Data from: Quantifying and reducing uncertainties in estimated soil CO2 fluxes with hierarchical data-model integration

Non-steady state chambers are often employed to measure soil CO2 fluxes. CO2 concentrations (C) in the headspace are sampled at different times (t), and fluxes (f) are calculated from regressions of C versus t based a limited number of observations. Variability in the data can lead to poor fits and unreliable f estimates; groups with too few observations or poor fits are often discarded, resulting in “missing” f values. We solve these problems by fitting linear (steady state) and non-linear (non-steady state, diffusion based) models of C versus t, within in a hierarchical Bayesian framework. Data are from the Prairie Heating and CO2 Enrichment (PHACE) study that manipulated atmospheric CO2, temperature, soil moisture, and vegetation. CO2 was collected from static chambers bi-weekly during five growing seasons, resulting in >12,000 samples and >3100 groups and associated fluxes. We compare f estimates based on non-hierarchical and hierarchical Bayesian (B vs HB) versions of the linear and diffusion-based (L vs D) models, resulting in four different models (BL, BD, HBL, HBD). Three models fit the data exceptionally well (R2 ≥ 0.98), but the BD model was inferior (R2 = 0.87). The non-hierarchical models (BL, BD) produced highly uncertain f estimates f (wide 95% CIs), whereas the hierarchical models (HBL, HBD) produced very precise estimates. Of the hierarchical versions, the linear model (HBL) underestimated f by ~33% relative to the non-steady state model (HBD). The hierarchical models offer improvements upon traditional non-hierarchical approaches to estimating f, and we provide example code for the models.

非稳态箱（Non-steady state chambers）常被用于土壤CO₂通量的测定工作。研究人员会在不同时刻（t）采集顶空（headspace）中的CO₂浓度（C），并基于有限的观测次数，通过C与t的回归分析计算通量（f）。观测数据的变异性可能导致拟合效果不佳，进而得到可靠性不足的f估计值；观测次数过少或拟合效果较差的分组常会被剔除，最终产生‘缺失’的f值。为解决上述问题，我们在分层贝叶斯（hierarchical Bayesian）框架下，针对C与t的关系分别拟合线性（稳态）模型与非线性（非稳态、基于扩散）模型。本数据集源自草原升温与CO₂富集（Prairie Heating and CO₂ Enrichment, PHACE）研究，该研究对大气CO₂浓度、温度、土壤湿度及植被群落进行了人工调控。研究人员在五个生长季内，每两周一次通过静态箱（static chambers）采集CO₂样本，最终获得超过12000个有效样本、3100余个分组及对应的通量数据。我们分别基于非分层贝叶斯与分层贝叶斯（B vs HB）框架下的线性模型，以及基于扩散的模型（L vs D）进行f值估算，由此得到四种不同的模型：BL、BD、HBL、HBD。其中三种模型的拟合效果极佳，决定系数（coefficient of determination, R²）≥0.98，但BD模型的拟合表现较差，R²仅为0.87。非分层模型（BL、BD）得到的f估计值不确定性极高，95%置信区间（confidence interval, CI）过宽；而分层模型（HBL、HBD）的估计结果则十分精准。在分层模型中，线性模型（HBL）相较于非稳态模型（HBD），其f估计值偏低约33%。相较于传统的非分层通量估算方法，分层模型实现了性能优化，本研究还提供了对应模型的示例代码。