Therunoff curve number (also called acurve number or simplyCN) is anempirical parameter used inhydrology for predicting directrunoff orinfiltration fromrainfall excess.^[1] The curve number method was developed by theUSDANatural Resources Conservation Service, which was formerly called theSoil Conservation Service orSCS — the number is still popularly known as a "SCS runoff curve number" in the literature. The runoff curve number was developed from anempirical 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 arainfall 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:

where

${\displaystyle Q}$ isrunoff ([L]; in)

${\displaystyle P}$ israinfall ([L]; in)

${\displaystyle S}$ is the potential maximumsoil moisture retention after runoff begins ([L]; in)

${\displaystyle I_a}$ is the initial abstraction ([L]; in), or the amount of water before runoff, such asinfiltration, 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.

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 0.30 in (7.6 mm) per hour).
• 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 0.15–0.30 in (3.8–7.6 mm) per hour).
• 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 0.05–0.15 in (1.3–3.8 mm) per hour).
• 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 (1.3 mm) per hour).

Selection of a hydrologic soil group should be done based on measured infiltration rates, soil survey (such as theNRCS 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, seeAdjustments.

Runoff is affected by thesoil moisture before a precipitation event, theantecedent moisture condition (AMC). A curve number, as calculated above, may also be termed AMC II or${\displaystyle C{N}_{II}}$, or average soil moisture. The other moisture conditions are dry, AMC I or${\displaystyle C{N}_I}$, and moist, AMC III or${\displaystyle C{N}_{III}}$. The curve number can be adjusted byfactors to${\displaystyle C{N}_{II}}$, where${\displaystyle C{N}_I}$ factors are less than 1 (reduce${\displaystyle CN}$ and potential runoff), while${\displaystyle C{N}_{III}}$ 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.

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:

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:${\displaystyle S=\frac{1000}{CN}-10}$
3. Convert this S value to${\displaystyle S_{0.05}}$ using the relationship above.
4. Calculate the runoff depth using the CN runoff equation above (with 0.05 substituted for the initial abstraction ratio).

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