Each pollutant parcel released at the outfall is tracked as an individual particle obeying the advection-diffusion equation, solved here with a Monte-Carlo random-walk (Langevin) scheme rather than a grid PDE solver — mathematically equivalent for a point source:
∂C/∂t + u·∇C = D∇²C − kC
dX = u(x)·dt + √(2D·dt)·N(0,1)
C(t) = C₀·e^(−k·t)
- Flow speed — sets the advection velocity u(x); the channel core moves faster than the banks (parabolic profile), so the plume stretches downstream and bends toward mid-channel.
- Release rate — how many pollutant parcels leave the outfall per second; higher rates raise peak concentration and push the ГДК-exceedance zone further downstream.
- Persistent vs biodegradable — sets the decay constant k in C(t)=C₀e^(−kt). Persistent compounds (PCBs, PFAS) use a small k and barely dilute away; biodegradable ones (many pesticides) use a large k and collapse within seconds.
- MAC threshold (ГДК) — the maximum admissible concentration; the riverbed heatmap turns red wherever local concentration exceeds it, and stays blue/green in water already safe to use.
Real-world relevance: this is the same particle-tracking approach environmental agencies use to model an accidental spill or an outfall pipe — predicting how far downstream a river stays above a legal safety limit, and how pollutant persistence changes that distance by orders of magnitude.