Flash Flood Model: From Rainfall to Runoff in Minutes

Not all rain becomes runoff

Before a drop of rain can flood anything, it has to fail to soak in. The SCS Curve Number method (developed by the US Soil Conservation Service, now NRCS) turns a watershed's soil type, land use and antecedent wetness into a single number, CN, between 30 (highly permeable) and 100 (fully impervious). From CN you get the maximum possible storage S and the runoff depth Q for a given rainfall P:

S  = (25400 / CN) - 254                    // mm
Ia = 0.2 * S                               // initial abstraction
Q  = (P - Ia)^2 / (P - Ia + S)   for P > Ia,  else Q = 0

A forested watershed with CN around 55 might turn a 50 mm storm into almost no runoff at all. A paved city block with CN around 98 turns nearly the whole storm into runoff, and turns it into runoff immediately — which is the entire mechanism of urban flash flooding.

The unit hydrograph: from a rain pulse to a flow curve

Runoff depth alone doesn't tell you when the flood peaks or how long it lasts. The unit hydrograph is the watershed's impulse response — the streamflow curve produced by exactly 1 unit of runoff spread evenly over the basin in a fixed time. The SCS dimensionless unit hydrograph is a standard shape scaled by the time to peak, which comes from the watershed's time of concentration Tc:

Tp = 0.5*D + 0.6*Tc            // time to peak, D = rainfall duration
Qp = 2.08 * Area / Tp           // peak discharge (SI), Area = basin area

// any real rainfall record is convolved against the unit hydrograph:
Q(t) = sum over tau of  P_excess(tau) * UH(t - tau)

A steep, small, urbanised watershed has a short Tc, so Tp is short and Qp is high and sharp — a flash flood. A large, flat, forested basin has a long Tc, so the same rainfall total spreads into a lower, broader peak over days rather than minutes.

Routing the wave downstream: lag and attenuation

Runoff generated across a watershed doesn't arrive at the outlet all at once — it has to travel down the channel network, and channel storage smooths and delays it. The Muskingum method models a reach as a linear reservoir with both prism and wedge storage, giving outflow as a weighted blend of current and past inflow and outflow:

S = K * [ X*I + (1-X)*O ]         // channel storage
O2 = C0*I2 + C1*I1 + C2*O1        // routed outflow, one time step

K = travel time through the reach     X = weighting (0 = pure attenuation)

The larger K is, the more a reach delays the peak; the smaller X is, the more it flattens it. Chain enough reaches together and a sharp, narrow flood pulse generated in the headwaters arrives downstream lower, wider and later — attenuation is the reason a flash flood watch upstream can still give people real, if short, warning time downstream.

Frequently asked questions

Try it live

Everything above runs in your browser — open Flash Flood Model and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.