Rain falls faster than the soil can drink, or it does not. Dry soil at first soaks up everything; as the wet zone deepens, the soil's intake slows toward its saturated conductivity and the surplus ponds, then runs off.
Both run fresh storms with the current soil, moisture and duration. Constant rain intensity, no depression storage, so the closed-form solution applies.
The science
Green-Ampt model. A sharp wetting front at depth zf = F/Δθ separates saturated soil above from soil at its initial moisture below. Darcy's law across the wetted zone gives the infiltration capacity f = Ks (1 + ψΔθ / F), with F the cumulative infiltration (cm), Ks the saturated conductivity, ψ the suction head at the front and Δθ = (φ − θr)(1 − Se) the moisture deficit.
Ponding. While rain intensity i is below capacity everything infiltrates (f = i). If i > Ks, capacity falls to i when Fp = Ks ψΔθ / (i − Ks), at time tp = Fp/i. After that, Ks(t − tp) = F − Fp − ψΔθ ln[(ψΔθ + F)/(ψΔθ + Fp)]. At late times f tends to Ks; at early times F ≈ √(2 Ks ψΔθ t).
Time stepping. Each 1.8 s step the model compares supply (rain plus ponded water) with the implicit capacity increment (the step's Green-Ampt equation solved by Newton iteration), infiltrates the smaller, and sends water above the depression storage to the tank as runoff. Mass is conserved to rounding error.
Simplifications. One uniform soil layer with a piston-like front; no redistribution when rain pauses, no evaporation, no lateral flow or overland routing delay (runoff arrives instantly), no air entrapment, no surface sealing, and an infinitely deep profile (the view is cropped at 1 m). Soil parameters are typical textbook values for each USDA texture class (Rawls et al., 1983, as tabulated in standard hydrology texts) and vary widely in real soils. Models built with Blender, scene by Three.js.