Methane Reaction-Diffusion Filter in Permafrost (2D)

Soil & Climate Controls

Water-table depth 40 cm

Soil temperature 5 °C

Methanotroph activity 1.0×

CH₄ production rate 1.0×

Live Readouts

Emission flux (atm.)

0.0 /s

Oxidized in soil

0.0 /s

Oxidation efficiency (filter strength)

0 %

CH₄ mass in soil cross-section

0.0

CH₄ concentration field (brighter = more)
Water table (saturated / unsaturated boundary)
Decomposition hotspots (patchy organic-rich zones)

How this 2D model differs from the 3D one

The 3D version tracks individual CH₄ molecules as instanced particles doing a random walk — a Monte Carlo stand-in for diffusion. This 2D version instead directly solves the governing advection-diffusion-reaction PDE on a finite-difference grid spanning a soil cross-section (width × depth), which is the actual continuum equation permafrost biogeochemistry models are built on:

∂C/∂t = D∇²C + v·∂C/∂z + S(x,z) − k_ox(z)·C

D∇²C   : Fickian diffusion (5-point Laplacian stencil)
v·∂C/∂z: upward advective drift (conservative upwind scheme)
S(x,z) : CH4 production, anoxic zone only, patchy hotspots
k_ox·C : pseudo-first-order oxidation, oxic zone only

k_ox = k0·B·Q10_ox^((T-Tref)/10)   (same form as the 3D sim)
P_total = P0·prod·Q10_p^((T-Tref)/10)

Unlike the rotationally-symmetric 3D column, this grid also resolves genuine lateral (x-axis) heterogeneity: methane production is concentrated in a few patchy hotspots near the thaw front — a real feature of permafrost active layers, where ice-wedge polygon troughs and organic-rich pockets produce far more CH₄ than the surrounding soil. You can watch plumes rise from individual hotspots and spread laterally as they diffuse toward the surface.

Water-table depth — the boundary between the anoxic production zone (below) and the oxic filter zone (above). A shallow water table leaves little oxic soil for the filter to work in.
Soil temperature — raises both the production rate and the oxidation rate constant, each with its own Q10 sensitivity, exactly as in the 3D model.
Methanotroph activity / CH₄ production rate — linear multipliers on the oxidation rate constant and the total source strength.

The top of the grid is an absorbing boundary (C = 0, representing a well-mixed atmosphere), the base and sides are no-flux (impermeable permafrost / symmetric column). A numerical check (see the simulation's build report) confirms the implementation conserves mass to floating-point precision: cumulative production always equals cumulative oxidation plus cumulative emission plus the change in stored CH₄.

CH₄ concentration Water table Hotspot

x-averaged C(depth)