INTERACTIVE COMPANION · REVIEW · SOIL SCIENCE

The Soil Carbon Bench

A live model accompanying “How Much Carbon Can Farmland Actually Hold?”

Two benches below. The first pools the same twelve effect sizes the article pools, and lets you refuse to count any study that did not dig deep enough. The second fills a soil to its ceiling and tells you how many years of sequestration a practice actually buys before it stops.

Everything here is the club's own arithmetic, identical to soil-carbon-review.py. On the default settings both benches reproduce the numbers printed in the article, which is the only way we know to keep an interactive honest.

Bench 1. Pool it, then demand a deeper core

The estimator is DerSimonian-Laird. Effects are log response ratios, $y = \ln(1 + p/100)$, weights are $w_i^* = 1/(v_i + \hat\tau^2)$, and the between-study variance is

$$\hat\tau^2 = \max\left(0,\ \frac{Q - (k-1)}{\sum w_i - \sum w_i^2 / \sum w_i}\right)$$

Drag the depth slider and watch two things at once. The diamond moves, which is the headline. And $k$ falls off a cliff, which is the real story: the literature that sampled below the plough layer barely exists.

Minimum sampling depth required any Start at zero, which is what most credit protocols effectively do. The pooled figure is +16.2%. Now drag to 30, which is what a careful protocol asks for, and then to 40. At 40 centimetres exactly one entry in our whole dataset still qualifies, and it reports +3.8%. Studies that never state their depth drop out as soon as you ask for any. Which practices to count Switch between the two families with depth set to zero. Rearranging practices pool to +10.9%, importing practices to +35.6%, and the heterogeneity in the importing group collapses to I² = 0. Three studies agreeing that closely is partly luck, but the gap between the families is not. Interval to draw The confidence interval says how well we know the average of these studies. The prediction interval says where a new field would land, and on the full pool it runs from −1.7% to +37.3%. Switch to it and see how much of the honest answer the confidence interval was hiding.

studies kept: 12 pooled: +16.2% 95% CI: 11.3 to 21.2 I²: 98.1% τ²: 0.0051

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Bench 2. Filling a soil, and finding the bottom of the well

Carbon enters the stable pool at some annual rate and leaves in proportion to how much is already there. One line of calculus, two constants, and a closed solution:

$$\frac{dC}{dt} = I - kC, \qquad C(t) = C_{\text{eq}} + (C_0 - C_{\text{eq}})e^{-kt}, \qquad C_{\text{eq}} = \frac{I}{k}$$

The baseline input is set to whatever holds your starting stock steady, $I_0 = kC_0$, so the field begins at equilibrium and the only thing changing anything is the extra input the practice brings. The annual gain in year $t$ is then $\Delta I\,e^{-kt}$, which is a decaying exponential, and the total available gain is $\Delta I / k$ no matter how long you wait.

Starting stock C₀ 45 Mg C/ha 45 is a mid-range arable soil over the top 30 centimetres. A degraded sandy soil might be 20, a long-term grassland 90. Move it and notice that the total gain available does not change at all. Only the ceiling moves, because the gain depends on the extra input and the loss constant, never on where you started. Extra input from the practice ΔI 0.50 Mg C/ha/yr This is additional carbon reaching the stable pool, not additional biomass. A vigorous cover crop might manage 0.5. Set it to zero and nothing happens, which is the point: the practice has to actually increase the input, and several of them mostly move carbon around instead. Loss constant k 0.030 per year How fast the stable pool respires away, and the single most important number here. Halve it to 0.015 and the ceiling doubles while the approach takes twice as long. Warm wet soils sit at the high end, which is why the same practice buys far less in the tropics. Call it finished below 0.10 Mg C/ha/yr A credit is not worth verifying below some rate, because the sampling error swamps it. Set your own threshold and the readout tells you how many years the practice buys before it crosses. On the defaults that is 53.6 years. Raise the threshold to 0.30 and it drops to 17. Sweep the decades Runs a cursor along the curve so you can watch the annual gain die. It respects a reduced-motion preference and stops on its own when the tab is hidden.

ceiling: 61.7 Mg C/ha total gain: 16.67 Mg C/ha banked by year 20: 7.52 years bought: 53.6 at $50/t CO₂e, year one: $91.67/ha

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Bench 1 default: k = 12, pooled +16.2%, 95% CI 11.3 to 21.2, I² = 98.1%
Depth ≥ 40 cm: k = 1, +3.8%, 95% CI 1.4 to 6.3
Bench 2 default: ceiling 61.67, total gain 16.67, year-20 gain 7.52, 53.6 years bought
Checked by hand: C(20) = 61.667 − 16.667·e^−0.6 = 52.52, so the gain is 7.52; ln(0.50/0.10)/0.03 = 53.6

One last thing the second bench makes obvious, and it is the reason we ended up sceptical rather than merely careful. Move the extra input up to its maximum and the ceiling climbs, but the shape never changes. There is no setting at which the annual gain stops decaying. Every soil carbon contract is therefore a contract on a quantity that shrinks every year it runs, which is an awkward thing to build a thirty-year market on.