Neural network estimation of thermal conductivity across full saturation for various soil types

Abstract

Soil thermal conductivity (λ) relates directly to heat conduction in soil. Numerous models have been developed to estimate soil thermal conductivity, but their applicability is often limited to specific types of soils. Recognizing the similarity between the soil water retention curve and the λ versus water content (θ) curve, Lu and Dong presented a λ(θ) model, which can provide accurate λ estimates for various soils but does not converge to the thermal conductivity value of a saturated soil (λ_sat) at saturation. In this study, we develop a modified form of the Lu and Dong (MLD) model. Additionally, we present a neural network (NN) approach to estimate parameters of the MLD model using soil porosity, sand, silt, and clay contents, as well as the thermal conductivity of soil solids (λ_s) as input features. The neural network is trained to optimize the hyperparameters, which are used to establish the NN-MLD model after the hyperparameter tuning process is completed. The NN-MLD model is then tested with an independent testing dataset and compared with five pre-existing models taken from the literature. Results show that the NN-MLD model outperforms the other models across four error metrics with a normalized root mean square error (NRMSE) of 0.049, a mean absolute error (MAE) of 0.098 W m⁻¹ K⁻¹, an Akaike’s information criterion (AIC) of −1699 and a coefficient of determination (R²) of 0.94. In addition, error analysis across varying degrees of saturation (S) reveals that the NN-MLD model consistently outperforms the other models across the entire range of saturation levels and its superiority is most pronounced at medium levels of saturation, where the other models yield NRMSEs and MAEs values three times larger than those of the NN-MLD model. The NN-MLD model is available in Python code in the Supplementary Material.