Runoff curve number explained

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.

Definition

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&forP\leqIa\\

2
(P-I
a)
{P-Ia

+S}&forP>Ia\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)

Ia

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

Ia=0.2S

, although more recent research has found that

Ia=0.05S

may be a more appropriate relationship in urbanized watersheds where the CN is updated to reflect developed conditions.[2]

The runoff curve number,

CN

, is then related

S=

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. It is important to note that the curve number methodology is an event-based calculation, and should not be used for a single annual rainfall value, as this will incorrectly miss the effects of antecedent moisture and the necessity of an initial abstraction threshold.

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]

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 Adjustments.

Values

Fully developed urban areas (vegetation established)
Cover descriptionCurve numbers for hydrologic soil group
A B C D
Open space (lawns, parks, golf courses, cemeteries, etc.)Poor condition (grass cover <50%)68 79 86 89
Fair condition (grass cover 50 to 75%)49 69 79 84
Good condition (grass cover >75%)39 61 74 80
Impervious areasPaved parking lots, roofs, driveways, etc. (excluding right of way)98 98 98 98
Streets and roadsPaved; 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 areasNatural 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 districtsCommercial and business (85% imp.)89 92 94 95
Industrial (72% imp.)81 88 91 93
Residential districts by average lot size acre or less (town houses) (65% imp.)77 85 90 92
acre (38% imp.)61 75 83 87
acre (30% imp.)57 72 81 86
acre (25% imp.)54 70 80 85
1 acre (20% imp.)51 68 79 84
2 acres (12% imp.)46 65 77 82
Cultivated agricultural lands
Cover descriptionCurve numbers for hydrologic soil group
Cover typeTreatmentHydrologic
condition
A B C D
FallowBare soil77 86 91 94
Crop residue cover (CR)Poor76 85 90 93
Good74 83 88 90
Row cropsStraight row (SR)Poor72 81 88 91
Good67 78 85 89
SR + CR Poor71 80 87 90
Good64 75 82 85
Contoured (C) Poor70 79 84 88
Good65 75 82 86
C + CR Poor 69 78 83 87
Good64 74 81 85
Contoured & terraced (C&T) Poor66 74 80 82
Good62 71 78 81
C&T + RPoor65 73 79 81
Good61 70 77 80
Small grainSRPoor65 76 84 88
Good63 75 83 87
SR + CRPoor64 75 83 86
Good60 72 80 84
CPoor63 74 82 85
Good61 73 81 84
C + CRPoor62 73 81 84
Good60 72 80 83
C&TPoor61 72 79 82
Good59 70 78 81
C&T + RPoor60 71 78 81
Good58 69 77 80
Close-seeded or broadcast legumes or rotation meadowSRPoor66 77 85 89
Good58 72 81 85
CPoor64 75 83 85
Good55 69 78 83
C&TPoor63 73 80 83
Good51 67 76 80
Crop residue cover applies only if residue is on at least 5% of the surface throughout the year.
Other agricultural lands
Cover descriptionCurve numbers for hydrologic soil group
Cover typeHydrologic
condition
A B C D
Pasture, grassland, or range—continuous forage for grazing.Poor68 79 86 89
Fair49 69 79 84
Good39 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.Poor48 67 77 83
Fair35 56 70 77
Good30 48 65 73
Woods—grass combination (orchard or tree farm).Poor57 73 82 86
Fair43 65 76 82
Good32 58 72 79
Woods.Poor45 66 77 83
Fair36 60 73 79
Good30 55 70 77
Farmsteads—buildings, lanes, driveways, and surrounding lots.59 74 82 86
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.
Poor: <50% ground cover; Fair: 50-75% ground cover; Good: >75% ground cover.
Actual curve number is less than 30; use CN = 30 for runoff computation.
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.
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 descriptionCurve numbers for hydrologic soil group
Cover typeHydrologic
condition
A B C D
Herbaceuous—mixture of grass, weeds, and low-growing brush, with brush the minor elementPoor80 87 93
Fair71 81 89
Good62 74 85
Oak-aspen—mountain brush mixture of oak brush, aspen, mountain mahogany, bitter brush, maple, and other brushPoor66 74 79
Fair48 57 63
Good30 41 48
Pinyon-juniper—pinyon, juniper, or both; grass understoryPoor75 85 89
Fair58 73 80
Good41 61 71
Sagebrush with grass understoryPoor67 80 85
Fair51 63 70
Good35 47 55
Desert shrub—major plants include saltbush, geasewood, creosotebush, blackbrush, bursage, palo verde, mesquite, and cactus.Poor63 77 85 88
Fair55 72 81 86
Good49 68 79 84
Poor: <30% ground cover (litter, grass, and brush overstory); Fair: 30 to 70% ground cover; Good: >70% ground cover.
Curve numbers for group A have been developed only for desert shrub.

Adjustments

Runoff is affected by the soil moisture before a precipitation event, the antecedent moisture condition (AMC). A curve number, as calculated above, may also be termed AMC II or

CNII

, or average soil moisture. The other moisture conditions are dry, AMC I or

CNI

, and moist, AMC III or

CNIII

. The curve number can be adjusted by factors to

CNII

, where

CNI

factors are less than 1 (reduce

CN

and potential runoff), while

CNIII

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
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

Ia=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

Ia

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

Ia

to

S

varies from storm to storm and watershed to watershed and that the assumption of

Ia/S=0.20

is usually high. More than 90 percent of

Ia/S

ratios were less than 0.2. Based on this study, use of

Ia/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&forP\leq0.05S\\

(P-0.05S0.05)2
P+0.95S0.05

&forP>0.05S\end{cases}

In this equation, note that the values of

S0.05

are not the same as the one used in estimating direct runoff with an

Ia/S

ratio of 0.20, because 5 percent of the storage is assumed to be the initial abstraction, not 20 percent. The relationship between

S0.05

and

S0.20

was obtained from model fitting results, giving the relationship:

S0.05=1.33{S0.20

}^

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

  1. Use the traditional tables of curve numbers to select the value appropriate for your watershed.
  2. Calculate

S0.20

using the traditional equation:

S=

1000
CN

-10

  1. Convert this S value to

S0.05

using the relationship above.
  1. Calculate the runoff depth using the CN runoff equation above (with 0.05 substituted for the initial abstraction ratio).

See also

External links

Notes and References

  1. Book: United States Department of Agriculture . Urban hydrology for small watersheds . 1986 . Second . Technical Release 55 (TR-55) . Natural Resources Conservation Service, Conservation Engineering Division .
  2. Hawkins . R.H. . Jiang . R. . Woodward . D.E. . Hjelmfelt . A.T. . Van Mullem . J.A. . 2006 . EFFECTS OF INITIAL ABSTRACTION AND URBANIZATION ON ESTIMATED RUNOFF USING CN TECHNOLOGY1 . Jawra Journal of the American Water Resources Association . 42 . 3 . 629–643 . 10.1111/j.1752-1688.2006.tb04481.x. 2006JAWRA..42..629L . 130013737 .
  3. Book: Ward . Andy D. . Trimble . Stanley W. . 2004 . Environmental Hydrology . Boca Raton, Florida . CRC Press LLC . 9781566706162 .