A hierarchical modeling approach to estimating soil trace gas fluxes from static chambers

Static chambers are often employed to measure soil trace gas fluxes. Gas concentrations (C) in the headspace are sampled at different times (t), and for each group of chamber measurements, flux rates are frequently calculated as the slope of linear regressions of C versus t (ultimately, statistical analyses are performed with the flux rate "data"). While non-linear regressions are recognized to be more accurate than linear regressions, a trade-off with precision can arise due to variability in raw data leading to poor curve fits, and groups of data with too few observations or with poor regression fits (i.e., low R2) are often discarded. We solve these problems via a hierarchical Bayesian approach that fits a simple, dynamic non-linear model of C versus t based on Fick's law. Data are from the Prairie Heating and CO2 Enrichment (PHACE) study that involves manipulations of atmospheric CO2, temperature, soil moisture, and vegetation. CO2, CH4, and N2O gas samples were collected from static chambers bi-weekly during five growing seasons, resulting in >12,000 individual gas samples and >3100 groups of samples and associated fluxes. Using these data, we compare flux estimates from our non-linear model to those obtained from a linear model, and we evaluate the effect of conducting independent regressions for each group of samples versus simultaneously estimating the fluxes for all groups within a hierarchical framework motivated by the PHACE experimental design. The CO2 flux estimates from the hierarchical linear and non-linear models fit the observed CO2 data well (R2 = 0.97) and were highly correlated with each other (r = 0.99), but the linear model resulted in estimates that were ~10% lower than the non-linear model. The hierarchical versus non-hierarchical models also produced similar flux estimates (r = 0.94), but the non-hierarchical version yielded notably less precise estimates (the 95% CIs for its fluxes were 1-2 orders of magnitude wider that the hierarchical model). Hence, the hierarchical, non-linear approach to estimating trace gas fluxes from static chambers is a significant improvement upon the non-hierarchical (independent groups) and linear regression approaches, which tend to produce highly uncertain (non-hierarchical models) and biased (underestimated, linear model) flux estimates.