Runoff curve number

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The runoff curve number (also called a curve number or simply CN) is an empirical parameter used in hydrology for predicting direct runoff or infiltration from rainfall excess.^[1] The curve number method was developed by the USDA Natural Resources Conservation Service, which was formerly called the Soil Conservation Service or SCS — the number is still popularly known as a "SCS runoff curve number" in the literature. The runoff curve number was developed from an empirical analysis of runoff from small catchments and hillslope plots monitored by the USDA. It is widely used and is an efficient method for determining the approximate amount of direct runoff from a rainfall event in a particular area.

The runoff curve number is based on the area's hydrologic soil group, land use, treatment and hydrologic condition. References, such as from USDA^[1] indicate the runoff curve numbers for characteristic land cover descriptions and a hydrologic soil group.

The runoff equation is:

$Q={\begin{cases}0&{\text{for }}P\leq I_{a}\\{\frac {(P-I_{a})^{2}}{{P-I_{a}}+S}}&{\text{for }}P>I_{a}\end{cases}}$

where

$Q$ is runoff ([L]; in)

$P$ is rainfall ([L]; in)

$S$ is the potential maximum soil moisture retention after runoff begins ([L]; in)

$I_{a}$ is the initial abstraction ([L]; in), or the amount of water before runoff, such as infiltration, or rainfall interception by vegetation; historically, it has generally been assumed that $I_{a}=0.2S$ , although more recent research has found that $I_{a}=0.05S$ may be a more appropriate and accurate relationship.^[2]

The runoff curve number, $CN$ , is then related

$S={\frac {1000}{CN}}-10$

$CN$ has a range from 30 to 100; lower numbers indicate low runoff potential while larger numbers are for increasing runoff potential. The lower the curve number, the more permeable the soil is. As can be seen in the curve number equation, runoff cannot begin until the initial abstraction has been met.

Curve Number Selection

The NRCS curve number is related to soil type, soil infiltration capability, land use, and the depth of the seasonal high water table. To account for different soils' ability to infiltrate, NRCS has divided soils into four hydrologic soil groups (HSGs). They are defined as follows.^[1]

HSG Group A (low runoff potential): Soils with high infiltration rates even when thoroughly wetted. These consist chiefly of deep, well-drained sands and gravels. These soils have a high rate of water transmission (final infiltration rate greater than 0.3 in./h).
HSG Group B Soils with moderate infiltration rates when thoroughly wetted. These consist chiefly of soils that are moderately deep to deep, moderately well drained to well drained with moderately fine to moderately course textures. These soils have a moderate rate of water transmission (final infiltration rate of 0.15 to 0.30 in./h).
HSG Group C: Soils with slow infiltration rates when thoroughly wetted. These consist chiefly of soils with a layer that impedes downward movement of water or soils with moderately fine to fine textures. These soils have a slow rate of water transmission (final infiltration rate 0.05 to 0.15 in./h).
HSG Group D (high runoff potential): Soils with very slow infiltration rates when thoroughly wetted. These consist chiefly of clay soils with a high swelling potential, soils with a permanent high water table, soils with a claypan or clay layer at or near the surface, and shallow soils over nearly impervious materials. These soils have a very slow rate of water transmission (final infiltration rate less than 0.05 in./h).

Selection of a hydrologic soil group should be done based on measured infiltration rates, soil survey (such as the NRCS Web Soil Survey), or judgement from a qualified soil science or geotechnical professional. The table below presents curve numbers for antecedent soil moisture condition II (average moisture condition). To alter the curve number based on moisture condition or other parameters, see the CN adjustment section.

Runoff curve numbers

Fully developed urban areas (vegetation established)

Cover description	Curve numbers for hydrologic soil group
Cover description	A	B	C	D
	A	B	C	D
Open space (lawns, parks, golf courses, cemeteries, etc.)
Poor condition (grass cover <50%)	68	79	86	89
Poor condition (grass cover 50 to 75%)	49	69	79	84
Poor condition (grass cover >75%)	39	61	74	80
Impervious areas:
Paved parking lots, roofs, driveways, etc. (excluding right of way)	98	98	98	98
Streets and roads:
Paved; curbs and storm sewers (excluding right-of-way)	98	98	98	98
Paved; open ditches (including right-of-way)	83	89	92	93
Gravel (including right of way)	76	85	89	91
Dirt (including right-of-way)	72	82	87	89
Western desert urban areas:
Natural desert landscaping (pervious area only)	63	77	85	88
Artificial desert landscaping (impervious weed barrier, desert shrub with 1- to 2-inch sand or gravel mulch and basin borders)	96	96	96	96
Urban districts:
Commercial and business (85% imp.)	89	92	94	95
Industrial (72% imp.)	81	88	91	93
Residential districts by average lot size:
1/8 acre or less (town houses) (65% imp.)/small>	77	85	90	92
1/4 acre (38% imp.)	61	75	83	87
1/3 acre (30% imp.)	57	72	81	86
1/2 acre (25% imp.)	54	70	80	85
1 acre (20% imp.)	51	68	79	84
2 acres (12% imp.)	46	65	77	82

Developing urban areas

Cover description	Curve numbers for hydrologic soil group
Cover description	A	B	C	D
Newly graded areas (pervious areas only, no vegetation)	77	86	91	94

Cultivated agricultural lands

Cover description			Curve numbers for hydrologic soil group
Cover type	Treatment^[A]	Hydrologic condition	A	B	C	D
Fallow	Bare soil	--	77	86	91	94
	Crop residue cover (CR)	Poor	76	85	90	93
	Crop residue cover (CR)	Good	74	83	88	90
Row crops	Straight row (SR)	Poor	72	81	88	91
	Straight row (SR)	Good	67	78	85	89
	SR + CR	Poor	71	80	87	90
	SR + CR	Good	64	75	82	85
	Contoured (C)	Poor	70	79	84	88
	Contoured (C)	Good	65	75	82	86
	C + CR	Poor	69	78	83	87
	C + CR	Good	64	74	81	85
	Contoured & terraced (C&T)	Poor	66	74	80	82
	Contoured & terraced (C&T)	Good	62	71	78	81
	C&T + R	Poor	65	73	79	81
	C&T + R	Good	61	70	77	80
Small grain	SR	Poor	65	76	84	88
	SR	Good	63	75	83	87
	SR + CR	Poor	64	75	83	86
	SR + CR	Good	60	72	80	84
	C	Poor	63	74	82	85
	C	Good	61	73	81	84
	C + CR	Poor	62	73	81	84
	C + CR	Good	60	72	80	83
	C&T	Poor	61	72	79	82
	C&T	Good	59	70	78	81
	C&T + R	Poor	60	71	78	81
	C&T + R	Good	58	69	77	80
Close-seeded or broadcast legumes or rotation meadow	SR	Poor	66	77	85	89
	SR	Good	58	72	81	85
	C	Poor	64	75	83	85
	C	Good	55	69	78	83
	C&T	Poor	63	73	80	83
	C&T	Good	51	67	76	80

^A Crop residue cover applies only if residue is on at least 5% of the surface throughout the year.

Other agricultural lands

Cover description		Curve numbers for hydrologic soil group
Cover type	Hydrologic condition	A	B	C	D
Pasture, grassland, or range—continuous forage for grazing.^A	Poor	68	79	86	89
	Fair	49	69	79	84
	Good	39	61	74	80
Meadow—continuous grass, protected from grazing and generally mowed for hay.	---	30	58	71	78
Brush—brush-weed-grass mixture with brush the major element.^B	Poor	48	67	77	83
	Fair	35	56	70	77
	Good	30^C	48	65	73
Woods—grass combination (orchard or tree farm).^D	Poor	57	73	82	86
	Fair	43	65	76	82
	Good	32	58	72	79
Woods.^E	Poor	45	66	77	83
	Fair	36	60	73	79
	Good	30	55	70	77
Farmsteads—buildings, lanes, driveways, and surrounding lots.	---	59	74	82	86

^A Poor: <50% ground cover or heavily grazed with no mulch; Fair: 50-75% ground cover and not heavily grazed; Good: >75% ground cover and light or only occasionally grazed.

^B Poor: <50% ground cover; Fair: 50-75% ground cover; Good: >75% ground cover.

^C Actual curve number is less than 30; use CN = 30 for runoff computation.

^D CN's shown were computed for areas with 50% woods and 50% grass (pasture) cover. Other combinations of conditions may be computed from the CN's for woods and pasture.

^E Poor: Forest litter, small trees, and brush are destroyed by heavy grazing or regular burning; Fair: Woods are grazed but not burned, and some forest litter covers the soil; Good: Woods are protected from grazing, and litter and brush adequately cover the soil.

Arid and semiarid rangelands

Cover description		Curve numbers for hydrologic soil group
Cover type	Hydrologic condition^A	A^B	B	C	D
Herbaceuous—mixture of grass, weeds, and low-growing brush, with brush the minor element	Poor		80	87	93
	Fair		71	81	89
	Good		62	74	85
Oak-aspen—mountain brush mixture of oak brush, aspen, mountain mahogany, bitter brush, maple, and other brush	Poor		66	74	79
	Fair		48	57	63
	Good		30	41	48
Pinyon-juniper—pinyon, juniper, or both; grass understory	Poor		75	85	89
	Fair		58	73	80
	Good		41	61	71
Sagebrush with grass understory	Poor		67	80	85
	Fair		51	63	70
	Good		35	47	55
Desert shrub—major plants include saltbush, geasewood, creosotebush, blackbrush, bursage, palo verde, mesquite, and cactus.	Poor	63	77	85	88
	Fair	55	72	81	86
	Good	49	68	79	84

^A Poor: <30% ground cover (litter, grass, and brush overstory); Fair: 30 to 70% ground cover; Good: >70% ground cover.

^B Curve numbers for group A have been developed only for desert shrub.

Curve Number Adjustments

Runoff is affected by the soil moisture before a precipitation event, or the antecedent moisture condition (AMC). A curve number, as calculated above, may also be termed AMC II or $CN_{{II}}$ , or average soil moisture. The other moisture conditions are dry, AMC I or $CN_{{I}}$ , and moist, AMC III or $CN_{{III}}$ . The curve number can be adjusted by factors to $CN_{{II}}$ , where $CN_{{I}}$ factors are less than 1 (reduce $CN$ and potential runoff), while $CN_{{III}}$ factor are greater than 1 (increase $CN$ and potential runoff). The AMC factors can be looked up in the reference table below. Find the CN value for AMC II and multiply it by the adjustment factor based on the actual AMC to determine the adjusted curve number.

Adjustments to Select Curve Number for Soil Moisture Conditions^[3]

Curve Number (AMC II)	Factors to Convert Curve Number for AMC II to AMC I or III
Curve Number (AMC II)	AMC I (dry)	AMC III (wet)
10	0.40	2.22
20	0.45	1.85
30	0.50	1.67
40	0.55	1.50
50	0.62	1.40
60	0.67	1.30
70	0.73	1.21
80	0.79	1.14
90	0.87	1.07
100	1.00	1.00

Initial Abstraction Ratio Adjustment

The relationship $I_{a}=0.2S$ was derived from the study of many small, experimental watersheds . Since the history and documentation of this relationship are relatively obscure, more recent analysis used model fitting methods to determine the ratio of $I_{a}$ to $S$ with hundreds of rainfall-runoff data from numerous U.S. watersheds. In the model fitting done by Hawkins et al. (2002)^[2] found that the ratio of $I_{a}$ to $S$ varies from storm to storm and watershed to watershed and that the assumption of $I_{a}/S=0.20$ is usually high. More than 90 percent of $I_{a}/S$ ratios were less than 0.2. Based on this study, use of $I_{a}/S$ ratios of 0.05 rather than the commonly used value of 0.20 would seem more appropriate. Thus, the CN runoff equation becomes:

$Q={\begin{cases}0&{\text{for }}P\leq 0.05S\\{\frac {(P-0.05S_{{0.05}})^{2}}{P+0.95S_{{0.05}}}}&{\text{for }}P>0.05S\end{cases}}$

In this equation, note that the values of $S_{{0.05}}$ are not the same as the one used in estimating direct runoff with an $I_{a}/S$ ratio of 0.20, because 5 percent of the storage is assumed to be the initial abstraction, not 20 percent. The relationship between $S_{{0.05}}$ and $S_{{0.20}}$ was obtained from model fitting results, giving the relationship:

$S_{{0.05}}=1.33{S_{{0.20}}}^{{1.15}}$

The user, then, must do the following to use the adjusted 0.05 initial abstraction ratio:

Use the traditional tables of curve numbers to select the value appropriate for your watershed.
Calculate $S_{{0.20}}$ using the traditional equation: