Clumped-isotope measurements in CO₂ and carbonates (Δ₄₇) present a number of technical challenges and require correcting for various sources of analytical nonlinearity. For now, we lack a formal description of the analytical errors associated with these correction steps, which are not accounted for in most data processing methods currently in use. Here we formulate a quantitative description of Δ₄₇ error propagation, fully taking into account standardization errors and their properties. We find that standardization errors are highly sensitive to the isotopic compositions (δ₄₇, Δ₄₇) of unknown samples relative to the standards used for analytical corrections, and in many cases constitute a non-negligible source of uncertainty, causing true measurements errors to exceed traditionally reported error estimates by a factor of 1.5 (typically) to 3.5 (in extreme cases). Using Monte Carlo simulations based on the full InterCarb data set, we find that this model yields accurate error estimates in spite of small non-Gaussian effects which remain entirely negligible in practice. We also describe various standardization strategies, along with the assumptions they rely on, in the context of this model, and propose a new, “pooled” standardization approach designed to yield more robust/accurate corrections. Among other uses, the mathematical framework described here may be helpful to improve standardization protocols (e.g., anchor/unknown ratios) and inform future efforts to define community reference materials. What is more, these models imply that the inter-laboratory scatter (N = 5,329) observed in the InterCarb exercise (Bernasconi, Daëron, et al., 2021) can be entirely explained as the effects of current standardization procedures. Based on these findings, we recommend that future studies systematically report full analytical uncertainties taking standardization errors into account. In line with this recommendation, we provide user-friendly online resources and an open-source Python library designed to facilitate the use of these error models.

中文翻译：

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充分传播Δ47测量中的分析不确定性

在CO结块同位素测量₂和碳酸盐（Δ ₄₇）存在许多技术挑战和需要校正用于分析非线性的各种来源。目前，我们还没有对与这些校正步骤相关的分析误差的正式描述，在当前使用的大多数数据处理方法中都没有考虑这些误差。在这里，我们制定Δ的定量描述₄₇错误传播，充分考虑到标准化的错误和他们的财产。我们发现，标准化误差的同位素组成高度敏感（δ ₄₇，Δ ₄₇）相对于用于分析校正的标准的未知样品），并且在许多情况下构成了不可忽略的不确定性来源，导致真实的测量误差比传统报告的误差估计高出1.5（通常）至3.5（在极端情况下） ）。使用基于完整InterCarb数据集的蒙特卡洛模拟，我们发现尽管存在很小的非高斯效应，但该模型仍可产生准确的误差估计，但在实践中仍然可以忽略不计。在此模型的背景下，我们还将描述各种标准化策略，以及它们所依赖的假设，并提出一种新的“合并的”标准化方法，旨在产生更可靠/更准确的校正。除其他用途外，此处描述的数学框架可能有助于改善标准化协议（例如，锚/未知比率），并为将来定义社区参考材料的工作提供信息。而且，这些模型暗示着实验室间的分散性（ 在InterCarb演习中观察到的N = 5,329（Bernasconi，Daëron等，2021）可以完全解释为当前标准化程序的效果。基于这些发现，我们建议未来的研究系统地报告所有分析不确定性，并考虑标准化误差。根据此建议，我们提供了用户友好的在线资源和旨在简化这些错误模型的使用的开源Python库。