Slot Canyon Flash Flood (2D)

What happens

A thunderstorm falls on a rocky catchment several kilometres upstream of a narrow slot canyon. The slot itself stays dry and sunny, yet a few tens of minutes later a wall of brown water arrives. The page follows the water through three stages and lets you change every number in them.

1. Rain to runoff: SCS curve number

Cumulative rain P (mm) is split into losses (infiltration, filling hollows) and runoff R:

S = 25400/CN - 254, Ia = 0.2 S, R = (P - Ia)² / (P - Ia + S) for P > Ia, else 0.

A bare-rock catchment (CN near 96) turns most of the rain into runoff; deep sandy soil (CN near 60) swallows a moderate storm completely. The runoff rate is dR/dt = (dR/dP) × rain rate with dR/dP = (P - Ia)(P - Ia + 2S) / (P - Ia + S)².

2. Catchment lag: linear reservoir

Water takes time to reach the canyon head. The catchment is a linear reservoir with storage K q and K = 0.6 Tc, where Tc is the time of concentration: dq/dt = (Ac dR/dt - q) / K. For a step of inflow the outflow rises as 1 - e-t/K, so a short intense burst gives a high but brief peak and a long gentle rain a low broad one. The page integrates this exactly for each time step.

3. Routing down the slot: Manning and the kinematic wave

For a rectangular channel of width b and depth h, the Manning equation gives the discharge Q = (1/n) A Rh2/3 √S0 with A = b h and hydraulic radius Rh = A/(b + 2h). Mass conservation, ∂A/∂t + ∂Q/∂x = 0, with this rating Q(A) is the kinematic wave equation. Disturbances travel at c = dQ/dA, which grows with depth, so deeper water catches up with shallower water and the flood front steepens into a bore. The solver uses 120 first-order upwind finite-volume cells with a CFL time step.

The Froude number Fr = v/√(g h) and the depth-velocity product h v are shown live. A depth-velocity product of about 0.5 m²/s is used as an indicative wading limit: above it a person cannot keep a foothold even in water that is only knee deep. Published thresholds vary with body size and bed; treat it as a teaching marker, not a safety rule.

Checks run in the page

1. Steady inflow into the quiet slot: the numerical depth at the downstream end equals the Manning normal depth found by bisection. 2. A 5 % rise of inflow reaches mid-canyon in the time x/c given by the analytic kinematic wave speed. 3. Mass ledger of the whole event: rain, runoff, catchment outflow plus storage, and the slot inflow minus outflow minus storage, must close. 4. The curve-number runoff rate integrates back to the closed-form runoff depth.

Honest simplifications

The slot is a straight prismatic rectangle in the physics (the 3D walls wind and flare for looks only) with a uniform slope and roughness. The kinematic wave has no backwater, no hydraulic jump and no real shock physics (first-order upwind smears the bore over a few cells), no sediment bulking (real flash floods carry so much mud and boulders that Manning n and density change), no channel losses into the bed, one lumped catchment and one storm cell. The curve-number method is an empirical event model. Numbers are for learning how the ingredients combine, not for forecasting a real canyon. When a real canyon looks dry and the sky is clear, flash flood danger is judged from the forecast and the whole upstream catchment.

Controls

Click or drag in the longitudinal section to move the gauge. "Skip to the flood" fast-forwards to just before the front reaches the gauge. Changing a storm, catchment or slot parameter restarts the event; the ledge height and the gauge position update in place.