How To Calculate Curve Number With Hydrograph Example

Calculate runoff curve numbers and visualize hydrograph results for hydrologic analysis

Comprehensive Guide: How to Calculate Curve Number with Hydrograph Example

The Curve Number (CN) method is a widely used hydrologic technique developed by the U.S. Department of Agriculture’s Natural Resources Conservation Service (NRCS) to estimate direct runoff from rainfall events. When combined with hydrograph analysis, it becomes a powerful tool for watershed management, flood prediction, and stormwater design.

Understanding the Curve Number Method

The CN method relates land use, soil type, and antecedent moisture conditions to potential runoff. The fundamental equation is:

Key Equation

Q = (P – Ia)² / (P – Ia + S)

Where:

• Q = Direct runoff (inches)
• P = Total rainfall (inches)
• Ia = Initial abstraction (inches) [typically 0.2S]
• S = Potential maximum retention (inches)

The relationship between CN and S is given by:

S = (1000/CN) – 10

Step-by-Step Calculation Process

1. Determine Base CN:

   Select the appropriate CN from NRCS tables based on:

   • Land use/cover type (urban, agricultural, forest, etc.)
   • Hydrologic soil group (A, B, C, or D)
   • Hydrologic condition (poor, fair, good for rangeland)
2. Adjust for Antecedent Moisture Condition (AMC):

   Modify the base CN based on soil moisture conditions:

   AMC	Condition Description	CN Adjustment Formula
   AMC I	Dry (5-day antecedent rain < 0.5 in)	CNⅠ = 4.2CNⅡ / (10 – 0.058CNⅡ)
   AMC II	Average (5-day antecedent rain 0.5-1.1 in)	Base CN (no adjustment)
   AMC III	Wet (5-day antecedent rain > 1.1 in)	CNⅢ = 23CNⅡ / (10 + 0.13CNⅡ)

3. Calculate Potential Maximum Retention (S):

   Using the adjusted CN value:

   S = (1000/CN) – 10

   Where S is in inches

4. Determine Initial Abstraction (Ia):

   Typically estimated as:

   Ia = 0.2S

   Though some studies suggest Ia = 0.05S for more accurate results in certain conditions

5. Compute Direct Runoff (Q):

   Apply the runoff equation when P > Ia:

   Q = (P – Ia)² / (P – Ia + S)

   If P ≤ Ia, then Q = 0 (no runoff occurs)

6. Generate Hydrograph:

   Convert runoff depth to discharge using:

   Q = CIA/360

   Where:

   • Q = Peak discharge (cfs)
   • C = Runoff coefficient (Q/P)
   • I = Rainfall intensity (in/hr)
   • A = Watershed area (acres)

Practical Example Calculation

Let’s work through a complete example for a 100-acre watershed with the following characteristics:

• Land use: Pasture (good condition)
• Soil group: B
• AMC: II (average conditions)
• Rainfall: 3.5 inches

1. Base CN Selection:

   From NRCS tables, pasture in good condition on soil group B has CNⅡ = 61

2. AMC Adjustment:

   Since we’re using AMC II, no adjustment needed. CN = 61

3. Calculate S:

   S = (1000/61) – 10 = 6.39 inches

4. Determine Ia:

   Ia = 0.2 × 6.39 = 1.28 inches

5. Compute Runoff (Q):

   Q = (3.5 – 1.28)² / (3.5 – 1.28 + 6.39) = 1.03 inches

6. Estimate Peak Discharge:

   Assuming uniform rainfall over 6 hours (I = 3.5/6 = 0.58 in/hr):

   Q_peak = (1.03/3.5) × 0.58 × 100 / 360 = 0.046 cfs

   Note: Actual peak flow would use a more sophisticated hydrograph method like the NRCS Unit Hydrograph

Hydrograph Analysis

A hydrograph represents the time distribution of runoff at a watershed outlet. Key components include:

• Rising limb: Period of increasing discharge as runoff reaches the outlet
• Peak flow: Maximum discharge rate
• Recession limb: Decreasing discharge as storage is depleted
• Time of concentration (Tc): Time for water to travel from most remote point to outlet

The NRCS Dimensionless Unit Hydrograph provides a standardized approach:

t/Tp	Q/Qp (Rising)	Q/Qp (Recession)
0.0	0.000	–
0.1	0.030	0.820
0.2	0.100	0.680
0.3	0.190	0.560
0.4	0.310	0.460
0.5	0.470	0.390
0.6	0.660	0.330
0.7	0.820	0.280
0.8	0.930	0.240
0.9	0.990	0.210
1.0	1.000	0.180
1.1	–	0.160
1.2	–	0.140
1.5	–	0.100
2.0	–	0.050
2.5	–	0.020

Where:

• Tp = Time to peak (hours) ≈ 0.6Tc
• Qp = Peak discharge (cfs) = 484AQ/Tp (for English units)
• A = Watershed area (mi²)
• Q = Runoff depth (inches)

Advanced Considerations

For professional applications, consider these refinements:

1. Composite CN:

   For mixed land uses, calculate area-weighted average:

   CN_composite = (Σ(CN_i × A_i)) / A_total

   Where A_i are sub-area contributions

2. Urban Adjustments:

   Impervious areas require special handling:

   • Directly connected impervious: Use CN = 98
   • Unconnected impervious: Use composite method
3. Seasonal Variations:

   CN values change with:

   • Vegetation growth cycles
   • Frozen ground conditions
   • Snowmelt contributions
4. Spatial Distribution:

   For large watersheds, consider:

   • Distributed CN values
   • Rainfall spatial variability
   • Sub-watershed routing

Common Applications

The CN method with hydrograph analysis supports:

• Stormwater Management: Sizing detention basins and designing drainage systems
• Floodplain Delineation: Estimating design floods for FEMA studies
• Agricultural Planning: Optimizing irrigation and erosion control
• Urban Development: Assessing impacts of land use changes
• Climate Adaptation: Evaluating increased runoff from intense rainfall

Limitations and Alternatives

While powerful, the CN method has limitations:

• Assumes uniform rainfall and watershed characteristics
• Less accurate for very small or very large events
• Doesn’t explicitly model infiltration processes

Alternatives include:

• Green-Ampt: Physics-based infiltration model
• HEC-HMS: Comprehensive hydrologic modeling system
• SWMM: EPA’s Storm Water Management Model for urban areas

Regulatory Context

The CN method is referenced in numerous regulations:

• NRCS Technical Release 55 (TR-55) for urban hydrology
• FEMA guidelines for floodplain management
• EPA stormwater permitting requirements
• State-specific drainage manuals (e.g., California DWR, Texas DOT)

Professional Tip

For critical projects, always:

1. Calibrate CN values with local rainfall-runoff data
2. Consider using GIS tools for spatial CN analysis
3. Validate results with observed hydrographs when available
4. Document all assumptions and data sources

Authoritative Resources

For official guidance on curve number calculations and hydrograph methods:

• NRCS National Water Management Center – Official source for CN tables and TR-55 documentation
• USGS Water Resources – Hydrograph analysis methods and streamflow data
• Purdue University Engineering – Academic resource on unit hydrograph theory