标题： 基于模型的MRV估计：如何在不损害科学完整性的前提下提高SOC固存项目的经济效益 显示英文标题

标题： Model-assisted estimation for MRV: How to boost the economics of SOC sequestration projects without compromising on scientific integrity

摘要： 土壤有机碳（SOC）封存项目需要无偏、精确且成本效益高的监测、报告和核查（MRV）系统，这些系统需在采样成本与监管框架施加的不确定性扣除之间取得平衡。 基于设计的估计量保证无偏性，但无法利用辅助数据。 基于模型的方法（VCS 方法学 VT0014 v1.0（2025））可以提高精度，但每个项目都需要独立验证。 模型辅助估计提供了一种稳健的折中方案，将模型预测与概率抽样相结合，在保留基于设计的保证的同时提高精度。 我们通过一项广泛的模拟研究评估了简单回归估计量（SRE）的科学完整性和效率，这是一种广为人知的模型辅助估计量。 我们的模拟涵盖了多样的SOC储量方差、样本量和模型性能。 我们评估了三个核心属性：经验偏差、经验置信区间覆盖率以及相对于基于设计的Horvitz-Thompson估计量（HTE）的精度提升。 结果表明，当n > 40时，无论SOC储量方差如何，偏差都很小且覆盖概率有效。 在此阈值以下，方差近似和正态性假设会产生不可靠的不确定性估计。 当辅助变量相关（r^2 = 0.3）时，SRE相对于HTE的精度提高了30%。 当辅助变量不相关时，没有观察到精度提升，但当n >= 40时，性能会趋近于HTE。 模型辅助估计可以在不损害科学严谨性的情况下提高项目经济效益。 监管机构应允许此类估计量，同时规定最低样本量阈值。 当存在相关辅助变量时，项目发起人应常规使用此类估计量。 行业应优先获取高质量的项目特定协变量，以最大化精度提升并从而提高项目经济效益。 显示英文摘要

摘要： Soil organic carbon (SOC) sequestration projects require unbiased, precise and cost-effective Monitoring, Reporting, and Verification (MRV) systems that balance sampling costs against uncertainty deductions imposed by regulatory frameworks. Design-based estimators guarantee unbiasedness but cannot exploit auxiliary data. Model-based approaches (VCS Methodology VT0014 v1.0 (2025)) can improve precision but require independent validation for each project. Model-assisted estimation offers a robust compromise, combining model predictions with probability sampling to retain design-based guarantees while improving precision. We evaluate the scientific integrity and efficiency of the simple regression estimator (SRE), a well-known model-assisted estimator, via an extensive simulation study. Our simulations span diverse SOC stock variances, sample sizes, and model performances. We assess three core properties: empirical bias, empirical confidence interval coverage, and precision gain relative to the design-based Horvitz-Thompson estimator (HTE). Results show negligible bias and valid coverage probabilities for n > 40, regardless of SOC stock variance. Below this threshold, variance approximations and normality assumptions yield unreliable uncertainty estimates. With correlated ancillary variables (r^2 = 0.3), SRE achieves 30% precision gains over HTE. With uncorrelated variables, no gains are observed, but performance converges to HTE for n >= 40. Model-assisted estimation can enhance project economics without compromising scientific rigor. Regulators should permit such estimators while mandating minimum sample size thresholds. Project proponents should routinely employ such estimators when correlated ancillary variables exist. The industry should prioritize the retrieval of high-quality, project-specific covariates to maximize precision gains and thereby the project economics.