Compositional spatial modelling of soil organic and inorganic carbon fractions with calibrated joint uncertainty propagation

Abstract. Farm-scale soil-carbon assessments require more than a map on total carbon. They need the organic fractions, the inorganic pool, and calibrated uncertainty around each estimate. We developed a probabilistic compositional framework that propagates uncertainty jointly from mid-infrared (mid-IR) spectroscopic predictions through probabilistic trend and Bayesian spatial modelling. The framework preserves closure among particulate organic carbon (POC), mineral-associated organic carbon (MAOC) and an instrument-defined residual organic carbon (ROC), and preserves mass balance among total organic carbon (TOC), total inorganic carbon (TIC) and total carbon (TC). We applied the framework at a Mediterranean-type semi-arid farm to map POC, MAOC, ROC, TOC, TIC and TC at 0–10, 10–30 and 0–30 cm. Spectroscopic uncertainty was represented by bootstrap prediction distributions, propagated through Natural Gradient Boosting (NGBoost) trend models and Bayesian spatial models based on stochastic partial differential equations (SPDE), estimated using the Integrated Nested Laplace approximation (INLA). Predictive calibration was strong: 95 % probability-integral-transform (PIT) coverage was 0.94–0.95 across all response-depth combinations. Posterior intervals also bracketed bulk laboratory measurements (Kling–Gupta efficiency, KGE 0.64–0.79) and independent measurements (KGE 0.12 for ROC to 0.66 for MAOC, and up to 0.84 in the managed-pasture cohort). The maps showed consistent land-use effects on organic carbon. Cropping, managed pasture and natural vegetation formed the ordering crop < managed < natural for every organic-C pool and depth, with the largest deficits at the surface. Cropping also shifted composition toward the protected pools, with a lower labile-to-protected ratio (POC/[MAOC+ROC]) than pasture. TIC and ROC showed little land-use contrast. Spatial controls differed among pools: gamma-radiometric ratios dominated MAOC, electromagnetic induction conductivity dominated POC at depth, and topographic redistribution organised pools integrating multiple mechanisms. The calibrated posterior, rather than the point estimate, is the appropriate basis for soil-C management, monitoring and accounting.