Time 0 minRain 0 mm/hPonding 0 cmKerb 15 cmreadyFPS 0

Drag to orbit, wheel or pinch to zoom. Blue sheet = water standing on the street (depth shown 1 : 1); the kerb is the pale line along the road edge. Grates glow orange when the drain is at capacity. Rain streaks thicken with intensity.

Cloudburst: Clausius-Clapeyron Rain Intensity, Storm-Drain Capacity and Street Ponding

Warmer air holds about 7 percent more water per kelvin, so a cloudburst gets heavier. Follow one street block: rain on roofs and tarmac, a storm drain with a hard capacity, and the water that has nowhere to go.

Storm

Street and drain

Clock

Live readouts

Rain intensity (mm/h)

Water flows (m3/s): inflow, outflow, pipe capacity

Ponding depth on the street (cm)

Experiment: how much worse does warming make it?

Runs the storm for 0 to 6 K of warming with your other settings. Peak rain follows the Clausius-Clapeyron law, yet ponding depth grows much faster than 7 percent per kelvin because the drain has a fixed capacity.

Independent numerical checks

Controls

Warming raises the air temperature; the exponent s = 1 is plain Clausius-Clapeyron, values up to 2 mimic the faster "super-Clausius-Clapeyron" growth seen in some observations of short storms.
Contributing area is the roofs, roads and yards that drain to this one pipe. Soil infiltration only matters for the unpaved share.
Clogging blocks part of the grates (leaves, litter). Pipe diameter and slope set the full-pipe capacity from Manning's formula.
The clock runs the storm in simulated minutes per second; drag the Time slider to scrub.

The science

Clausius-Clapeyron. Saturation vapour pressure follows the Magnus formula e_s(T) = 6.112 exp(17.62 T / (243.12 + T)) hPa, so d ln e_s/dT = 17.62 x 243.12 / (243.12 + T)², about 6.4 % per kelvin at 15 C. The peak intensity is scaled as I = I₀ (e_s(T₀ + dT) / e_s(T₀))^s. This is a scaling argument for the moisture available to a storm, not a weather forecast; real changes depend on dynamics, storm type and location.

Storm shape. The rain rate is a Gaussian in time with sigma = D/6, so the storm depth in mm is I sigma sqrt(2 pi) erf(3/sqrt 2); the page checks this against numerical integration.

Runoff. Q_in = A (phi i + (1 - phi) max(0, i - f)): the impervious share phi sheds all rain, the rest sheds only what exceeds the soil infiltration rate f (a constant-capacity simplification of Horton infiltration). No travel time and no roof storage, so the inflow follows the rain instantly; real catchments smooth and delay it.

Drain. The pipe can carry at most the Manning full-flow capacity Q_cap = (1/n) A R^2/3 S^1/2 (n = 0.013, A = pi D²/4, R = D/4). Water reaches the pipe through grates acting as weirs, Q = N (1 - clog) C_w P h^1.5 with C_w = 1.66 and P = 1 m per grate (typical textbook values). The outflow is the smaller of the two. Standing water obeys A_p dh/dt = Q_in - Q_out on 400 m2 of street (RK4, 2 s steps); where the water goes once it passes the kerb is not modelled.

Simplifications. One pipe, one pond, no surcharge or backwater, no overland flow paths, no sewer network interaction, flat street. Numbers such as the baseline 100 mm/h peak are illustrative. Models built with Blender, scene by Three.js.