Flash Flood Model — SCS Curve Number Runoff & Flood Wave Routing

Rain falls on a steep watershed. The SCS Curve Number method splits it into infiltration and runoff, and the runoff routes downstream as a flood wave with a real travel-time delay and an attenuating peak.

Land use:
Drag to orbit, scroll to zoom — inset shows the rainfall hyetograph (top) and outlet hydrograph (bottom)
78
Curve number CN
0.0
Runoff depth Q (mm)
0.0
Peak discharge (m³/s)
0.0
Time to peak (hr)
0.00
Current flood stage (m)
Agricultural land (CN ≈ 78): Row crops and pasture soak up a moderate share of rainfall. S = (1000/CN)−10, Ia ≈ 0.2S — runoff only starts once rainfall exceeds Ia, then follows Q = (P−Ia)²/(P−Ia+S).
About the Flash Flood Model

SCS Curve Number method: Q = (P−Ia)²/(P−Ia+S), with S = (1000/CN)−10 (inches) or S = (25400/CN)−254 (mm), and Ia ≈ 0.2S. CN encodes soil group and land cover — roughly 30–40 for forest, 70–85 for agricultural land, 85–98 for impervious urban surfaces.

Time of concentration: estimated with the Kirpich formula, Tc = 0.0195·L0.77·Sc−0.385 (L in metres, Sc as a fraction, Tc in minutes) — steeper watersheds concentrate flow faster.

SCS triangular unit hydrograph: Tp = D/2 + 0.6·Tc, Qp = 2.08·A/Tp (A in km², Tp in hours, Qp in m³/s per cm of excess rainfall), base time Tb = 2.67·Tp. Convolving this unit hydrograph with the incremental excess-rainfall hyetograph gives the outlet discharge hydrograph — its peak and time to peak drive the animation.

Downstream routing: the outlet hydrograph is delayed and attenuated along the visualised reach using a kinematic-wave celerity c ≈ (5/3)·V, then converted to a water depth at each point with Manning's equation for a trapezoidal channel — this is what makes the flood wave swell, travel and submerge low ground realistically.

About this simulation

This simulation turns rainfall into a real flash flood using the SCS Curve Number method, Q = (P−Ia)²/(P−Ia+S), where S = (1000/CN)−10 depends on soil and land use and Ia ≈ 0.2S is soaked up before runoff starts. The resulting excess rainfall is convolved with an SCS triangular unit hydrograph to produce a genuine outlet discharge hydrograph, which is then delayed and attenuated downstream by a kinematic-wave celerity and converted to channel depth with Manning's equation — a real flood wave, not a scripted animation.

🔬 What it shows

A 3D valley with a river channel: rain accumulates on the watershed, the SCS Curve Number equation splits it into infiltration and runoff, and the runoff routes downstream as a rising, travelling, attenuating water surface that submerges low-lying ground exactly where its elevation drops below the current flood stage.

🎮 How to use

Pick Forest, Agricultural or Urban land use to set a realistic curve number, then adjust peak rainfall intensity (10–150 mm/hr), storm duration (0.5–6 hr) and watershed slope (1–20%). Watch the CN, runoff depth, peak discharge, time to peak and live flood-stage readouts respond, and the inset chart trace the rainfall hyetograph against the outlet hydrograph.

💡 Did you know?

Paving a watershed can push its curve number from ~35 (forest) to ~95 (impervious urban) — for the exact same storm, that alone can multiply runoff several times over and shorten the time to peak, which is why urbanized creeks flash-flood far more readily than forested ones.

Frequently asked questions

What is the SCS Curve Number method?

The SCS (now NRCS) Curve Number method estimates runoff depth Q from storm rainfall depth P: Q = (P−Ia)²/(P−Ia+S). S = (1000/CN)−10 (inches) or (25400/CN)−254 (mm) is the watershed's potential maximum retention, and Ia ≈ 0.2S is the initial abstraction — interception, depression storage and early infiltration — that must be satisfied before any runoff occurs.

What do the curve number presets mean?

Curve numbers summarise how much a soil and land cover combination resists runoff. Forest litter and root channels give CN ≈ 30–40; cultivated or pasture land gives CN ≈ 70–85; impervious urban surfaces such as roofs and pavement give CN ≈ 85–98. Higher CN means less infiltration and more, faster runoff for the same rainfall.

How is the flood wave routed downstream?

The outlet hydrograph from the unit-hydrograph convolution is delayed at each point along the reach by a fraction of the total travel time (proportional to distance downstream) and its peak is reduced, mimicking kinematic-wave translation and attenuation. The travel time itself comes from a wave celerity c ≈ (5/3)·V, with V from Manning's equation at the peak discharge.

Why do flash floods arrive with so little warning?

Small, steep, low-infiltration watersheds have a short time of concentration (via the Kirpich formula, Tc shrinks as slope rises) and a high curve number sheds rainfall almost immediately as runoff. The unit hydrograph's time to peak is directly tied to Tc, so a steep, urbanized basin can go from first rain to peak flood stage in under an hour.

What does the "current flood stage" readout mean?

It is the water depth in the channel, in metres, at a fixed downstream reference point, computed by inverting Manning's equation for a trapezoidal channel at the locally routed discharge. As the flood wave arrives at that point the stage rises, peaks, then recedes — exactly the sequence a streamgauge downstream would record.

Why does storm duration change the peak discharge?

Spreading the same total rainfall over a longer duration lowers the peak rainfall intensity for a given depth and gives more time for the unit-hydrograph response to spread out, so short, intense storms on the same watershed generally produce a sharper, higher peak than long, gentle ones — the essence of why flash floods are tied to short, intense convective rainfall.