A one-metre soil monolith holds carbon in three pools that turn over in years, decades and centuries. Pick a land use change or a warming scenario, press Start and watch the stock, the CO2 flux and the darkening of the topsoil.
Run an experiment. They run on copies and do not disturb the live run.
The science
Three-pool cascade. Active (microbial biomass, fresh residues), slow (stabilised organic matter) and passive (mineral-bound, charcoal-like) carbon obey dA/dt = I − kAA, dS/dt = hASkAA − kSS, dP/dt = hSPkSS − kPP (t C ha-1 yr-1). The humification fractions are hAS = 0.35 and hSP = 0.06; the rest of what each pool decomposes is respired as CO2. Reference rates at 15 °C and optimal moisture are kA = 0.5, kS = 0.05, kP = 0.003 yr-1. These are illustrative values in the spirit of the Century and RothC models, tuned so that stocks land in the realistic 40–150 t C/ha range for the top metre; they are not calibrated to a site.
Equilibrium and transients. With constant conditions the stock settles at C* = I (1/kA + hAS/kS + hAShSP/kP), and the whole time course is a sum of three exponentials with rates kA, kS, kP — the page solves that closed form independently and compares it to the time-stepped (RK4) solution. The passive pool needs centuries, so management changes pay back (or cost) slowly at first in the fast pools and only much later in the large slow pools.
Climate, moisture, tillage, clay. Every rate is multiplied by Q10(T−15)/10 (Q10 default 2) and a moisture factor fW = max(0.05, 1 − ((θ − 0.6)/0.55)²). Tillage multiplies kA by 1.5 and kS by 1.25 (aeration and broken aggregates; assumption). Clay protects slow and passive carbon: kS, kP are multiplied by 1 − 0.012 × clay% and kA by 1 − 0.1 × clay%/30 (assumption). Warming ramps linearly over 80 years.
Not modelled: depth structure (the darkening with depth in the picture is drawn, not simulated), nitrogen limitation, priming, erosion, leaching and dissolved carbon, plant-growth feedback on inputs (inputs are fixed numbers you choose), methane, real weather. Soil carbon sequestration claims need measured data; treat this as a teaching model of turnover times, not a carbon-credit calculator.