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NRCS Curve Number Runoff Depth

Mediumcurve numberNRCSrunoff
A watershed has a composite NRCS curve number A design storm delivers in of rainfall. Using the NRCS (SCS) rainfall-runoff relation with the standard initial abstraction of the direct runoff depth is most nearly:
  1. A1.7 in
  2. B2.4 in
  3. C3.0 in
  4. D3.3 in
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Answer: B. 2.4 in

Start with the maximum retention: S = 1000/CN − 10 = 1000/75 − 10 = 3.33 in. The initial abstraction is 0.2S = 0.67 in, so the effective rainfall is P − 0.2S = 4.33 in. Runoff Q = (P − 0.2S)²/(P + 0.8S) = 4.33²/(5.0 + 2.67) = 18.8/7.67 = 2.4 in. Dropping the initial abstraction and using P²/(P + S) gives 3.0 in; simply subtracting S from P gives 1.7 in; and 3.3 in is the retention S itself, not the runoff.
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