Rainfall-Runoff Simulator: Predict Hydrograph Response to Storms

simulator intermediate ~10 min
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Qp = 42.3 m³/s — peak discharge for 50mm/hr storm on CN-75 basin

A 50 mm/hr storm lasting 3 hours on a 50 km² basin with CN 75 produces a peak discharge of approximately 42.3 m³/s, with runoff beginning after initial abstraction is satisfied.

Formula

S = (25400 / CN) - 254 (maximum retention, mm)
Qe = (P - 0.2S)² / (P + 0.8S) (excess rainfall, mm)
Qp = 0.208 × A × Qe / Tp (peak discharge, m³/s)

From Rain to River

When rain falls on a catchment, only a fraction becomes streamflow. The rest infiltrates into the soil, evaporates, or is intercepted by vegetation. The rainfall-runoff process transforms spatially distributed precipitation into a concentrated discharge hydrograph at the basin outlet. Understanding this transformation is essential for flood prediction, dam design, and stormwater management.

The SCS Curve Number Method

Developed by the US Soil Conservation Service in the 1950s, the CN method condenses complex infiltration processes into a single dimensionless parameter. CN values encode soil permeability (A through D hydrologic soil groups), land cover type, and antecedent moisture conditions. The method computes maximum retention S from CN, then estimates runoff depth from the rainfall-retention balance equation — elegant simplicity that remains the global standard for ungauged basins.

Hydrograph Shape and Timing

The unit hydrograph concept, introduced by Sherman in 1932, assumes that a basin's runoff response to a unit of excess rainfall is consistent regardless of storm magnitude. Time to peak depends on storm duration and basin lag time, which itself depends on flow path length and slope. This simulation generates synthetic triangular hydrographs showing how changing CN or storm intensity reshapes the peak, volume, and recession limb.

Urbanization and Flood Risk

Converting forests and farmland to impervious surfaces dramatically alters the rainfall-runoff relationship. Urban basins with CN values above 90 produce flashy hydrographs with high peaks and rapid recession. A parking lot that was once meadow may generate five times the peak runoff for the same storm. Green infrastructure — bioswales, permeable pavement, retention ponds — attempts to restore pre-development hydrology by lowering effective CN values.

FAQ

What is the SCS Curve Number method?

The SCS (now NRCS) Curve Number method is an empirical approach developed by the US Soil Conservation Service to estimate direct runoff from rainfall. The curve number (CN) ranges from 30 to 98, representing soil type, land cover, and antecedent moisture. Higher CN values mean more runoff; lower values mean more infiltration.

How is peak discharge calculated?

The SCS unit hydrograph method estimates peak discharge as Qp = 0.208 × A × Qe / Tp, where A is basin area in km², Qe is excess rainfall depth in mm, and Tp is time to peak in hours. The constant 0.208 accounts for the triangular hydrograph shape assumption.

What causes flash floods?

Flash floods result from intense rainfall over short durations on basins with high CN (impervious surfaces, saturated soils), steep slopes, and small area. Urban development dramatically increases CN values, converting previously absorbent land into rapid-runoff surfaces.

What is initial abstraction in hydrology?

Initial abstraction (Ia) is the rainfall captured before runoff begins — including interception by vegetation, depression storage, and initial infiltration. The SCS method estimates Ia = 0.2S, where S is maximum retention. No runoff occurs until cumulative rainfall exceeds Ia.

Sources

Embed

<iframe src="https://homo-deus.com/lab/hydrology/rainfall-runoff/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub