Prediction of soil selenium content and model optimization for a watershed in the Taihang Mountains based on machine learning models

Technical Summary: Prediction of Soil Selenium Content and Model Optimization in a Taihang Mountain Watershed

Problem Statement
Selenium (Se) is a critical trace element for human health, with its spatial distribution in soil directly influencing regional ecological security and agricultural product quality. However, predicting soil Se content in small mountainous watersheds, such as those in the Taihang Mountains, presents significant challenges. These areas are characterized by rugged terrain, complex parent materials, and strong spatial heterogeneity, which restrict sampling accessibility and often result in small sample sizes (N < 150). Existing studies have largely focused on large-sample datasets in plain areas, leaving a gap in understanding model stability and driving mechanisms under small-sample, high-heterogeneity conditions. Furthermore, the relationship between soil Se and geochemical factors is often nonlinear, complicating traditional geostatistical approaches.

Methodology
The study focused on a typical watershed in Pingshan County, Hebei Province, covering approximately 251.51 km². Researchers collected 107 topsoil samples (0–20 cm depth) from cultivated land, orchards, grasslands, and forests. The samples were analyzed for 17 predictive variables, including soil organic matter (SOM), pH, major oxides (e.g., SiO₂, Al₂O₃), and trace elements (Se, Cd, Pb, Hg, As, Cu, Zn, Ni, Cr).

To address the prediction challenge, the authors constructed and compared three machine learning models:

1. LASSO Regression: A linear model with L1 regularization used for feature selection and handling multicollinearity.
2. Random Forest (RF): A nonlinear ensemble learning algorithm based on decision trees.
3. Support Vector Machine (SVM): A nonlinear kernel mapping model based on structural risk minimization, specifically utilizing a Radial Basis Function (RBF) kernel.

The dataset was split into training (70%, 76 samples) and test (30%, 31 samples) subsets using stratified random sampling. Model performance was evaluated using Mean Square Error (MSE), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and the coefficient of determination (R²). Feature importance was assessed via coefficient absolute values (LASSO) and permutation importance (RF and SVM).

Key Results

• Model Performance: The SVM model demonstrated superior performance and stability. It achieved an R² of 0.7381 on the test set with an RMSE ratio (training/test) of 0.996, indicating no significant overfitting or underfitting. In contrast, the RF model exhibited severe overfitting (R² dropped from 0.9267 on training to 0.6479 on testing, with an RMSE ratio of 2.517), likely due to the small sample size and complex terrain. The LASSO model showed moderate performance (R² = 0.5907) but suffered from slight underfitting, attributed to its inability to capture nonlinear relationships.
• Optimal SVM Parameters: Through grid search and cross-validation, the optimal SVM parameters were identified as: Gamma = 1×10⁻⁵, Cost = 1000, and Epsilon = 0.2. The final model utilized 53 support vectors (69.74% of the training set).
• Driving Factors: All three models consistently identified Soil Organic Matter (SOM), Cadmium (Cd), and Lead (Pb) as the dominant controlling factors for soil Se content.
  • SOM acts as a primary driver, providing adsorption sites and forming stable complexes with Se.
  • Cd and Pb share homologous geogenic sources with Se (derived from rock weathering and atmospheric deposition) and compete with Se for adsorption sites on SOM-bearing soil colloids.
  • Correlation analysis confirmed significant positive correlations between Se and SOM, Cd, and Pb, even after controlling for confounding variables.

Key Contributions

1. Model Selection for Small Samples: The study provides empirical evidence that SVM is the optimal algorithm for predicting soil Se content in small-sample (N < 150), high-heterogeneity mountainous watersheds, outperforming both RF and LASSO in terms of generalization and stability.
2. Geochemical Mechanism Elucidation: The research identifies a coupled geochemical assemblage (Se-Cd-Pb-SOM) as the intrinsic driving mechanism. It clarifies that the spatial variation of Se is regulated not only by common geochemical provenance but also by competitive adsorption dynamics between Se, Cd, and Pb on SOM surfaces.
3. Practical Framework: The study offers a validated technical workflow for screening influencing factors and predicting soil element distribution in complex mountainous terrains where large-scale sampling is unfeasible.

Significance and Claims
The authors claim that this work provides a reliable technical approach for soil Se prediction and factor screening in analogous mountainous watersheds. By confirming SVM as the preferred model for small-sample scenarios, the study addresses a critical gap in environmental geochemistry. The identification of SOM, Cd, and Pb as core factors offers specific geochemical support for selenium resource evaluation and ecological security assessments in the Taihang Mountains. The study acknowledges limitations, noting that machine learning models act as "black boxes" regarding internal mechanisms and that future work should integrate multi-source environmental covariates (e.g., DEM, remote sensing) and expand sampling scopes to further clarify scale effects.