9.3 NRCS Curve Number and Unit Hydrographs

When NRCS Methods Fit

NRCS (formerly Soil Conservation Service, SCS) methods apply 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, pre- versus post-development comparison, and watershed-scale stormwater work. The exam may label the method SCS or NRCS interchangeably; treat the SCS Curve Number and NRCS Curve Number as the same runoff framework unless a problem says otherwise.

The method begins with total storm rainfall P and estimates direct runoff depth Qd after abstractions. It does not assume every inch of rain becomes runoff: some rainfall is intercepted, infiltrates, fills surface depression storage, or is otherwise abstracted before runoff begins. The initial abstraction Ia lumps interception, depression storage, and infiltration before ponding.

Curve Number Runoff Equation

For US customary units:

With the default Ia = 0.2S, the runoff equation is often written Qd = (P - 0.2S)^2 / (P + 0.8S). Use the form that matches the stated abstraction. Worked example: if CN = 80, then S = 1000/80 - 10 = 2.5 in and Ia = 0.2(2.5) = 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. Note CN ranges from a theoretical 0 to 100; CN = 100 gives S = 0, meaning all rainfall runs off (an impervious surface).

Selecting and Combining CN Values

Curve number depends on land use, hydrologic soil group (HSG A through D), cover/hydrologic condition, conservation treatment, and antecedent moisture condition (AMC I dry, II average, III wet) when specified. Higher CN means lower retention S and more runoff. Group A soils have high infiltration and low CN; group D soils have low infiltration and high CN for the same land use. Default published CN values assume AMC II; the exam will state if you must convert to dry or wet conditions.

For mixed watersheds, follow the problem instructions. A simple area-weighted CN is accepted for moderate variation, but the equation is nonlinear. When one subarea is pavement (CN near 98) and another is open space (CN near 60-70), the safer professional workflow is to compute Qd by subarea, then area-weight the runoff volumes, not the curve numbers. That distinction matters most when P is near the initial-abstraction threshold, where small CN differences flip a subarea between runoff and no runoff.

Unit Hydrograph Logic

A unit hydrograph is the direct-runoff hydrograph produced by one unit depth (1 inch) of excess rainfall distributed uniformly over the watershed during a specified duration. It translates runoff depth into discharge over time; doubling the excess depth doubles every ordinate (linearity), and successive bursts are added with appropriate time lags (superposition).

NRCS dimensionless hydrograph procedures use lag time and time to peak. A common PE-level relationship is lag time tlag = 0.6 Tc when permitted. If the excess-rainfall duration is D, then time to peak Tp = D/2 + tlag. The NRCS triangular peak estimate is qp = 484 A Qd / Tp, where A is in square miles, Qd is in inches, Tp is in hours, and qp is in cfs. The constant 484 is the standard peak-rate factor (it places 3/8 of the hydrograph volume under the rising limb); it can range from about 600 in steep terrain to roughly 300 in flat, swampy terrain, so use the exact factor the handbook or problem supplies.

Calculation Workflow and Symbol Traps

1. Determine CN from land use, soil group, and condition.
2. Compute S and Ia, then runoff depth Qd.
3. Convert Qd to runoff volume when needed: volume = depth x watershed area (watch ac-in vs. ac-ft vs. ft^3).
4. Determine Tc, lag time tlag, excess duration D, and time to peak Tp.
5. Build the hydrograph or compute qp from the supplied relationship.
6. Check that the area under the direct-runoff hydrograph equals the runoff volume.

The exam rewards knowing what each symbol is: Qd is a depth in inches, not a flow; qp is a flow rate in cfs, not a depth; CN is not a runoff coefficient; and Ia is a one-time depth, not a steady infiltration rate.

Volume Conversions and a Worked Volume

Volume errors cost more points than equation errors here. The handy identity is that 1 inch of runoff over 1 acre equals 3,630 ft^3, and 1 acre-foot equals 43,560 ft^3. So a runoff depth Qd over an area A in acres gives a volume V (ft^3) = Qd (in) x A (ac) x 3,630, or simply V (ac-ft) = Qd (in)/12 x A (ac). Worked example continuing the CN = 80 case: Qd = 2.04 in over a 30-acre site gives V = 2.04 x 30 x 3,630 = 222,000 ft^3, or equivalently (2.04/12)(30) = 5.1 ac-ft. Detention and pre/post comparison problems almost always require this step, so commit the 3,630 and 43,560 factors to memory.

NRCS vs. Rational at a Glance

Knowing which tool a prompt expects, before you compute, prevents the most expensive mistake: solving a volume question with a peak-only method or vice versa.