This is the same one-box permafrost-carbon feedback loop as the 3D version — warming thaws soil → thawed soil decomposes and releases CO₂/CH₄ → those gases add radiative forcing → that forcing adds to warming — but shown as two native 2D diagrams instead of a 3D soil block: a scrolling depth-time stratigraphy (like a scientific Hovmöller diagram) and a live phase portrait of active-layer depth vs. temperature anomaly.
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
- Stratigraphy panel — depth on the vertical axis, time scrolling left-to-right; the brown/blue boundary is the active-layer front L(t) deepening as ΔT rises, and the surface tint at each column shows that instant's CO₂ (grey) / CH₄ (orange) release mix.
- Phase portrait — active-layer depth L on the x-axis, temperature anomaly ΔT on the y-axis. The pale arrows are the instantaneous flow field (dL/dt, dΔT/dt) evaluated at the current slider settings; the bright trace is the system's actual trajectory since the last reset, spiralling toward whatever equilibrium the current forcing, density, wetness and gain settle on.
- Feedback loop gain — set to 0 to see forcing-only warming with no carbon feedback at all (the trajectory settles at a fixed ΔT with no L-dependence); above 1× the trajectory bows further out before settling, showing the loop amplifying warming beyond the external driver alone.
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.