What is a unit hydrograph?

A unit hydrograph is the outlet response to one unit depth of effective rainfall spread uniformly over the watershed for a chosen duration. This page uses a normalized triangular response so the area under u(t) is one.

Why does infiltration reduce the peak so strongly?

Only excess rainfall contributes to quick runoff in this simplified picture. When much of the storm is consumed by initial abstraction and infiltration, the convolution receives less input and the peak drops.

How do basin lag and recession affect flooding?

Short time-to-peak concentrates runoff quickly and raises Q_p. A longer recession spreads the same runoff volume over more time, usually lowering and delaying the peak.

Is this the SCS curve-number method?

No. It uses an initial abstraction plus constant infiltration capacity because those losses are transparent on the hyetograph. Curve-number, Green-Ampt, and distributed hydrologic models are more detailed alternatives.

Watershed Runoff Hydrograph

Rainfall hyetograph, initial abstraction, infiltration losses, triangular unit hydrograph convolution, peak discharge, and time-to-peak.

Live graphs

About this model

This simulator turns a rainfall hyetograph into a watershed outlet hydrograph with a compact unit-hydrograph workflow. Rainfall is discretized into short time bins. Each bin first fills an initial abstraction store I_a, then loses up to f Δt to infiltration, leaving excess rainfall P_e. The outlet discharge is computed by convolving those excess depths with a normalized triangular unit hydrograph u(t): Q(t) = A Σ P_e(τ)u(t−τ), where 1 mm over 1 km² is 1000 m³ and ∫u dt = 1. The unit hydrograph time-to-peak controls catchment response speed, while the recession/base ratio controls the falling limb. The readouts show total rain, runoff excess, runoff coefficient, runoff volume, peak discharge Q_p, and time to peak. It is a teaching model: spatially distributed rainfall, channel routing, soil-moisture recovery, nonlinear saturation excess, reservoirs, and rating-curve uncertainty are intentionally omitted.

Who it's for: Hydrology, civil/environmental engineering, watershed management, and natural hazards students learning hyetographs, losses, and unit hydrograph routing.

Key terms

Runoff hydrograph
Rainfall hyetograph
Unit hydrograph
Excess rainfall
Initial abstraction
Infiltration loss
Peak discharge
Time to peak

How it works

Watershed runoff hydrograph simulator: rainfall hyetograph, infiltration and initial abstraction losses, unit hydrograph convolution, runoff volume, peak discharge, and peak timing.

Key equations

P_e(t) = max[0, P(t) − I_a − f Δt]

Q(t) = A · Σ P_e(τ) u(t−τ), ∫u(t)dt = 1

Frequently asked questions

What is a unit hydrograph?: A unit hydrograph is the outlet response to one unit depth of effective rainfall spread uniformly over the watershed for a chosen duration. This page uses a normalized triangular response so the area under u(t) is one.
Why does infiltration reduce the peak so strongly?: Only excess rainfall contributes to quick runoff in this simplified picture. When much of the storm is consumed by initial abstraction and infiltration, the convolution receives less input and the peak drops.
How do basin lag and recession affect flooding?: Short time-to-peak concentrates runoff quickly and raises Q_p. A longer recession spreads the same runoff volume over more time, usually lowering and delaying the peak.
Is this the SCS curve-number method?: No. It uses an initial abstraction plus constant infiltration capacity because those losses are transparent on the hyetograph. Curve-number, Green-Ampt, and distributed hydrologic models are more detailed alternatives.

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