# Runoff curve number

(Redirected from Curve number)

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:

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

where

${\displaystyle Q}$ is runoff ([L]; in)
${\displaystyle P}$ is rainfall ([L]; in)
${\displaystyle S}$ is the potential maximum soil moisture retention after runoff begins ([L]; in)
${\displaystyle I_{a}}$ 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 ${\displaystyle I_{a}=0.2S}$, although more recent research has found that ${\displaystyle I_{a}=0.05S}$ may be a more appropriate relationship in urbanized watersheds where the CN is updated to reflect developed conditions.[2]

The runoff curve number, ${\displaystyle CN}$, is then related

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

${\displaystyle CN}$ 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]

• 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 coarse 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.

## Values

Fully developed urban areas (vegetation established)
Cover description Curve 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 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 18 acre or less (town houses) (65% imp.) 77 85 90 92
14 acre (38% imp.) 61 75 83 87
13 acre (30% imp.) 57 72 81 86
12 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
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
Good 74 83 88 90
Row crops Straight row (SR) Poor 72 81 88 91
Good 67 78 85 89
SR + CR Poor 71 80 87 90
Good 64 75 82 85
Contoured (C) Poor 70 79 84 88
Good 65 75 82 86
C + CR Poor 69 78 83 87
Good 64 74 81 85
Contoured & terraced (C&T) Poor 66 74 80 82
Good 62 71 78 81
C&T + R Poor 65 73 79 81
Good 61 70 77 80
Small grain SR Poor 65 76 84 88
Good 63 75 83 87
SR + CR Poor 64 75 83 86
Good 60 72 80 84
C Poor 63 74 82 85
Good 61 73 81 84
C + CR Poor 62 73 81 84
Good 60 72 80 83
C&T Poor 61 72 79 82
Good 59 70 78 81
C&T + R Poor 60 71 78 81
Good 58 69 77 80
Close-seeded or broadcast legumes or rotation meadow SR Poor 66 77 85 89
Good 58 72 81 85
C Poor 64 75 83 85
Good 55 69 78 83
C&T Poor 63 73 80 83
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 30C 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 conditionA AB 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.

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 ${\displaystyle CN_{II}}$, or average soil moisture. The other moisture conditions are dry, AMC I or ${\displaystyle CN_{I}}$, and moist, AMC III or ${\displaystyle CN_{III}}$. The curve number can be adjusted by factors to ${\displaystyle CN_{II}}$, where ${\displaystyle CN_{I}}$ factors are less than 1 (reduce ${\displaystyle CN}$ and potential runoff), while ${\displaystyle CN_{III}}$ factor are greater than 1 (increase ${\displaystyle CN}$ 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

The relationship ${\displaystyle I_{a}=0.2S}$ 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 ${\displaystyle I_{a}}$ to ${\displaystyle S}$ 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 ${\displaystyle I_{a}}$ to ${\displaystyle S}$ varies from storm to storm and watershed to watershed and that the assumption of ${\displaystyle I_{a}/S=0.20}$ is usually high. More than 90 percent of ${\displaystyle I_{a}/S}$ ratios were less than 0.2. Based on this study, use of ${\displaystyle I_{a}/S}$ ratios of 0.05 rather than the commonly used value of 0.20 would seem more appropriate. Thus, the CN runoff equation becomes:

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

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

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

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

1. Use the traditional tables of curve numbers to select the value appropriate for your watershed.
2. Calculate ${\displaystyle S_{0.20}}$ using the traditional equation:
${\displaystyle S={\frac {1000}{CN}}-10}$
1. Convert this S value to ${\displaystyle S_{0.05}}$ using the relationship above.
2. Calculate the runoff depth using the CN runoff equation above (with 0.05 substituted for the initial abstraction ratio).