2D companion to the 3D insecticide fate-and-transport model: applied mass decays in the soil by first-order kinetics and a fraction is mobilised into the stream by rain-driven runoff:
dM_soil/dt = -k·M_soil - r(t)·M_soil
k = ln(2) / t½ (degradation rate)
r(t) = runoff coefficient × rainfall intensity
Stream concentration mixes the runoff load into a fixed water volume and, if the treatment wetland/GAC filter is switched on, removes a further fixed fraction each pass (activated-carbon adsorption is modelled as first-order removal too):
C_stream = M_runoff / V_stream
C_treated = C_stream · (1 − η_GAC), η_GAC ≈ 0.85
Bioaccumulation up the food chain uses a steady-state bioconcentration factor (BCF) — the ratio of tissue concentration to ambient water concentration at equilibrium, tracking toward it with a simple uptake/depuration lag per trophic level:
dC_organism/dt = k_uptake·(BCF·C_water − C_organism)
- Compound class — sets the degradation half-life and soil binding (Koc), matching neonicotinoids (persistent, water-soluble), pyrethroids (short-lived, strongly soil-bound) and organophosphates (intermediate).
- Application rate — total mass deposited on the field at t=0 of each application.
- Rainfall intensity — drives the runoff coefficient that moves soil-bound insecticide into the stream.
- Treatment toggle — simulates a granular-activated-carbon (GAC) filter or constructed wetland removing a fixed fraction of the stream load before it reaches downstream biota.
- Fix vs. the 3D source — the 3D engine's runoff-mobilisation and GAC-capture terms were applied once per animation frame with no time-step scaling, so the mobilisation/removal rate silently sped up or slowed down with the viewer's frame rate. This 2D model scales both terms by the elapsed simulated time, so the physics is identical at 30fps, 60fps or 144fps.
Real-world relevance: this is the same fate-and-transport logic environmental agencies use (via models like PRZM/EXAMS) to set buffer-strip widths, justify GAC upgrades at drinking-water plants, and explain why persistent, water-soluble compounds like neonicotinoids show up far downstream while soil-bound pyrethroids mostly stay local.