Digital soil mapping: a predictive performance assessment of spatial linear regression, Bayesian and ML-based models

Abstract

Nowadays, information on the spatial distribution of soil properties is considered a key element for environmental research and for agricultural planning and decision-making to monitor soil conditions, agricultural policies, etc. Developing models for spatial data is easy, but reliable predictions from such models are sometimes challenging due to the data features. Using simulation and data from the WoSI-ISRIC SoilGrid 250 m, we compared the predictive performance of five models: Spatial Linear Regression (SLR-REML), Machine learning (ML)-based models (Random Forest: RF and Random Forest Residual Kriging: RFRK), and Bayesian models (Integrated Laplace Approximation-Stochastic Partial Differential Equations: INLA-SPDE and spBAYES). Considering data characteristics such as spatial autocorrelation, range parameter, strength and type of relationship between the response variable and covariates, we cross-validated the models’ results using the following criteria: precision, unbiasedness, and uncertainty (RMSE, coefficient of determination (R$^{2}$), Lin’s concordance coefficient ($\rho _{c}$), and predicted interval coverage probability (PICP)). The results revealed the high precision of SLR-REML with a small bias in the case of low spatial autocorrelation. ML models (RF and RFRK) stood by their ability to account for nonlinearities, particularly the flexibility of RFRK to handle high spatial autocorrelation. The INLA-SPDE model was robust to all data characteristics. Despite its drawbacks related to the computation time observed, the SLR-REML model relaxed the minimum limit about the number of observations required in the classical regression by linear mixed modeling (REML-LMM) to make better predictions in Digital Soil Mapping (DSM). In addition to commonly used machine learning (ML) techniques, INLA-SPDE and SLR could be suitable for the understanding, characterization and mapping through spatiotemporal modeling of soil properties and environmental variables.

Appendices

Appendix A Simulated data on the 16 scenarios considered

See Fig. 8.

Fig. 8

Simulated Data (n = 1500)

Appendix B Predictive Power Scores Matrix

Fig. 9

Predictive power scores matrix

See Fig. 9.

Appendix C Individual relationships between soil properties and environmental covariates

See Fig. 10.

Fig. 10

Relationships between soil properties and environmental covariates