Bayesian hierarchical models for soil CO₂ flux and leak detection at geologic sequestration sites

Proper characterizations of background soil CO₂ respiration rates are critical for interpreting CO₂ leakage monitoring results at geologic sequestration sites. In this paper, a method is developed for determining temperature-dependent critical values of soil CO₂ flux for preliminary leak detection inference. The method is illustrated using surface CO₂ flux measurements obtained from the AmeriFlux network fit with alternative models for the soil CO₂ flux versus soil temperature relationship. The models are fit first to determine pooled parameter estimates across the sites, then using a Bayesian hierarchical method to obtain both global and site-specific parameter estimates. Model comparisons are made using the deviance information criterion (DIC), which considers both goodness of fit and model complexity. The hierarchical models consistently outperform the corresponding pooled models, demonstrating the need for site-specific data and estimates when determining relationships for background soil respiration. A hierarchical model that relates the square root of the CO₂ flux to a quadratic function of soil temperature is found to provide the best fit for the AmeriFlux sites among the models tested. This model also yields effective prediction intervals, consistent with the upper envelope of the flux data across the modeled sites and temperature ranges. Calculation of upper prediction intervals using the proposed method can provide a basis for setting critical values in CO₂ leak detection monitoring at sequestration sites.