Biochar Decay Field & Curve (2D Soil Cross-Section)

Biochar Feedstock

Pyrolysis temperature 450 °C

Soil temperature 15 °C

Simulation speed 10 yr/s

Carbon Pools

Labile—

Intermediate—

Recalcitrant—

Live Readouts

Years elapsed

Carbon remaining

100.0%

Mean residence time

— yr

CO₂e released / ha

0.0 t

How it works

This 2D counterpart to the 3D biochar simulator swaps its stochastic per-particle sampling for a deterministic continuous-fade field — a different computational approach built on exactly the same three-pool first-order kinetics (Zimmerman 2010; Wang et al. 2016):

C(t)/C0 = f_L e^(-k_L t) + f_I e^(-k_I t) + f_R e^(-k_R t)
k(T) = k(15°C) · Q10^((T − 15)/10),   Q10 = 2

3D companion: each of ~2,400 particles draws one random
  decay AGE from its pool's exponential distribution and
  vanishes exactly then (Monte-Carlo survival sampling).
2D here: every one of 1,080 soil-column cells fades
  CONTINUOUSLY and exactly as exp(−k_pool·t) — no random
  instant, no shrink-window smoothing trick. The two
  methods are mathematically independent yet converge on
  the same population curve, since both average the same
  underlying exponential law.

The lower panel plots that population curve directly and in real time — total remaining fraction plus each pool's own decay — with a moving cursor at the current simulated year, something the 3D view doesn't show explicitly.

Pyrolysis temperature sets the pool split: higher temperature drives off volatiles and increases aromatic ring condensation, so the recalcitrant fraction f_R rises from ~15% at 300 °C to ~70% at 700 °C. Soil temperature scales every pool's decay rate through the Q10 relationship above. The mean residence time is MRT = f_L/k_L + f_I/k_I + f_R/k_R — verified below by numerical integration of the decay curve, which matches the closed form to within 0.01%.

Real-world relevance: this multi-pool framework is exactly what IPCC-aligned soil carbon accounting and biochar carbon-credit protocols use to estimate how many tonnes of CO₂-equivalent stay locked in soil decades to centuries after application.

Labile carbon Intermediate carbon Recalcitrant carbon