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

Kiona Ogle, Edmund Ryan, Feike A. Dijkstra, Elise Pendall

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Nonsteady 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 on 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 nonlinear (nonsteady state, diffusion based) models of C versus t, within a hierarchical Bayesian framework. Data are from the Prairie Heating and CO2 Enrichment study that manipulated atmospheric CO2, temperature, soil moisture, and vegetation. CO2 was collected from static chambers biweekly during five growing seasons, resulting in >12,000 samples and >3100 groups and associated fluxes. We compare f estimates based on nonhierarchical and hierarchical Bayesian (B versus HB) versions of the linear and diffusion-based (L versus D) models, resulting in four different models (BL, BD, HBL, and HBD). Three models fit the data exceptionally well (R2 ≥ 0.98), but the BD model was inferior (R2 = 0.87). The nonhierarchical models (BL and BD) produced highly uncertain f estimates (wide 95% credible intervals), whereas the hierarchical models (HBL and HBD) produced very precise estimates. Of the hierarchical versions, the linear model (HBL) underestimated f by ~33% relative to the nonsteady state model (HBD). The hierarchical models offer improvements upon traditional nonhierarchical approaches to estimating f, and we provide example code for the models.

Original languageEnglish (US)
Pages (from-to)2935-2948
Number of pages14
JournalJournal of Geophysical Research: Biogeosciences
Issue number12
StatePublished - Dec 1 2016
Externally publishedYes


  • Bayesian modeling
  • Fick's law
  • borrowing of strength
  • diffusion equation
  • global change experiment
  • soil respiration

ASJC Scopus subject areas

  • Forestry
  • Aquatic Science
  • Ecology
  • Water Science and Technology
  • Soil Science
  • Atmospheric Science
  • Palaeontology


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