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

Soil incubation experiments are widely used to investigate soil organic carbon (SOC) decomposition and persistence. However, they often show short-lived respiration pulses after disturbances (e.g., rewetting or flask handling) that reflect rapid shifts in substrate availability and microbial activity. The original PROCS system model (two ordinary differential equations) could not reproduce these abrupt state changes, increasing uncertainty in SOC decomposability parameters. We extended PROCS by adding a third differential equation that represents an additive post-disturbance pulse component that decays with time since disturbance. We estimated all parameters of the extended model within a Bayesian inference framework using 30-month incubation time series from three long-term Brazilian cropland experiments across contrasting climatic regions, subjected to three sequential rewetting cycles with no carbon inputs. Relative to the original PROCS, the extension substantially improved model–data compatibility: Pearson correlation (tracking observed rises and declines) increased from 0.790 to 0.993, and R² (variance explained) increased from 0.623 to 0.973. Model skill improved from NSE = -43.223 (worse than the simple benchmark of using the mean) to 0.989, and KGE (jointly summarizing correlation, bias, and variability) improved from 0.078 to 0.986. Overall errors were low (RMSE = 0.0406; MAE = 0.0308). Posterior distributions for SOC stocks and decomposability were well constrained, and the model fit all sequential rewetting cycles, suggesting that the disturbance effect is compartment-independent. The proposed model extension enhanced the robustness of the PROCS model for its application in soil carbon experiments.