Bayesian Calibration of a Dynamic Model with Sequential Rewetting Disturbances Incubation Data

Soil incubation experiments are widely used to investigate soil organic carbon (SOC) decomposition and persistence. However they frequently exhibit short-term respiration pulses following disturbances such as rewetting, flask manipulation and/or carbon inputs events that reflect rapid changes in substrate availability and microbial activity. The original formulation of PROCS, a  system model of two ordinary differential equations (ODEs) designed to describe SOC dynamics, was unable to accurately  represent abrupt state changes, therefore amplifying uncertainty, particularly in the estimation of SOC decomposability parameters. We extended the PROCS model to improve its ability to reproduce short-term respiration pulses observed in soil incubation experiments. A decaying function was added as a new differential equation to represent the transient effect of rewetting on SOC decomposability, with a rapid initial response that smoothly relaxed back to standard PROCS dynamics. We estimated all parameters of the extended PROCS model within a Bayesian inference framework using 30-month soil incubation data with no carbon inputs from three long-term cropland experimental sites across contrasting Brazilian climatic regions, explicitly accounting for three rewetting cycles and jointly fitting observed CO₂ emissions and SOC stocks. The extended model accurately reproduced observed decomposability pulses associated with incubation disturbance  events, substantially improving model–data compatibility, and yielded well-constrained posterior distributions for SOC concentration and decomposability and turnover-related parameters across sites. The introduction of a post-disturbance decaying function in the PROCS model, combined with Bayesian calibration, enabled the fitting of a parsimonious statistical model that accurately represented the transient disturbances effects and provided posterior distributions of model parameters. The model’s ability to fit all sequential rewetting cycles consistently suggests that the disturbance effect was compartment-independent. Our model extension enhanced the robustness of the PROCS model for its application in soil incubation experiments.