An economic stochastic framework for optimizing soil sampling in carbon farming

Accurate estimation of soil organic carbon (SOC) stocks is crucial for climate mitigation initiatives and carbon markets; however, soil sampling remains costly and uncertain. Conventional sampling designs typically prioritize statistical precision while often neglecting the economic implications of sampling costs and uncertainty deductions on potential revenues. We present an economic stochastic framework to determine the optimal number of soil samples for estimating SOC stock changes in the topsoil (0–30 cm). Using empirical data from 371 Brazilian agricultural plots (≈40 ha each) sampled at two time points over a three-year interval, we model SOC stock changes under a hierarchical prior and propagate uncertainty through analytical variance estimation combined with Monte Carlo simulation. The optimization problem maximizes expected net returns by accounting for sampling costs, carbon prices, plot area, stock changes, and uncertainty deductions consistent with Verra’s VM0042 methodology, under alternative remuneration scenarios at both the individual plot and project levels. Results show that optimal sampling intensity varies nonlinearly with both carbon price and per-sample cost, with greater sensitivity to carbon price. The framework also reveals that uncertainty discounting strongly influences optimal decisions, particularly at lower carbon price levels (<5 USD per Mg CO₂e). This approach integrates stochastic modeling, economic optimization, and value-of-information analysis into soil carbon monitoring design, providing a transparent and scalable decision-support tool for carbon projects and protocol development. It enables dynamic, cost-effective sampling strategies that better align measurement efforts with economic incentives and uncertainty management in soil carbon accounting.