Parametric Modeling of the Unsaturated Soil Hydraulic Conductivity Function Using Tree-Based and Ensemble Machine Learning Algorithms: A Comparative Analysis of Cubist, Random Forest, and LightGBM

Modeling the unsaturated soil hydraulic conductivity function (SHCF) is essential for understanding water movement in unsaturated zones and supporting effective agricultural and environmental management. Accurate estimation of SHCF parameters, particularly the α and n parameters of the van Genuchten–Mualem (VGM) model, remains a challenging endeavor due to the complex interplay of soil physical properties. Tree-based machine learning methods have shown promising capabilities in this area. To further assess and compare the performance of tree-based approaches, this study aimed to evaluate the efficiency of three algorithms, Cubist, RF, and light gradient boosting machine (LightGBM), in the parametric estimation of SHCF using 196 soil samples from the UNSODA database. Input variables, including sand, clay, soil bulk density (BD), field capacity (FC), and permanent wilting point (PWP), were structured into four progressively complex pedotransfer functions (PTFs). Results indicate that Cubist demonstrated the best overall generalization during testing, achieving the lowest average RMSD (7.165) across the four PTFs compared to RF (7.602) and LightGBM (8.068), although RF and LightGBM achieved marginally better performance on individual PTF-metric combinations. All three algorithms achieved high coefficients of determination (R2 ≥ 0.95) across all PTFs. Specifically, in PTF4, the best-performing model, Cubist achieved a 6.8% lower RMSD than RF and a 12.4% improvement over LightGBM. Shapley additive explanations (SHAP) conducted via XGBoost surrogate models, suggested that FC and PWP were the most influential predictors of SHCF among the variables examined. These findings suggest that Cubist is a viable approach for estimating SHCF, particularly when input data are limited to basic soil properties.