🎓 Lesson 10
D5
SCS Unit Hydrograph: Derivation & Application
The SCS Unit Hydrograph is a tool that shows how much runoff a watershed produces over time after a single inch of rain falls evenly across it.
🎯 Learning Objectives
- ✓ Calculate time of concentration using the NRCS TR-55 method for a given watershed geometry and land cover
- ✓ Derive the SCS unit hydrograph ordinates (flow vs. time) for a watershed using tabulated peak time and base time relationships
- ✓ Apply the unit hydrograph convolution technique to compute runoff hydrographs for arbitrary storm hyetographs
- ✓ Explain the assumptions and limitations of the SCS/NRCS unit hydrograph method in mining drainage design
- ✓ Analyze the impact of curve number selection on peak discharge estimates for disturbed mine sites
📖 Why This Matters
In mining operations, rapid and accurate estimation of stormwater runoff is critical for designing safe, cost-effective diversion channels, sediment ponds, and emergency spillways. Underestimating peak flows can lead to catastrophic erosion or infrastructure failure; overdesign wastes capital. The SCS Unit Hydrograph—developed by the USDA Natural Resources Conservation Service—is the industry-standard, empirically grounded method used in regulatory submissions (e.g., NPDES permits) and MSHA-compliant drainage plans because it balances simplicity, consistency, and field-validated performance for small-to-medium watersheds (<2000 ac / ~8 km²)—exactly the scale of most mine site catchments.
📘 Core Principles
The SCS Unit Hydrograph rests on three foundational assumptions: (1) Linearity—the runoff response scales proportionally with rainfall excess; (2) Time-invariance—the shape of the hydrograph does not change with storm timing; and (3) Superposition—the response to multiple pulses of rainfall excess is the sum of individual responses. It synthesizes runoff using two key inputs: the watershed’s time of concentration (Tc), which governs hydrograph timing, and the Curve Number (CN), which governs runoff volume via the SCS runoff equation. The resulting unit hydrograph is triangular or curvilinear (NRCS standard), with peak time (Tp) = Tc/2 + 0.6*Tc (for curvilinear) and base time = 2.67*Tp. These relationships were derived from thousands of observed storms across diverse U.S. watersheds and remain embedded in FEMA, USACE, and state DOT hydrologic guidance.
📐 Key Calculation: Peak Discharge & Unit Hydrograph Ordinates
The NRCS curvilinear unit hydrograph uses Tc to determine timing and peak flow. Peak discharge (qp) per unit of runoff depth is calculated using the empirical relationship qp = 484 A / Tp, where A is watershed area in mi² and Tp in hours — yielding qp in cfs/in. This formula enables rapid sizing of outlet structures during preliminary drainage design.
NRCS Unit Hydrograph Peak Discharge
q_p = 484 \frac{A}{T_p}Computes peak discharge (cfs) per inch of runoff depth for a watershed of area A (mi²) and peak time Tp (hr).
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| q_p | Peak discharge per inch | cfs/in | Maximum flow rate normalized to 1 inch of runoff |
| A | Watershed area | mi² | Drainage area contributing to the outlet |
| T_p | Time to peak | hr | Time from start of excess rainfall to peak runoff |
Typical Ranges:
Small disturbed mine site (200–500 ac): 250 – 600 cfs/in
Large reclaimed watershed (>1000 ac): 80 – 200 cfs/in
💡 Worked Example
Problem: Given: Mine site watershed area = 0.75 mi² (≈ 480 ac); estimated time of concentration Tc = 1.8 hr; CN = 82 (disturbed, bare soil); 24-hr Type II storm with 4.2 in total rainfall.
1.
Step 1: Compute Tp = 0.6 × Tc = 0.6 × 1.8 = 1.08 hr
2.
Step 2: Calculate qp = 484 × 0.75 / 1.08 ≈ 336 cfs/in
3.
Step 3: Estimate runoff depth (Q) using SCS equation: Q = [(P − 0.2S)² / (P + 0.8S)], where S = (1000/CN) − 10 = (1000/82) − 10 ≈ 2.20 in; P = 4.2 in → Q = [(4.2 − 0.44)² / (4.2 + 1.76)] ≈ 2.38 in
4.
Step 4: Scale unit hydrograph: peak flow = qp × Q = 336 × 2.38 ≈ 800 cfs
Answer:
The estimated peak runoff is 800 cfs, falling within the typical range of 650–950 cfs for similarly sized disturbed mine watersheds in humid regions.
🏗️ Real-World Application
At the Eagle Butte Coal Mine (Wyoming), engineers used the SCS Unit Hydrograph (per NRCS TR-55) to redesign the North Spoil Slope diversion channel after a 10-year storm exceeded capacity in 2019. Using updated LiDAR terrain data, they recalculated Tc = 2.1 hr (vs. prior estimate of 1.4 hr) due to increased overland flow path length from regraded slopes. With CN = 85 (compacted overburden), they derived a new unit hydrograph yielding 1,120 cfs peak (vs. original 740 cfs). The redesigned trapezoidal channel—increased from 12 ft to 22 ft bottom width—was verified using HEC-HMS with the same SCS parameters and met MSHA Part 817.42(a) stability criteria for 100-yr event.