Robust calibration and evaluation of a percolation-based effective-medium approximation model for thermal conductivity of unsaturated soils

Thermal conductivity (& lambda;) is a property characterizing heat transfer in porous media, such as soils and rocks, with broad applications to geothermal systems and aquifer characterizations. Numerous empirical and physically-based models have been developed for thermal conductivity in unsaturated soils. Recently, Ghanbarian and Daigle (G & D) proposed a theoretical model using the percolation-based effective-medium approximation. An explicit form of the G & D model relating & lambda; to water content (& theta;) and equations to estimate the model parameters were also derived. In this study, we calibrated the G & D model and two widely applied empirical & lambda;(& theta;) models using a robust calibration dataset of 41 soils. All three & lambda;(& theta;) model performances were evaluated using a validation dataset of 58 soils. After calibration, the root mean square error (RMSE), mean absolute error (MAE) and coefficient of determination (R2) of the G & D model were 0.092 W-1 m-1 K-1, 0.067 W-1 m-1 K-1 and 0.97, respectively. For the two empirical models, RMSEs ranged from 0.086 to 0.096 W-1 m-1 K-1, MAEs from 0.063 to 0.071 W-1 m-1 K-1, and R2 values were about 0.97. All three metrics indicated that calibration improved the performance of the G & D model, and it had an accuracy similar to that of the two empirical & lambda;(& theta;) models. Such a robust performance confirmed that the theoretically-based G & D model can be applied to study soil heat transfer and potentially other related fields.

Automated summary

In this study, the performance of the G&D model and two empirical λ(θ) models were evaluated using calibration and validation datasets. The calibration improved the performance of the G&D model, resulting in a similar accuracy to the empirical models.