Compare carbon stocks on fixed-depth and equivalent-mass bases

Connect the Earth-system mechanism

Soil carbon concentration is a mass fraction, not an areal stock. To estimate stock, multiply the relevant fine-earth mass per area by its carbon fraction. Layer thickness, bulk-density definition and coarse fragments determine that mass. Weathering, organic inputs, erosion and compaction can change different parts of this calculation.

Build the declared budget

The original layer covers one hectare to 0.2 m depth, with 10% coarse-fragment volume. Bulk density is explicitly defined per fine-earth volume. Thus fine-earth mass is 10000×0.2×0.9×density Mg/ha, and carbon stock is that mass times the percentage divided by 100. If a measured density already incorporated the coarse-fragment correction, multiplying by 0.9 again would double-correct.

Separate the competing quantities

A fixed depth can contain different soil masses after compaction, swelling or erosion. An equal-soil-mass comparison asks about a common mass instead. Here the reference is 2520 Mg fine earth/ha; the uniform-profile assumption permits extending sampling depth to 0.28/density metres to represent it. Actual depth gradients require layer-specific measurements rather than automatic extrapolation.

Challenge the inference

An increased carbon percentage is not necessarily atmospheric carbon sequestration. Loss of mineral material, lateral deposition or changed sampled mass can alter the concentration or stock. A causal management claim needs repeated comparable inventories, uncertainty, soil history and other fluxes. These supplied values are a measurement-basis exercise, not a real carbon-credit calculation.

Worked original packet

At density 1.2 Mg/m³ and carbon 3%, fixed-depth mass 2160 Mg/ha gives 64.8 Mg C/ha. At the reference soil mass 2520, carbon stock is 75.6 Mg C/ha; required depth is 0.2333 m under the uniform-profile assumption. These are different comparison bases, not competing arithmetic answers.

Investigation

Hold carbon 2% and compare density 1.0 with 1.4. Reconstruct fixed-depth and equal-mass stocks and identify what additional profile information an actual equal-mass comparison needs.

Changed-case transfer

At density 1.0 and carbon 2%, calculate fixed-depth stock and equal-mass stock. Compare with density 1.4 at the same carbon fraction.

Feedback

Fixed-depth stock 36 versus 50.4 Mg C/ha; equal-mass stock 50.4 in both. The fixed-depth comparison samples different fine-earth masses, so it cannot alone establish carbon gain or loss from the same material.

Sources and evidence boundary

Original prose, numerical packets and exercises. Mechanism/method context checked 30 October 2026: primary source. These are conditional computational models, not measured field records, carbon credits, safe yields, treatment standards or independent mastery. No physical extraction, chemical addition or environmental release is requested.