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)

where $//$ is the accumulated precipitation excess, $//$ is the accumulated precipitation depth, $//$ is the initial abstraction (initial loss), and $//$ 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)

where $//$ is user-defined ratio typically between 0.05 and 0.2. The potential maximum soil retention $//$ is computed from the runoff curve number $//$ as

 3)

where $//$ is in inches. The curve number $//$ 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 $//$ 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. $//$ ) after a user-specified time in which the infiltration is zero. The excess rate is computed as

 4)

where $//$ is the change in the direct runoff from the previous time step. The infiltration is calculated as

 5)

where $//$ 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

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

Poor
Fair
Good

47
25
6

67
59
35

81
75
70

88
83
79

Good

30

58

71

78

Woods

Poor
Fair
Good

45
36
25

66
60
55

77
73
70

83
79
77

59

74

82

86

(hard surface)

72
74

82
84

87
90

89
92