Day 0.0Soil —Root-zone water — %Stress ——FPS 0

Left: the soil column coloured by water content (dry sand-beige to wet dark). The plant wilts when its roots cannot pull water at the potential rate. Right: water-content profile with the wetting front; dashed lines = field capacity and wilting point. Time runs fast (hours per second).

Soil Water Column: Richards Infiltration, Roots and Drought Stress

Rain soaks into a 1.2 m soil column; roots pull water out; the rest drains away. Choose sand, loam or clay and watch the wetting front, the ponding and the day the plant wilts.

Soil

Weather and plant

Live readouts

Water content profile (θ vs depth)

Root-zone water and plant stress over time

Retention curve θ(h) and conductivity K(h)

Independent numerical checks

Controls

Soil buttons change the van Genuchten parameters (typical Carsel and Parrish values); the sliders set storms, evaporative demand and rooting depth.
Storms repeat every N days. Irrigate adds 20 mm over 2 hours. Speed = simulated hours per real second.
Bottom boundary: free drainage (deep soil) or a water table at the base of the column.

The science

Richards equation (1-D, depth x downward, pressure head h in m of water, negative in unsaturated soil): ∂θ/∂t = ∂/∂x [K(h) ∂h/∂x] − ∂K/∂x − S, i.e. downward Darcy-Buckingham flux q = K(h)(1 − ∂h/∂x) and ∂θ/∂t = −∂q/∂x − S. It is solved with the mass-conservative modified-Picard scheme of Celia et al. (1990): implicit in h, arithmetic-mean conductivity between nodes, 1 cm grid, adaptive time step.

Soil hydraulics. van Genuchten retention θ(h) = θ_r + (θ_s − θ_r)[1 + (α|h|)ⁿ]^−m, m = 1 − 1/n, and Mualem conductivity K = K_s S_e^1/2 [1 − (1 − S_e^1/m)^m]². Field capacity is taken at h = −3.3 m and the wilting point at −150 m (15 bar).

Boundary conditions. Top: rain minus potential soil evaporation as a flux; if that would make the surface head positive, the surface is held at h = 0 (ponding) and the excess is runoff; if it would dry the surface below −100 m it is held there. Bottom: free drainage (q = K) or a water table (h = 0).

Roots. Potential transpiration T_p = K_c ET₀ · cover with a daytime sine shape, distributed over a linearly decreasing root density to the rooting depth and reduced by a Feddes factor α(h) (1 above −5 m, linear to 0 at −150 m). Stress = 1 − T_actual/T_p. This is a macroscopic sink, not a model of individual roots.

Checks on the page. Mass balance (rain − runoff − drainage − ET = Δstorage), hydrostatic equilibrium preserved, saturated flux → K_s, and cumulative ponded infiltration compared with the Green-Ampt solution F = K_s t + ψΔθ ln(1 + F/ψΔθ) (agreement is expected only to about 15 to 20 %).

Simplifications: homogeneous soil, no hysteresis, no vapour flow, no temperature or salinity, no surface ponding storage (all excess runs off), no preferential flow or cracks. Parameters are typical class values; real soils vary widely. Pure Canvas 2D, no Blender assets.