MY SIMULATOR

Hillslope Storm Runoff

Rain falls, soil drinks, the rest runs downhill.

INTERACTIVE 3D

Storm time 0.0 minRain 0 mm/hOutflow 0.0 L/sRunoff coeff. —FPS 0

Hillslope Storm Runoff: Rain, Infiltration, Overland Flow and the Hydrograph

A rectangular hillslope plot is shown as a soil cut-away diorama. Rain is split by the soil into water that soaks in (Green-Ampt) and water that runs downhill as a sheet (Manning kinematic wave). Pick a scenario, press Start storm, then change one thing at a time and watch the hydrograph.

Scenario

Soil texture

Surface cover

Live state dry

Hydrograph: where the rain goes (L/s over the whole plot)

Cumulative depth over the plot (mm)

1 · Storm

Constant intensity for the chosen duration, then the slope drains. Changing any slider restarts the plot.

2 · Soil

Green-Ampt: capacity f = Ks(1 + ψΔθ/F) falls as the wetting front deepens. Lower Ks to mimic a crust, compaction or burnt, water-repellent soil.

3 · Slope and surface

Manning roughness n: smooth pavement 0.015, tilled soil 0.05, pasture 0.15, forest litter 0.4 (typical values for sheet flow).

Experiments (measured vs predicted)

Run an experiment. They run on a copy of the plot and do not disturb the live one.

Independent numerical checks

Also run outside the browser: node src/check.js. Checks compare the grid solver to closed forms (kinematic-wave characteristics, equilibrium depth, Mein-Larson implicit infiltration) and to exact mass conservation.

The science

Overland flow (kinematic wave). Water depth h(x,t) in m obeys mass conservation along the slope, ∂h/∂t + ∂q/∂x = i − f, where i is rain, f infiltration (both m/s) and q the discharge per unit width (m²/s). Momentum is replaced by the Manning law for wide sheet flow q = (√S / n) h^5/3 (S slope, n roughness in s/m^1/3), so waves travel at speed c = (5/3)(√S/n) h^2/3. The solver is first-order upwind on 48 cells with a CFL number of 0.5; 16 independent lanes share the same slope so soil variability can be shown.

Time of concentration. With constant effective rain i_e on a plot of length L the outlet depth is i_e t until the first characteristic arrives at t_c = [ L n / (√S i_e^2/3) ]^3/5; afterwards outflow equals inflow (Q = i_e L W) at the equilibrium depth (i_e L n/√S)^3/5. If the storm ends before t_c the peak is only (√S/n)(i_eD)^5/3 W. That is why short intense storms on long, rough slopes produce small peaks — and why the “rational method” asks for duration ≥ t_c.

Infiltration (Green-Ampt). A sharp wetting front sits at depth F/Δθ; Darcy flow through the wetted layer gives capacity f = Ks (1 + ψΔθ/F). Δθ = effective porosity × (1 − initial saturation). Infiltration is the smaller of capacity and the water available (rain plus surface water). Under constant rain i > Ks the front starts ponding at F_p = Ks ψΔθ / (i − Ks) and then follows the implicit Mein-Larson solution Ks(t − t_p + t_p') = F − ψΔθ ln(1 + F/(ψΔθ)), which the check solves by bisection. In the cut-away the wet band depth is F/Δθ (1 diorama unit = 10 cm of soil).

Simplifications, honestly. No ponded-head term in Green-Ampt, no soil redistribution after the storm (infiltration continues only while surface water remains), no rills or channels, no rain-drop splash or crusting dynamics, uniform rain, no evaporation, no groundwater return flow. Soil texture parameters are typical Rawls et al. (1983) Green-Ampt values quoted from memory and should be spot-checked; cover roughness values and the scenario Ks values (crusted, burnt, forest litter) are illustrative. Heterogeneity multiplies Ks per lane by a log-normal factor. The vertical tilt of the diorama is drawn exaggerated 1.6× and the 40-unit plot is scaled to the chosen length.