The Soil Conservation Service (SCS) Curve Number (CN) method, now maintained by the Natural Resources Conservation Service (NRCS), is a widely adopted hydrological model for estimating direct runoff volume from a rainfall event. This technique provides a standardized approach for predicting how much precipitation converts into surface water flow across a watershed. It is frequently employed in water resource management for planning and designing structures related to flood control, soil conservation, and agricultural drainage systems. The method simplifies the complex interactions between soil, land cover, and precipitation into a single index, making it suitable for un-gaged or small areas where detailed hydrologic data may be scarce.
Understanding the Runoff Equation
The foundation of the Curve Number method is an equation that mathematically links total rainfall to the resulting runoff. The formula calculates the depth of direct runoff, \(Q\) (in inches), based on the total accumulated precipitation, \(P\) (in inches). The formula is expressed as \(Q = \frac{(P – I_a)^2}{(P – I_a + S)}\), with the condition that \(Q=0\) if \(P\) is less than the initial abstraction \(I_a\).
The variable \(S\) represents the potential maximum retention of water in the watershed after runoff begins. \(I_a\) is the initial abstraction, which is the amount of water lost before runoff starts. Runoff only occurs once the accumulated rainfall \(P\) exceeds the initial losses \(I_a\). As \(S\) increases, the amount of runoff \(Q\) from a given storm will decrease.
The practical application of this formula requires determining the values for \(I_a\) and \(S\) for the specific watershed. Since \(P\) is a known input, calculations focus on deriving the Curve Number (CN). The CN is the single index that defines the landscape’s runoff potential and allows for the determination of \(S\) and subsequently \(I_a\).
Determining the Curve Number Value
The Curve Number (CN) is an empirical index quantifying an area’s potential for generating runoff, ranging from 0 to 100. A low CN (around 30) indicates a highly permeable surface with low runoff potential, while a CN of 100 represents an impervious surface where all rainfall becomes runoff. Determining the appropriate CN requires analyzing two primary factors: the Hydrologic Soil Group (HSG) and the land use or cover condition.
Hydrologic Soil Groups
The NRCS classifies soils into four Hydrologic Soil Groups (A, B, C, and D) based on their infiltration rate when thoroughly wetted. Group A soils, such as deep sands, have the highest infiltration rates and the lowest runoff potential. Group B soils consist of loams with moderate infiltration rates. Group C soils have slow infiltration rates due to layers that impede water movement, resulting in higher runoff potential. Group D soils, including heavy clays or those with a high water table, have the slowest infiltration rates and the highest runoff potential.
Land cover is the second factor, categorizing the surface into types like cultivated land, pasture, or impervious cover, and assessing the quality of that cover (e.g., poor, fair, or good condition).
Once the CN is selected based on the intersection of the HSG and land cover type, it is used to calculate the potential maximum retention \(S\) using the formula \(S = \frac{1000}{CN} – 10\). The result for \(S\) is in inches. \(S\) is a theoretical value representing the total amount of water the soil and surface could retain.
Calculating Initial Abstraction
Initial abstraction (\(I_a\)) represents all water losses that occur before the onset of direct surface runoff. These losses include rainfall interception by vegetation, infiltration into the soil before saturation, and storage in small surface depressions. Runoff cannot begin until the accumulated rainfall has satisfied this initial demand for water storage.
Since measuring \(I_a\) in the field is complex, the CN method uses a standard empirical simplification relating it directly to the maximum retention \(S\). The standard relationship used in the NRCS methodology is \(I_a = 0.2S\), meaning initial losses are assumed to be 20 percent of the potential maximum retention.
This factor of 0.2 was derived from the analysis of numerous small agricultural watersheds during the method’s original development. Although subsequent research has suggested lower values for certain regions, \(I_a = 0.2S\) remains the widely accepted standard for general application. Using this standard allows the runoff calculation to depend only on the rainfall depth \(P\) and the single watershed parameter, CN.
Step-by-Step Runoff Calculation
The calculation of runoff depth \(Q\) is a sequential application of the determined formulas and parameters.
- Identify the total accumulated precipitation \(P\) for the storm event.
- Select the appropriate Curve Number (CN) for the area by combining the Hydrologic Soil Group with the specific land use and cover condition.
- Calculate the potential maximum retention \(S\) using the formula \(S = \frac{1000}{CN} – 10\), where \(S\) is expressed in inches.
- Determine the initial abstraction \(I_a\) by applying the standard empirical relationship \(I_a = 0.2S\).
- Substitute the values for \(P\), \(I_a\), and \(S\) into the main runoff equation: \(Q = \frac{(P – I_a)^2}{(P – I_a + S)}\).
For example, if a CN of 80 is selected, \(S\) would be \(1000/80 – 10 = 2.5\) inches, and \(I_a\) would be \(0.2 \times 2.5 = 0.5\) inches. If the total rainfall \(P\) is 3 inches, the resulting runoff \(Q\) is calculated as \(\frac{(3 – 0.5)^2}{(3 – 0.5 + 2.5)} = \frac{6.25}{5.0} = 1.25\) inches.