Catchment Runoff and Detention

What is modelled

A Gaussian burst of rain falls on a slope that is part paved, part soil. The soil absorbs up to its infiltration capacity; the rest runs down the plane as a shallow kinematic wave whose speed follows Manning roughness. The outflow fills a basin that drains through an orifice gate and a pump and spills over a weir when full.

Equations

• Kinematic wave ∂h/∂t + ∂q/∂x = reff, q = √S h5/3 / n.
• Time of concentration tc = (n L / (√S i2/3))3/5.
• Orifice Q = Cd a Ao √(2 g h); weir Q = 1.7 B H3/2.
• Basin balance Ab dh/dt = Qin − Qgate − Qpump − Qspill.

Checks run in the page

• Rain = infiltration + surface + basin + drained + spilled.
• Finite-difference time of concentration.
• Orifice drain time against the Torricelli integral.
• Storm depth against the error function.

Honest simplifications

One uniform plane, constant infiltration capacity, no pipes or backwater, a weir of fixed width and model time sped up by a fixed factor. It is a classroom hydrology model, not a flood design tool.

• Press Cloudburst on pavement and watch the basin reach the spill level.
• Open the gate or raise the pump and see the peak depth fall.
• Press Long gentle rain: the soil absorbs most of it and the basin barely rises.