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.