Abstract. Leading an effective response to the accelerating crisis of anthropogenic climate change will require improved understanding of global carbon cycling. A critical source of uncertainty in Earth Systems Models (ESMs) is the role of microbes in mediating both the formation and decomposition of soil organic matter, and hence in determining patterns of CO₂ efflux. Traditionally, ESMs model carbon turnover as a first order process impacted primarily by abiotic factors, whereas contemporary biogeochemical models often explicitly represent the microbial biomass and enzyme pools as the active agents of decomposition. However, the combination of non-linear microbial kinetics and ecological heterogeneity across space guarantees that upscaled dyamics will violate mean-field assumptions via Jensen’s Inequality. Violations of mean-field assumptions mean that parameter estimates from models fit to upscaled data (e.g. eddy covariance towers) are likely systematically biased. Here we present a generic mathematical analysis of upscaling michaelis-menten kinetics under heterogeneity, and provide solutions in dimensionless form. We illustrate how our dimensionless form facilitates qualitative insight into the significance of this scale transition, and argue that it will facilitate cross site intercomparisons of flux data. We also identify the critical terms that need to be constrained in order to unbias parameter estimates.

中文翻译：

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从生物地球化学模型中的Michaelis-Menten微生物动力学的升级中获得的理论见解：无量纲方法

摘要。要对人为气候变化加剧的危机做出有效反应，就需要对全球碳循环有更好的了解。地球系统模型（ESM）中不确定性的一个关键来源是微生物在介导土壤有机物的形成和分解，从而确定CO _2的模式方面的作用。外排。传统上，ESM将碳转化建模为主要受非生物因素影响的一阶过程，而现代生物地球化学模型通常明确表示微生物生物量和酶库是分解的活性剂。但是，非线性微生物动力学和整个空间的生态异质性的结合保证了放大的动力学将通过Jensen不等式违反均值场假设。违反均场假设意味着来自模型的参数估计值适合放大的数据（例如，涡度协方差塔），可能会系统地产生偏差。在这里，我们提出了在异质性下提升迈克尔斯-门腾动力学的一般数学分析，并提供了无量纲形式的解决方案。我们说明了我们的无量纲形式如何促进对这种尺度转变的重要性的定性见解，并认为这将促进通量数据的跨站点比对。我们还确定了一些关键术语，这些参数必须加以约束才能使参数估计不偏不倚。