Spatiotemporal modeling of soil organic matter in the black soil area of Northeast China with INLA-SPDE and remote sensing data

Spatiotemporal variation of soil organic matter (SOM) contents was significant to research on global warming, greenhouse effect, and ecosystem health and quality. However, the spatiotemporal modeling for soil properties in most studies focused on a discrete-time calibration and validation, and faced the problems of missing observations. Integrated Nested Laplace Approximation with the Stochastic Partial Differential Equation (INLA-SPDE) model that is robust to missing data and unbalanced sampling design was proposed as a potential model for spatiotemporal soil modeling. This study presented an application of INLA-SPDE for spatiotemporal modeling of SOM (2006, 2010, 2018) using 924 samples and 8 environmental covariates in Lishu County, Northeast China. The results demonstrated that the INLA-SPDE model incorporating spatiotemporal information generally outperformed the two-phase methods based on Cubist and Random Forest, particularly in years requiring greater temporal extrapolation (2006 and 2018), while achieving comparable performance in 2010. This superiority can be attributed to its comprehensive consideration of various sources of uncertainty. Furthermore, the posterior distributions derived from the model provided valuable insights into the effects of environmental covariates on SOM spatiotemporal variation, with clay content showing the strongest positive influence and annual precipitation exhibiting a notable negative effect. The spatial pattern of SOM consistently exhibited higher values in the east and lower values in the west. After an overall decline from 2006 to 2010, mean SOM content increased from 17.97 g kg^-1 to 20.85 g kg^-1 between 2010 and 2018 (a total increase of 2.88 g kg^-1 at an annual rate of 0.36 g kg^-1 yr^-1), with notable recovery in central and eastern areas, likely associated with the implementation of straw returning practices. In addition to prediction accuracy, computational complexity, and uncertainty analysis, the study evaluated the model from new perspectives, including covariate interpretability and flexibility. This research provides a promising spatiotemporal modeling framework for digital soil mapping.