Each field cell holds a moisture level θ that rises where water is applied and
slowly diffuses to neighbouring cells and drains away over time. Delivery method
controls where water lands and how much escapes as runoff before it can
infiltrate the soil.
dθ/dt = application(x,y) + D·∇²θ − k_drain·θ
runoff_fraction = method-dependent (drip ≈ 5%, sprinkler ≈ 25%, flood ≈ 45%)
- Drip — narrow emitters at each plant deliver water directly to roots; lowest runoff, slowest coverage.
- Sprinkler — a rotating overhead jet wets a circular zone; some water drifts off-target.
- Flood — the whole field is sheeted with water; fastest but most runoff and evaporation loss.
- Flow rate — total water pumped per minute, shared across active emitters.
Field efficiency = water that stayed in the root zone ÷ total water applied —
the number real irrigation engineers optimise for.