The benefits of sequestering carbon are many, including improved crop productivity, reductions in greenhouse gases, and financial gains through the sale of carbon credits. Achieving better understanding of the sequestration process has motivated many deterministic models of soil carbon dynamics, but none of these models address uncertainty in a comprehensive manner. Uncertainty arises in many ways - around the model inputs, parameters, and dynamics, and subsequently model predictions. In this paper, these uncertainties are addressed in concert by incorporating a physical-statistical model for carbon dynamics within a Bayesian hierarchical modelling framework. This comprehensive approach to accounting for uncertainty in soil carbon modelling has not been attempted previously. This paper demonstrates proof-of-concept based on a one-pool model and identifies requirements for extension to multi-pool carbon modelling. Our model is based on the soil carbon dynamics in Tarlee, South Australia. We specify the model conditionally through its parameters, soil carbon input and decay processes and observations of those processes. We use a particle marginal Metropolis-Hastings approach specified using the LibBi modelling language. We highlight how samples from the posterior distribution can be used to summarise our knowledge about model parameters, to estimate the probabilities of sequestering carbon and to forecast changes in carbon stocks under crop rotations not represented explicitly in the original field trials.
