SCS Curve Number Runoff Depth

Where the rational method gives a peak flow, the curve number gives a volume, and a volume is what a detention pond needs. The Soil Conservation Service built it in the 1950s from thousands of plot-years of rainfall and runoff, and the whole soil-and-cover story is compressed into one number between 30 and 98. That number sets $S$, the potential maximum retention: $S = 25400/CN - 254$ in millimetres. A curve number of 75 gives $S = 84.7$ mm, and 127 mm of rain then produces $(127-16.9)^2/(127+67.7) = 62.2$ mm of runoff, or 2.45 inches in the units the method was fitted in.

Two features surprise people the first time. The initial abstraction is fixed at 0.2S, so nothing at all runs off until the rain clears that threshold, which for CN 75 means the first 17 mm vanish into interception, depression storage and infiltration. And the relationship is strongly non-linear at the wet end: doubling the rainfall more than doubles the runoff, because $S$ is being used up. That is why a curve-number catchment behaves gently in a 2-year storm and viciously in a 100-year one, with no change in any parameter.

The classic mistake is treating the curve number as a fixed property of the site. It is a wet-condition-average value, AMC II, and the published conversions to dry (AMC I) and wet (AMC III) antecedent conditions move it by ten to fifteen points in each direction, which changes the computed runoff by more than any coefficient you will argue about in review. The 0.2 ratio itself has been under attack since the 1990s, with reanalysis of the original data suggesting 0.05 fits better, and several agencies now allow it. Also worth knowing: the method has no time in it at all. It says how much water leaves, never when, which is exactly why it is always paired with a unit hydrograph.