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Commerce · IV.10 · MMXXVI · daylight
ASSESSMENT · Chapter IV.10 — Measuring Regeneration
Three instruments: a ten-point quiz, eight reflection questions, five essay prompts. The quiz checks comprehension rather than recall. The reflections are private and first-person. The essays are arguable from more than one side.
THE QUIZ — ten points
Four on recall.
1. Define kappa and state the three bands that matter.
κ is total verification cost divided by the value of the claim verified. Below about 0.10 the claim is a commodity; between 0.10 and 0.25 it is workable with discipline; above 1.00 it costs more to prove than it is worth. One mark for the ratio, one for recognising that κ > 1 is a statement about the claimant and the method, not about whether the carbon is real.
2. Write the paired-difference variance and say what ρ represents.
σ_d² = 2σ²(1 − ρ), where ρ is the correlation between the two visits to the same georeferenced point. It is high in soil because most within-field variance is spatial rather than temporal, and a relocated point carries its spatial term forward into both readings.
3. State GEDI's published error requirement and why publishing it that way matters.
The 1 km cell mean aboveground biomass density is required to fall within 20 Mg/ha or 20 percent. It matters because the mission states a bound rather than a value, which is what makes the instrument usable by somebody who has to decide whether it can resolve their effect.
4. Name the three structures that move kappa, and which term of the cost each one attacks.
Aggregation attacks the fixed cost
C_fixed. Tiered assurance attacks the marginal costc_ha. Outcome proxies attack both and pay for it in a wider uncertainty deduction. Full marks require naming which term, not just the three names.
Four on application.
5. A consultant offers your co-operative annual soil sampling at 20 points per field, presented as rigorous because it is yearly. Diagnose it.
Two failures. Twenty points is below the 45 the paired design needs at ρ = 0.90, so the minimum detectable difference is wider than 1.4942 t C/ha. And the interval is wrong in the opposite direction: even at 45 points the smallest resolvable change takes 4.98 years to accrue at 0.30 t C/ha/yr, so every annual reading is inside the noise band. The stronger answer notes that the same money spent on more points at a five-year interval buys an answer, and that a published near-zero reading is very hard to withdraw.
6. A developer says their remote-sensing method makes verification "ten times cheaper." What do you ask for, and why?
The measured error of the proxy against direct observation on a calibration subsample, and the uncertainty deduction set from that measurement. A cheap proxy with an asserted error term produces systematic over-crediting that is invisible in any individual transaction — the finding Badgley and colleagues documented in California's forest offsets. Credit answers that also ask for the calibration fraction as a covenanted minimum, since trimming it in year four changes no published number.
7. A 300-hectare estate wants to sell a soil carbon claim at $20 a tonne and asks whether it can go alone. Answer with a number.
No. At 300 ha the value is 300 × 79.20 = $23,760.00 against a verification cost of $30,900.00 for two strata, so κ = 1.301. More decisively, the per-hectare cost of $24.75 already exceeds 25 percent of the $79.20 per-hectare value, so no area clears at that tolerance under direct measurement. It must either pool, adopt tiered assurance, or wait for a higher price.
8. Why does the chapter treat the marker register as a balance-sheet asset rather than an expense?
Because it is a one-off expenditure producing a stream of future verification capability: it is what buys ρ = 0.90, and it survives changes of owner, standard, registry and government. Expensing it invites its removal in a cost review; capitalising it and conveying it with title makes the saving durable. The stronger answer prices it: $135.00 of markers avoids $44,220.00 of field and laboratory cost, a return of 327.6 times.
Two that require the arithmetic to be done.
9. A soil has σ = 8.00 t C/ha. You must detect Δ = 1.50 t C/ha at 95 percent confidence and 80 percent power. How many cores do you need sampling independently at two dates, and how many revisiting the same points at ρ = 0.90? Show your working.
k = (1.959964 + 0.841621)² = 7.848880. Independent:n = 2kσ²/Δ² = 2 × 7.848880 × 64 ÷ 2.25 = 446.51→ 447 cores per date. Paired:σ_d² = 2 × 64 × 0.10 = 12.80, son = 7.848880 × 12.80 ÷ 2.25 = 44.65→ 45 cores, which is 9.93 times fewer. Credit any method reaching roughly 450 and roughly 45. The point of the question is that the ratio between them is bought with a stake in the ground.
10. A pool has C_fixed of $16,500.00 and a marginal cost of $2.74 per hectare. Saleable abatement is 3.080 t CO₂e/ha over five years. At a 25 percent tolerance, how many hectares must be pooled at $20 a tonne, and how many two-hectare holdings is that?
V_ha = 3.080 × 20 = $61.60.κ_max · V_ha = 0.25 × 61.60 = $15.40.H = 16,500 ÷ (15.40 − 2.74) = 16,500 ÷ 12.66 = 1,303.1 ha, which is 652 holdings of two hectares. The stronger answer states the conclusion in the right register: this is not a measurement problem, it is a membership problem, and a membership problem is solved by a list the co-operative already has.*
REFLECTION — eight questions, for one person and a pen
These are not for a room. Write the answers by hand if you can; the slowness is the point.
- What is the most important thing you currently assert about your work that you have never measured? What would it cost to find out, and what has stopped you paying it?
- Where have you gone back to exactly the same place to take a second reading — in any part of your life — and what did the repetition let you see that a single visit never would?
- Think of a time you were told a number and did not ask for its error bar. What did that cost, and what made asking feel impolite?
- What in your work is the equivalent of the three-dollar stake: a small, unglamorous, one-off decision that would make everything downstream cheaper and that nobody has taken because it is not interesting?
- Where are you measuring something more often than it can possibly change? Name it honestly, including the things you check daily out of anxiety rather than information.
- What claim would you like to be able to make that you currently cannot prove? Write out what proving it would actually require, in hours and in money, before deciding how you feel about the figure.
- When have you belonged to something that bought you a capability you could never have bought alone? What did membership cost you that was not money?
- Where in your life is the honest answer I do not know, and finding out costs more than the answer is worth? Sit with that sentence rather than resolving it. Notice whether it feels like a defeat or a relief.
ESSAY PROMPTS — five
Each is arguable from more than one side. Each requires at least one source the chapter cites and at least one it does not.
1. The unverifiable majority. The chapter computes κ between 31.6 and 327.7 for a two-hectare holding depending on price and audit depth, and observes that 84 percent of the world's farms are under two hectares. Argue either that the correct response is to build pooling structures until every smallholder can access a verified market, or that the correct response is to abandon outcome-based crediting for smallholders entirely in favour of practice-based payment. Use Lowder, Sánchez and Bertini (2021), and one source on smallholder carbon project outcomes that the chapter does not cite.
2. Is a proxy a measurement? Outcome proxies reduce κ from 0.366 to 0.058 at five thousand hectares, and pay for it with a deduction widening from 10 to 30 percent. Argue whether a claim verified by calibrated proxy is epistemically the same kind of object as one verified by direct sampling, or a different and lesser one that should be traded in a separate market. Engage Badgley et al. (2022) directly, and at least one defence of model-based quantification the chapter does not cite.
3. The aggregator's power. Once verification is carried at pool level, no individual member's claim is verifiable even in principle, and the aggregator becomes the only counterparty a farmer has. Write the case that this is an acceptable and well-precedented concentration — cooperatives, mutual insurers and audit firms all do it — and then the strongest rebuttal. Use Ostrom (1990) on congruence between rules and local conditions, and one account of aggregator capture or cooperative governance failure that the chapter does not cite.
4. Measurement as intervention, applied to soil. Chapter II.10 argues that a measure enters the system it reports on. Apply that to a soil carbon market: argue whether paying for measured stock change will produce genuine soil recovery or a farming practice optimised for the top thirty centimetres at the expense of everything below it. Use Kravchenko and Robertson (2011) on whole-profile stocks, and one source on agronomic response to incentive design that the chapter does not cite.
5. Who should pay for verification? The chapter assumes the claimant funds their own proof out of the claim's proceeds, which is what produces κ. Argue instead that verification is a public good — like the LUCAS network, like national statistical offices, like the Rothamsted archive — and should be funded as infrastructure rather than as a transaction cost. Then argue the opposite: that publicly funded verification becomes captured by the interests it verifies. Use Orgiazzi et al. (2018) or Johnston and Poulton (2018), and one source on the political economy of official statistics that the chapter does not cite.