This is a cross-section of the wetland bed (x = inlet→outlet, y = water surface→bed bottom), simulated as three continuous concentration fields — [NH4+], [NO3-], [N2] — on a grid, rather than as tracked particles. Each field is advected downstream by the flow, spreads by numerical diffusion, and reacts in place using the same Monod-saturation kinetics the real process follows:
Nitrification (needs O2, saturating):
r_nit = k_nit · [NH4+] · O2/(K_O2 + O2)
Denitrification (needs carbon, inhibited by O2):
r_denit = k_denit · [NO3-] · C/(K_C + C) · (1 − O2/(O2 + K_i))
∂[NH4+]/∂t = −v·∂[NH4+]/∂x + D∇²[NH4+] − r_nit
∂[NO3-]/∂t = −v·∂[NO3-]/∂x + D∇²[NO3-] + r_nit − r_denit
∂[N2]/∂t = −v·∂[N2]/∂x − w·∂[N2]/∂y + D∇²[N2] + r_denit
The oxygen field O2(x,y) is the sum of each root's radial-oxygen-loss halo (a linear falloff from the root column out to the aerobic radius set by the ROL slider), evaluated only over the root's own depth span — exactly mirroring the 3D model's spherical microzones, but as a continuous field instead of a boundary test on discrete particles. N2 also rises (the −w·∂/∂y term) and is removed from the field the moment it reaches the water surface, tallied as gas released.
- Radial oxygen loss — widens the O2 halo around each root, feeding the nitrification saturation term.
- Organic carbon (BOD) — raises the denitrification saturation term; without it nitrate simply accumulates and advects to the outlet.
- Hydraulic loading — raises the advection velocity v, cutting residence time near roots for both reactions.
- Root density — more O2 halos distributed along x, so more of the field ever sees aerobic conditions.
Same coupled nitrification–denitrification pathway as the 3D particle model (Vymazal 2007; Brix 1997), computed here as an Eulerian reaction–diffusion–advection field — a genuinely different numerical mechanism arriving at the same biogeochemistry.