Propagating Uncertainty in Predicting Individuals and Means Illustrated with Foliar Chemistry and Forest Biomass

IF 4.3 3区材料科学 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC ACS Applied Electronic Materials Pub Date : 2024-01-22 DOI:10.1007/s10021-023-00886-6

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Abstract

Quantifying uncertainty is important to establishing the significance of comparisons, to making predictions with known confidence, and to identifying priorities for investment. However, uncertainty can be difficult to quantify correctly. While sampling error is commonly reported based on replicate measurements, the uncertainty in regression models used to estimate forest biomass from tree dimensions is commonly ignored and has sometimes been reported incorrectly, due either to lack of clarity in recommended procedures or to incentives to underestimate uncertainties. Even more rarely are the uncertainty in predicting individuals and the uncertainty in the mean both recognized for their contributions to overall uncertainty. In this paper, we demonstrate the effect of propagating these two sources of uncertainty using a simple example of calcium concentration of sugar maple foliage, which does not require regression, then the mass of foliage and calcium content of foliage, and finally an entire forest with multiple species and tissue types. The uncertainty due to predicting individuals is greater than the uncertainty in the mean for studies with few trees—up to 30 trees for foliar calcium concentration and 50 trees for foliar mass and calcium content in the data set we analyzed from the Hubbard Brook Experimental Forest. The most correct analysis will take both sources of uncertainty into account, but for practical purposes, country-level reports of uncertainty in carbon stocks can safely ignore the uncertainty in individuals, which becomes negligible with large enough numbers of trees. Ignoring the uncertainty in the mean will result in exaggerated confidence in estimates of forest biomass and carbon and nutrient contents.

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用叶面化学和森林生物量说明在预测个体和平均值时传播不确定性

摘要量化不确定性对于确定比较的重要性、以已知的置信度进行预测以及确定投资的优先次序非常重要。然而，不确定性可能难以正确量化。根据重复测量通常会报告采样误差，而根据树木尺寸估算森林生物量的回归模型的不确定性通常会被忽视，有时还会被错误报告，其原因可能是推荐程序不明确，也可能是低估了不确定性。预测个体的不确定性和平均值的不确定性对总体不确定性的影响也很少得到认可。在本文中，我们以糖枫叶片钙浓度（无需回归）、叶片质量和叶片钙含量以及具有多个物种和组织类型的整片森林为例，展示了传播这两个不确定性来源的影响。在我们分析的哈伯德布鲁克实验林数据集中，叶钙浓度的不确定性高达 30 棵树，叶片质量和钙含量的不确定性高达 50 棵树。最正确的分析应将这两种不确定性都考虑在内，但在实际应用中，国家级碳储量不确定性报告可以安全地忽略个体的不确定性，因为个体的不确定性在树木数量足够多时可以忽略不计。忽略平均值的不确定性将导致对森林生物量、碳含量和养分含量估计的可信度过高。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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