Permafrost Carbon Feedback Loop

Forcing & Soil

External radiative forcing 2.5 W/m²

Soil organic carbon density 18 kg/m³

Soil wetness (anaerobic fraction) 35%

Feedback loop gain 1.0×

System State

Temp. anomaly ΔT

0.00 °C

Active layer depth

0.00 m

Cumulative carbon released

0.00 kg/m²

Feedback forcing (added to external)

0.00 W/m²

CO₂ 100%CH₄ 0%

Simulated time elapsed

0.0 yr

How it works

This is a simplified one-box climate model that closes the actual permafrost–carbon feedback loop: warming thaws soil → thawed soil decomposes and releases CO₂/CH₄ → those gases add radiative forcing → that forcing adds to warming. It is a teaching-scale model, not a literal global energy budget — the point is the shape of the loop, not planetary-scale calibration.

Active layer growth (Stefan-like, bounded):
  dL/dt = k · max(ΔT, 0) · (1 − L / L_max)

Carbon released this step:
  dC = ρ_soil · dL             (kg C / m²)
  CH₄ fraction = wetness × 0.5  (rest → CO₂)

Feedback forcing (illustrative coefficients):
  F_fb = gain · (a_CO2 · C_CO2 + a_CH4 · C_CH4)
       a_CH4 ≈ 30 × a_CO2  (methane's much higher GWP)

Temperature response (1-box energy balance):
  dΔT/dt = (F_ext + F_fb − λ·ΔT) / C_eff

External radiative forcing — the warming driver you'd get from CO₂ already in the atmosphere from other sources (a stand-in for an emissions scenario).
Soil organic carbon density — how much carbon is locked in each newly-thawed meter of ground; Arctic permafrost soils hold roughly 10–30 kg C/m³ near the surface, more in carbon-rich Yedoma deposits.
Soil wetness — waterlogged, oxygen-poor soil decomposes anaerobically and produces methane (CH₄) instead of carbon dioxide (CO₂); methane traps far more heat per molecule, so the same carbon mass does more warming.
Feedback loop gain — set to 0 to see forcing-only warming with no carbon feedback at all; above 1× shows how the loop amplifies warming beyond the external driver alone. λ (climate feedback parameter) and the bounded L_max keep the model from a literal runaway, mirroring how the real active layer only deepens so far each season.

Real-world relevance: this reinforcing loop is one of the main reasons the Arctic is warming roughly 3–4× faster than the global average, and why permafrost carbon (an estimated ~1,500 billion tonnes stored in frozen ground worldwide) is treated as a major climate tipping risk.

CO₂ released CH₄ released Thawed active layer Frozen permafrost

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