Rainfall Runoff Hydrograph

Runoff Hydrograph Generator

Manual Hyetograph Convolution

1. Watershed Parameters
Drainage Area (A)		km²
Time of Conc. (Tc)
SCS Curve Number (CN)

TR-55 Flow Path Analysis

A: Sheet Flow (Max 300') 0.0 min

Length

m

Slope

Mann. n

2-Yr Rain ($P_2$):

mm

B: Shallow Conc. 0.0 min

Length

m

Slope

SurfaceUnpavedPaved

C: Open Channel / Pipe 0.0 min

Length

m

Velocity (V)

m/s

Land Cover CN Matrix (AMC II)

Land Use	A	B	C	D

2. Design Storm (Rainfall)

Input Source

Synthetic SCS Curve Manual Hyetograph

NRCS Curve Type	Type IType IA Type IIType III
Total 24-Hr Depth (P)		mm

Incremental Depth Series (mm) Create data

Paste a single column of depths from Excel. Each row represents one time step ($\Delta t$).

3. Simulation Settings
Time Step ($\Delta t$)	1 Min 5 Mins 10 Mins 15 Mins 30 Mins

Runoff Depth 0.0 mm

Total Volume 0.0 m³

Peak Flow (Qp) 0.0 m³/s

Time to Peak Hr 0.0

Composite Runoff Hydrograph Visualizer

Intermediate Routing Variables

Max Retention (S)	0.00 mm
Init. Abstraction (Ia)	0.00 mm
Lag Time (0.6 * Tc)	0.00 hr
UH Time to Peak (Tp)	0.00 hr
Unit Peak Flow (qp)	0.00 m³/s/mm

Time-Series Routing Results

Time (hr)	Inc. Rain (mm)	Inc. Excess (mm)	Runoff Flow (m³/s)

Theoretical Background

1. Rainfall Abstraction (SCS Curve Number Method) Before runoff occurs, rainfall must satisfy initial abstraction ($I_a$), which consists of depression storage, interception, and initial infiltration. Total runoff depth ($Q$) is calculated from total precipitation ($P$) and maximum potential retention ($S$).

• Maximum Retention: $S = \frac{25400}{CN} - 254$ (Metric) or $S = \frac{1000}{CN} - 10$ (Imperial)
• Initial Abstraction: $I_a = 0.2 \cdot S$ (standard assumption)
• Runoff Depth: $Q = \frac{(P - I_a)^2}{(P - I_a) + S}$    (Only applies when $P > I_a$)

2. Time of Concentration ($T_c$) - TR-55 Method The time required for runoff to travel from the hydraulically most distant point to the outlet. It is the sum of three flow regimes:

• Sheet Flow (Kinematic Wave): $T_t = \frac{0.007(nL)^{0.8}}{P_2^{0.5} S^{0.4}}$ (where $P_2$ is the 2-year 24-hr rainfall)
• Shallow Concentrated Flow: $V = k \cdot S^{0.5}$ (where $k=16.1$ for unpaved, $20.3$ for paved)
• Open Channel Flow: Uses Manning's equation to find velocity, then $T_t = L/V$

3. SCS Dimensionless Unit Hydrograph (DUH) A synthetic unit hydrograph translates $1$ unit of excess rainfall into a continuous flow profile for the specific watershed.

• Lag Time ($L$): $L \approx 0.6 \cdot T_c$
• Time to Peak ($T_p$): $T_p = \frac{\Delta t}{2} + L$
• Peak Discharge ($q_p$): $q_p = \frac{K \cdot A}{T_p}$    (where $K$ is the shape factor: $0.208$ metric, $484$ imperial)

4. Hydrograph Convolution The final composite runoff hydrograph is generated mathematically. For every time step ($\Delta t$), the incremental excess rainfall is multiplied by the Unit Hydrograph ordinates. These resulting sub-hydrographs are lagged in time and summed together to create the continuous flow curve.

References & Sources

• USDA Natural Resources Conservation Service (NRCS). (1986). Urban Hydrology for Small Watersheds (TR-55). Conservation Engineering Division. (Source for Time of Concentration and CN methodology). [Download TR-55 PDF]
• USDA NRCS. (2007). National Engineering Handbook (NEH), Part 630: Hydrology. Chapter 10: Estimation of Direct Runoff from Storm Rainfall, and Chapter 16: Hydrographs. [View NEH Chapter 16]
• Chow, V. T., Maidment, D. R., & Mays, L. W. (1988). Applied Hydrology. McGraw-Hill. (Comprehensive coverage of unit hydrograph convolution algorithms).

Version 1.0

CivilSheets by Sothearith Seak