Purpose Identifying optimal predictors and constructing universal thermal conductivity models that coincide with priori heat transfer knowledge in unsaturated soils are crucial for accurately quantifying soil processes in land surface models at large spatial scales. The nonlinear coupling relationships among influencing factors pose significant challenges to accurately determining soil thermal conductivity (λ). While data-driven machine learning models for predicting λ have made some progress, they often neglect the heat transfer mechanisms and lack physical consistency. Methods A representative thermal conductivity database was compiled, and a combination of multi-parametric analysis, prior physical knowledge, and post hoc methods were applied to elucidate the heat transfer mechanisms between influencing factors and λ, facilitating the identification of optimal predictors. Subsequently, five interpretable machine learning models with physical constraints (PC-IML) were developed and benchmarked against 24 normalized empirical models from multiple perspectives to validate their performance. Finally, the decision-making processes of PC-IML models were further interpreted and visualized using Shapley Additive exPlanations (SHAP) and partial dependence plots (PDPs). Leveraging these insights, an improved normalized model was proposed, systematically incorporating intrinsic, structural, and environmental factors. Results Relying on parametric analysis alone can misinterpret the underlying heat transfer laws, ultimately impeding ML modeling. In contrast, a comprehensive scoring effectively identified key predictors, quartz content, saturation, dry density, and temperature, aligning with the results of SHAP and PDPs. PC-IML achieved a five-fold improvement in accuracy compared to normalized models (p > 0.05) and yielded good performance in the analysis of thermal properties for land surface modeling over the Tibetan Plateau. Validation of PC-IML model in simulating soil thermal properties on the land surface of the Tibetan Plateau. Visualizations of sensitivities, response patterns, and coupling effects aligned well with prior heat transfer mechanisms, verifying the physical consistency of both the decision-making and outputs. Using the identified optimal λdry and Ke, the improved normalized model exhibited strong robustness and accuracy. Conclusions This research offers valuable insights for the development of PC-IML-enabled hydrothermal simulations for land surface modeling.

Exploring the performance and explainability of soil thermal conductivity model coupling physical knowledge and machine learning

期刊论文
发表日期：

2025年6月5日

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Shengkui Tian,
Qiong Wang,
Wei Su,
Yichun Liu,
Weimin Ye,
Guanshi Liu

摘要

Purpose

Identifying optimal predictors and constructing universal thermal conductivity models that coincide with priori heat transfer knowledge in unsaturated soils are crucial for accurately quantifying soil processes in land surface models at large spatial scales. The nonlinear coupling relationships among influencing factors pose significant challenges to accurately determining soil thermal conductivity (λ). While data-driven machine learning models for predicting λ have made some progress, they often neglect the heat transfer mechanisms and lack physical consistency.

Methods

A representative thermal conductivity database was compiled, and a combination of multi-parametric analysis, prior physical knowledge, and post hoc methods were applied to elucidate the heat transfer mechanisms between influencing factors and λ, facilitating the identification of optimal predictors. Subsequently, five interpretable machine learning models with physical constraints (PC-IML) were developed and benchmarked against 24 normalized empirical models from multiple perspectives to validate their performance. Finally, the decision-making processes of PC-IML models were further interpreted and visualized using Shapley Additive exPlanations (SHAP) and partial dependence plots (PDPs). Leveraging these insights, an improved normalized model was proposed, systematically incorporating intrinsic, structural, and environmental factors.

Results

Relying on parametric analysis alone can misinterpret the underlying heat transfer laws, ultimately impeding ML modeling. In contrast, a comprehensive scoring effectively identified key predictors, quartz content, saturation, dry density, and temperature, aligning with the results of SHAP and PDPs. PC-IML achieved a five-fold improvement in accuracy compared to normalized models (p > 0.05) and yielded good performance in the analysis of thermal properties for land surface modeling over the Tibetan Plateau. Validation of PC-IML model in simulating soil thermal properties on the land surface of the Tibetan Plateau. Visualizations of sensitivities, response patterns, and coupling effects aligned well with prior heat transfer mechanisms, verifying the physical consistency of both the decision-making and outputs. Using the identified optimal λ_dry and K_e, the improved normalized model exhibited strong robustness and accuracy.

Conclusions

This research offers valuable insights for the development of PC-IML-enabled hydrothermal simulations for land surface modeling.