Why more sampling can make Enhanced Rock Weathering cheaper!

Sampling is one of the most consequential parts of an Enhanced Rock Weathering (ERW) monitoring, reporting and verification strategy. It is also one of the most visible MRV costs. So, there is an understandable tendency to ask:

What is the minimum number of samples we need?

But from an economic perspective, that may be the wrong question. A better question is:

How much should we sample to minimize the total cost of generating an issued carbon removal credit?

Those two questions can lead to very different answers. The reason is measurement uncertainty. Taking additional samples costs money, but additional sampling can reduce uncertainty. And when uncertainty leads to conservative deductions from measured carbon dioxide removal (CDR), reducing uncertainty has a financial value. In some circumstances, spending more on sampling can therefore make an ERW project cheaper, not more expensive.

Sampling is fundamental to ERW quantification

ERW projects are trying to quantify a relatively small geochemical change occurring within naturally heterogeneous environmental systems. Consider soil-based quantification. Soil concentrations of calcium, magnesium or other elements used to quantify weathering can vary substantially across a project area because of differences in parent material, soil properties, land management, crop history, fertilizer use, hydrology and many other factors. Against that natural variability, we are trying to detect the additional change caused by silicate weathering. The difficulty of doing so depends broadly on three things: the size of the weathering signal, the variability of the system, and the number and design of the samples used to estimate that signal. A large weathering signal in a relatively homogeneous field is comparatively easy to detect. A small weathering signal across highly heterogeneous soils is much harder. Sampling design therefore does much more than determine how much an MRV campaign costs. It determines how precisely we can estimate the CDR signal itself.

The hidden cost of uncertainty

This is where sampling economics become interesting. The direct cost of sampling is straightforward:

Sampling cost = number of samples × cost per sample

But that is only one side of the equation. There can also be an economic cost associated with uncertainty. If uncertainty causes part of the gross measured CDR to be conservatively discounted, those tonnes cannot be issued as credits. Their value can therefore be treated as an opportunity cost of measurement uncertainty. A simplified representation is:

Total MRV-related economic cost = sampling cost + value of CDR lost through uncertainty discounting

Now the trade-off becomes clearer. With very few samples, sampling expenditure is low, but uncertainty may be high. As sampling density increases, sampling expenditure rises, while uncertainty generally falls and more of the measured CDR may become eligible for issuance. Eventually, however, diminishing returns appear. Sampling uncertainty commonly decreases approximately with the square root of sample size. This means that halving the sampling component of uncertainty may require roughly four times as many samples. At some point, another sample costs more than the economic value of the additional uncertainty reduction it provides. That is the sampling optimum.

Minimum sampling is not necessarily optimal sampling

Methodologies understandably establish minimum sampling requirements. These are necessary to ensure that projects meet an acceptable baseline level of measurement robustness. But a compliance minimum and an economic optimum are fundamentally different concepts. A methodology may effectively tell a project “you must collect at least this much evidence”. It does not necessarily mean “Collecting exactly this much evidence will maximize the economics of your project.” This distinction becomes especially important where uncertainty is high and carbon removal credits have significant economic value.

For example, our modelling shows the characteristic U-shaped relationship between sampling density and all-in cost per issued credit. At low sampling densities, the dominant cost can be the value of credits lost through uncertainty. At very high densities, direct sampling expenditure starts dominating instead. The lowest point between those two regimes represents the cost-optimal sampling strategy. In other words:

The objective should not necessarily be to minimize the cost of sampling. It should be to minimize the cost of producing a robust, issuable tonne of CDR.

Variability matters just as much as sample number

There is another important implication. Sampling optimization should not be considered independently from stratification. If highly heterogeneous fields are treated as one statistical population, variability may be large and detecting the weathering signal can require a substantial number of samples. If the project can instead identify meaningful, relatively homogeneous strata based on factors such as soil type, climate, land management, crop system and relevant baseline soil properties, within-stratum variability may decrease. The same weathering signal can then potentially be estimated with greater precision.

This gives ERW developers two complementary levers:

1. Reduce variability through good experimental design and appropriate stratification.

2. Reduce sampling error through sufficient replication.

Simply increasing sample numbers without understanding the underlying spatial structure of a project can be expensive. But attempting to save money by undersampling a highly variable system can be even more expensive if the resulting uncertainty substantially reduces issuance. The sampling strategy therefore needs to be designed around the actual characteristics of the deployment.

Small weathering signals make the problem harder

Sampling optimization can also change over the lifetime of an ERW project. The relationship between signal and noise matters enormously. If a monitoring period produces a large weathering signal relative to background variability, a moderate number of samples may characterize it reasonably well. If the incremental weathering signal becomes smaller in a later monitoring period while environmental variability remains similar, relative uncertainty can increase sharply.

Our modelling illustrates exactly this behaviour: as the assumed annual weathering signal decreases, substantially greater sampling effort can be required to maintain comparable relative uncertainty. Under sufficiently high variability and a sufficiently small signal, the measurement can eventually become economically difficult to resolve even with substantial additional sampling. This means that a fixed sampling density applied mechanically every year is not necessarily the most efficient MRV strategy. Sampling should ideally respond to expected signal magnitude, observed variability and the economics of the project.

Finding the sampling sweet spot

There is no universal optimum number of samples for an ERW project. The answer depends on the project's heterogeneity, expected weathering rate, quantification approach, spatial design, analytical costs, carbon value and applicable uncertainty requirements. But those parameters can be modelled. And ideally, that modelling should happen before the monitoring campaign is designed, rather than after samples have already been collected.

At CDRexperts, we work on sampling design, uncertainty propagation and techno-economic modelling for ERW MRV. We can model how changes in sampling density and environmental variability affect measurement uncertainty, potential conservativeness deductions and the resulting cost per issued tonne of CDR.

If you are designing an ERW sampling campaign and want to understand whether collecting more samples could actually save your project money, get in touch with us.