Xu et al. (2026) Semi-empirical model of soil organic matter and soil moisture content with bayesian joint inversion

Identification

• Journal: Journal of Soils and Sediments
• Year: 2026
• Date: 2026-03-24
• Authors: Jiawei Xu, Yuteng Liu, Changxiang Yan, Jing Yuan
• DOI: 10.1007/s11368-026-04265-1

Research Groups

• Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences
• University of Chinese Academy of Sciences
• Center of Materials Science and Optoelectrics Engineering, University of Chinese Academy of Science

Short Summary

This study developed a novel semi-empirical radiative transfer model (SW-ETM) and a Bayesian joint inversion framework to simultaneously estimate soil organic matter (SOM) and soil moisture content (SMC) from spectral reflectance, effectively addressing their mutual interference and significantly improving prediction accuracy.

Objective

• To develop and validate a novel semi-empirical radiative transfer model (SW-ETM) that couples soil organic matter (SOM) and soil moisture content (SMC) to account for their complex interactions in spectral reflectance.
• To introduce and apply a Bayesian inversion framework for the simultaneous and accurate estimation of SOM and SMC from spectral data, overcoming the limitations of traditional single-parameter or deterministic multi-parameter inversion methods.

Study Configuration

• Spatial Scale: 76 composite soil samples collected from Gongzhuling City, Jilin Province, China.
• Temporal Scale: Not explicitly stated as a time-series study; laboratory measurements on collected samples.

Methodology and Data

• Models used:
  • SOM-W Semi-Empirical Transfer Model (SW-ETM), based on principles of Hapke and Kubelka-Munk models.
  • Bayesian inversion framework, utilizing the No-U-Turn Sampler (NUTS) algorithm for posterior distribution sampling.
  • Wavelength selection: Interval Combination Optimization (ICO) and Differential Evolution (DE) algorithms.
  • Spectral curve reconstruction: Cubic spline and Third-order Hermite interpolation.
  • Comparative inversion methods: Trust Region Framework (TRF) and Particle Swarm Optimization (PSO).
  • Sensitivity assessment: Partial Least Squares (PLS) regression.
• Data sources:
  • Laboratory-measured spectral reflectance (500–2400 nm) using an ASD Field-Spec 3 high-resolution spectrometer.
  • Laboratory-determined Soil Organic Matter (SOM) content (Agricultural Soil Inventory (ASI) method).
  • Laboratory-controlled Soil Moisture Content (SMC) at six gradients (12%, 14%, 16%, 18%, 20%, 22%).

Main Results

• SW-ETM Model Validation: The SW-ETM model demonstrated high accuracy in fitting spectral reflectance within the 500–2400 nm range (R²p = 0.945, RMSEp = 0.0094).
• Spectral Curve Reconstruction: 20 key feature wavelengths were identified, enabling precise full-wavelength curve fitting (R²p = 0.9976, RMSEp = 0.0021) using third-order Hermite interpolation.
• SOM Sensitive Wavelength Selection: A two-stage selection process (ICO + DE) identified 10 SOM-sensitive wavelengths, which significantly improved PLSR prediction accuracy for SOM (R²p = 0.685, RMSEp = 2.6454 g/kg) compared to full-wavelength PLSR (R²p = 0.568, RMSEp = 3.3858 g/kg), effectively reducing moisture interference.
• Bayesian Joint Inversion Performance (Test Set):
  • SOM prediction: R²p = 0.767, RMSEp = 3.8132 g/kg.
  • SMC prediction: R²p = 0.967, RMSEp = 0.5780%.
  • Sampler evaluation (Bayesian Fraction of Missing Information (BFMI) > 0.8) and multi-chain convergence (R-hat ≈ 1.0) confirmed the reliability and stability of the Bayesian approach.
• Comparative Inversion Methods (Test Set):
  • Particle Swarm Optimization (PSO): SOM (R²p = 0.351, RMSEp = 3.7968 g/kg), SMC (R²p = 0.938, RMSEp = 0.7938%).
  • Trust Region Framework (TRF): SOM (R²p = 0.328, RMSEp = 3.8652 g/kg), SMC (R²p = 0.972, RMSEp = 0.5372%).
  • The Bayesian method demonstrated significantly superior accuracy for SOM and comparable/slightly better performance for SMC compared to PSO and TRF.

Contributions

• Developed a novel dual-factor semi-empirical soil radiative transfer model (SW-ETM) that explicitly couples SOM and SMC, quantifying their interaction mechanisms and overcoming the limitations of traditional single-factor models.
• Introduced a robust Bayesian inversion framework for the simultaneous estimation of SOM and SMC, leveraging prior information and spectral dimensionality reduction (using 20 key wavelengths for curve reconstruction and 10 SOM-sensitive wavelengths for inversion) to achieve high accuracy and stability in complex, nonlinear multi-parameter problems.
• Established a comprehensive technical pathway for rapid, in-situ, and simultaneous acquisition of soil information, providing a reliable approach for applications in precision agriculture, environmental monitoring, and digital mapping.

Funding

• Jilin Key R&D Program of China (Grant 20230201036GX)
• National Natural Science Foundation of China (NSFC) (Grant 62105331, Grant 62275114)

Citation

@article{Xu2026Semiempirical,
  author = {Xu, Jiawei and Liu, Yuteng and Yan, Changxiang and Yuan, Jing},
  title = {Semi-empirical model of soil organic matter and soil moisture content with bayesian joint inversion},
  journal = {Journal of Soils and Sediments},
  year = {2026},
  doi = {10.1007/s11368-026-04265-1},
  url = {https://doi.org/10.1007/s11368-026-04265-1}
}