residential with lot sizes of 1/8 ac or less (65% impervious)	77	85	90	92
Residential average lot size:
1/4 ac (38% impervious)	61	75	83	87
1/3 ac (30% impervious)	57	72	81	86
1/2 ac (25% impervious)	54	70	80	85
1 ac (20% impervious)	51	68	79	84
2 ac (12% impervious)	46	65	77	82
Developing urban area (newly graded; no vegetation)	77	86	91	94

Adapted from SCS (1985)

 

Table 3-12: Description of NRCS Soil Classifications

Group	Description	Min. infiltration (in/hr)
A	Deep sand; deep losses; aggregated silts	0.30-0.45
B	Shallow loess; sandy loam	0.15-0.30
C	Clay loams; shallows sandy loam; soils low in organic content; soils usually high in clay	0.05-0.15
D	Soils that swell significantly	0-0.05

Adapted from SCS (1985)

 

Table 3-13: Overland Texture Factor N

Overland flow surface	Low	Medium	High
Smooth asphalt pavement	0.010	0.012	0.015
Smooth impervious surface	0.011	0.013	0.015
Tar and sand pavement	0.012	0.014	0.016
Concrete pavement	0.014	0.017	0.020
Rough impervious surface	0.015	0.019	0.023
Smooth bare packed soil	0.017	0.021	0.025
Moderate bare packed soil	0.025	0.030	0.035
Rough bare packed soil	0.032	0.038	0.045
Gravel soil	0.025	0.032	0.045
Mowed poor grass	0.030	0.038	0.045
Average grass, closely clipped sod	0.040	0.055	0.070
Pasture	0.040	0.055	0.070
Timberland	0.060	0.090	0.120
Dense grass	0.060	0.090	0.120
Shrubs and bushes	0.080	0.120	0.180
Land use	Low	Medium	High
Business	0.014	0.022	0.35
Semi-business	0.022	0.035	0.050
Industrial	0.020	0.035	0.050
Dense residential	0.025	0.040	0.060
Suburban residential	0.030	0.055	0.080
Parks and lawns	0.040	0.075	0.120

Adapted from Yen and Chow (1983)