Isotope partitioning of soil respiration: A Bayesian solution to accommodate multiple sources of variability

Isotopic methods offer great potential for partitioning trace gas fluxes such as soil respiration into their different source contributions. Traditional partitioning methods face challenges due to variability introduced by different measurement methods, fractionation effects, and end-member uncertainty. To address these challenges, we describe a hierarchical Bayesian (HB) approach for isotopic partitioning of soil respiration that directly accommodates such variability. We apply our HB method to data from an experiment conducted in a shortgrass steppe ecosystem, where decomposition was previously shown to be stimulated by elevated CO₂. Our approach simultaneously fits Keeling plot (KP) models to observations of soil or soil-respired δ¹³C and [CO₂] obtained via chambers and gas wells, corrects the KP intercepts for apparent fractionation (Δ) due to isotope-specific diffusion rates and/or method artifacts, estimates method- and treatment-specific values for Δ, propagates end-member uncertainty, and calculates proportional contributions from two distinct respiration sources (“old” and “new” carbon). The chamber KP intercepts were estimated with greater confidence than the well intercepts and compared to the theoretical value of 4.4‰, our results suggest that Δ varies between 2 and 5.2‰ depending on method (chambers versus wells) and CO₂ treatment. Because elevated CO₂ plots were fumigated with ¹³C-depleted CO₂, the source contributions were tightly constrained, and new C accounted for 64% (range = 55–73%) of soil respiration. The contributions were less constrained for the ambient CO₂ treatments, but new C accounted for significantly less (47%, range = 15–82%) of soil respiration. Our new HB partitioning approach contrasts our original analysis (higher contribution of old C under elevated CO₂) because it uses additional data sources, accounts for end-member bias, and estimates apparent fractionation effects.