Curve Number

The Curve Number (CN) method is an empirical surface runoff method developed by the US Department of Agriculture (USDA) Natural Resources Conservation Service (NRCS) while it was formerly called the Soil Conservation Service (SCS) (SCS 1985). The SCS CN method estimates precipitation excess as a function of the cumulative precipitation depth, soil cover, land use, and antecedent soil moisture as

1)	$\begin{array}{l}\displaystyle P_e = \left\{ \begin{matrix} 0 & for P< I_a \\ \frac{(P-I_a)^2}{P-I_a+S} & otherwise \end{matrix}\end{array}$

where $\begin{array}{l}P_e\end{array}$ is the accumulated precipitation excess, $\begin{array}{l}P\end{array}$ is the accumulated precipitation depth, $\begin{array}{l}I_a\end{array}$ is the initial abstraction (initial loss), and $\begin{array}{l}S\end{array}$ is the potential maximum soil retention (moisture after runoff begins). Runoff begins once the initial abstraction begins once the initial abstraction is met. The initial abstraction may be estimated as a function of the potential maximum retention. By default it is computed as

2)	$\begin{array}{l}\displaystyle I_a =rS\end{array}$

where $\begin{array}{l}r\end{array}$ is user-defined ratio typically between 0.05 and 0.2. The potential maximum soil retention $\begin{array}{l}S\end{array}$ is computed from the runoff curve number $\begin{array}{l}CN\end{array}$ as

3)	$\begin{array}{l}\displaystyle \displaystyle S= \frac{1000}{CN} -10\end{array}$

where $\begin{array}{l}S\end{array}$ is in inches. The curve number $\begin{array}{l}CN\end{array}$ values range from approximately 30 for permeable soils with high infiltration rates to 100 for water bodies and soils with low infiltration rates. Publications from the Soil Conservation Service (1971, 1986) provide further background and details on use of the $\begin{array}{l}CN\end{array}$ model. The incremental excess for a time interval is computed as the difference between the accumulated excess at the end of and beginning of the period. The infiltration is then computed as the rainfall minus the excess. The recovery method for the SCS CN consists of setting the cumulative rainfall depth to zero (i.e. $\begin{array}{l}P=0\end{array}$ ) after a user-specified time in which the infiltration is zero. The excess rate is computed as

4)	$\begin{array}{l}\displaystyle \displaystyle v= \frac{\Delta Q}{\Delta t}\end{array}$

where $\begin{array}{l}\Delta Q\end{array}$ is the change in the direct runoff from the previous time step. The infiltration is calculated as

5)	$\begin{array}{l}\displaystyle f=R-v\end{array}$

where $\begin{array}{l}R\end{array}$ is the rainfall intensity.

One thing to keep in mind with the SCS CN is the method was not developed for simulating historic events. The same loss amount of excess will be computed for a rainfall of 5 inches regardless of whether it occurred in 1 hour or 1 day. Another problem with the standard SCS CN method is that as the rainfall increases, the infiltration may become unrealistically small. For this reason, the SCS CN method has been modified in HEC-RAS so that there is a minimum user-specified infiltration rate which is utilized whenever the infiltration rate falls below this rate and there is sufficient rainfall.

Table 3. Runoff Curve Numbers for Hydrologic Soil-Cover Complexes

Cover			Hydrologic Soil Group
Land Use	Treatment or Practice	Hydrologic Condition	A	B	C	D
Fallows	Straight row		77	86	91	94
Row crops	Straight row	Poor Good	7267	81 78	88 85	91 89
	Contoured	Poor Good	7065	79 75	84 82	88 86
	Contoured and terraced	Poor Good	6662	74 71	80 78	82 81
Small grain	Straight row	Poor Good	65 63	76 75	84 83	88 87
	Contoured	Poor Good	63 61	74 73	82 81	85 84
	Contoured and terraced	Poor Good	61 59	72 70	79 78	82 81
Close-seeded legumes or rotation meadow	Straight row	Poor Good	66 58	77 72	85 81	89 85
	Contoured	Poor Good	64 55	75 69	83 78	85 83
	Contoured and terraced	Poor Good	63 51	73 67	80 76	83 80
Pasture or range	Contoured	Poor Fair Good	68 49 39	79 69 61	86 79 74	89 84 80
Pasture or range	Contoured	Poor Fair Good	47 25 6	67 59 35	81 75 70	88 83 79
Meadow		Good	30	58	71	78
Woods		Poor Fair Good	45 36 25	66 60 55	77 73 70	83 79 77
Farmsteads			59	74	82	86
Roads (dirt) (hard surface)			72 74	82 84	87 90	89 92