| 01 Jun 2026
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.
Competing interests: R.A.V.R is an executive editor or SOIL
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.
The paper is well-written and the analyses are rigorous. However, the method section is very long and difficult to follow for the non-specialist. I would recommend transferring parts to an annex.
Is there any reason why the equations are not numbered anymore after equation 3?
Line 392 I there any reason why you were not able to re-sample 4 out of 59 locations within an acceptable distance?
Figs 3, 4, 10, 11 What does the red dot refer to? Please explain in the caption.
Table 2 and all tables and figures. Abbreviations should be defined in the caption
Section 4.1 I miss a consideration on the practical application. To what extend is this rather complex analysis realistic for farm management? Is there any key indicator that the authors can recommend for practical purposes?
Lines 674 and 692 What does ‘bulk soliTOC’ ?