9.3 NRCS Curve Number and Unit Hydrographs
Key Takeaways
- The NRCS Curve Number method converts storm rainfall depth to direct runoff depth using watershed storage S, initial abstraction Ia, and the condition that no direct runoff occurs when P is less than or equal to Ia.
- For US customary calculations, S = 1000/CN - 10 in inches and the common default initial abstraction is Ia = 0.2S unless the problem gives another value.
- Curve number is based on land use, hydrologic soil group, cover condition, treatment, and antecedent moisture assumptions, not on Rational Method C.
- A unit hydrograph converts a unit depth of excess rainfall over a watershed into a discharge hydrograph, allowing peak flow and timing to be estimated from runoff volume.
- Because the CN runoff equation is nonlinear, computing runoff separately by subarea is often more defensible than using a single weighted CN when land cover and soils vary widely.
When NRCS Methods Fit
NRCS methods are used when a problem needs runoff depth, runoff volume, or a hydrograph rather than only a peak rate. They are common for subdivision drainage, detention routing, post-development comparison, and watershed-scale stormwater work. The PE WRE exam may call the method SCS or NRCS; for exam purposes, treat SCS Curve Number and NRCS Curve Number as the same runoff framework unless a problem states otherwise.
The method begins with total storm rainfall P and estimates direct runoff depth Qd after abstractions. It does not say that every inch of rain becomes direct runoff. Some rainfall is intercepted, infiltrates, fills surface storage, or is otherwise abstracted before runoff begins.
Curve Number Runoff Equation
For US customary units:
| Quantity | Equation | Unit |
|---|---|---|
| Potential retention | S = 1000/CN - 10 | inches |
| Initial abstraction | Ia = 0.2S unless given otherwise | inches |
| Runoff depth | Qd = (P - Ia)^2 / (P - Ia + S), if P > Ia | inches |
| No runoff condition | Qd = 0 if P <= Ia | inches |
With the default Ia = 0.2S, the denominator is often written P + 0.8S. Use the version that matches the stated abstraction assumption. If CN = 80, then S = 1000/80 - 10 = 2.5 in and Ia = 0.5 in. For P = 4.0 in, Qd = (4.0 - 0.5)^2 / (4.0 - 0.5 + 2.5) = 12.25 / 6.0 = 2.04 in.
Selecting and Combining CN Values
Curve number depends on land use, hydrologic soil group, cover condition, conservation treatment, and antecedent moisture condition if specified. Higher CN means lower storage and more runoff. Hydrologic soil group A generally has higher infiltration potential than group D, so group D conditions usually have higher CN values for the same land use.
For mixed watersheds, follow the problem instructions. A simple area-weighted CN may be accepted for moderate variation, but the equation is nonlinear. If one subarea is pavement and another is open space, a safer professional workflow is to compute runoff depth by subarea and then area-weight the runoff volumes. That distinction can matter when rainfall is near the initial abstraction threshold.
Unit Hydrograph Logic
A unit hydrograph is the direct-runoff hydrograph caused by one unit depth of excess rainfall uniformly distributed over the watershed for a specified duration. It translates runoff depth into discharge over time. NRCS dimensionless hydrograph procedures commonly use lag time and time to peak.
A common PE-level relationship is lag time tlag = 0.6Tc when the problem provides or permits it. If the excess rainfall duration is D, then Tp = D/2 + tlag. In US customary units, a standard triangular or NRCS peak estimate is often given as q_p = 484 A Qd / Tp, where A is in square miles, Qd is in inches, Tp is in hours, and q_p is in cfs. Use the exact coefficient and hydrograph shape supplied by the handbook or problem.
Calculation Workflow
- Determine CN from land use, soil group, and condition.
- Compute S and Ia, then runoff depth Qd.
- Convert Qd to runoff volume when needed: volume = depth times watershed area.
- Determine Tc, lag time, rainfall excess duration, and time to peak.
- Build the hydrograph or compute peak using the provided unit hydrograph relationship.
- Check that the area under the direct-runoff hydrograph equals the runoff volume.
The exam often rewards recognizing what each symbol represents. Qd in the CN equation is a depth, not cfs. q_p is a flow rate, not a depth. CN is not a runoff coefficient, and Ia is not the same thing as infiltration rate.
Using the standard NRCS Curve Number assumptions, a watershed has CN = 80 and receives P = 4.0 inches of rainfall. What direct runoff depth is closest?
A 1.2-square-mile watershed has Qd = 1.5 in, excess rainfall duration D = 0.5 hr, and Tc = 2.0 hr. If tlag = 0.6Tc and q_p = 484 A Qd / Tp, what peak discharge is closest?