Curve Number

A curve number is a type of runoff coefficient, but it is not a simple percentage value like the coefficient used in the rational method.  The curve number is a concept developed initially by the Soil Conservation Service (SCS) and hence it is often referred to as the SCS Curve Number.  It is typically cited as simply CN as an abbreviation of curve number.  CN values were derived from empirical data and not from direct physics.  It is a function of both land use and soil and is used to determine potential losses (or watershed storage, S) using the following equation:

S = (1000/CN) -10

Where:    S = Potential losses (inches)
                CN = SCS curve number

Initial abstractions are typically estimated as 20% of the potential losses, or 0.2*S.  Effective rainfall is then computed using the following equation:

R = (P - .2S)^2 / (P + .8S)

Where:   R = Rainfall Excess (or the part of rainfall that becomes runoff)
               P = precipitation depth
               S = potential losses (storage of the watershed)

The equation is only valid when the rainfall P > .2S since lower values would actually produce negative runoff.  When using a curve number in a numerical model like TR-55 or HEC-1 the depth for initial abstractions must first be satisfied.  In their derivation of the CN concept a series of tables were created relating CN to different hydrologic soil groups and land use covers.  These tables are available in the TR-55 documentation and adaptations in almost any text on hydrology.  The hydrologic soil group is either A, B, C, or D, where A soils are loose (sands) and have high infiltration rates, B and C are in the middle and D soils are tight (clays) and have relatively low infiltration rates.

To determine a CN you must know the hydrologic soil group and land cover of your watershed and then use a look-up table from the SCS publications or a standard hydrology text.  If multiple land uses and/or soil groups exist within the watershed then a composite (area-weighted average) CN should be computed.  GIS files for soils and land use exist for many areas and can be used to automate composite CN computations.  Move your mouse over the animation below to understand better how these calculations are performed.