Validation of the percolation-based effective-medium approximation model to estimate soil thermal conductivity

Abstract

Soil thermal conductivity (λ) has broad applications in soil science, hydrology, and engineering. In this study, we applied the percolation-based effective-medium approximation (P-EMA) to estimate the saturation dependence of thermal conductivity ($\lambda \left(\theta \right)$) using data from 38 undisturbed soil samples collected across the state of Kansas. The P-EMA model has four parameters including a scaling exponent (t_s), critical water content (θ_c), and thermal conductivities at oven-dry (λ_dry) and full saturation (λ_sat) conditions. To estimate the $\lambda -\theta$ curve, the values of λ_dry and λ_sat were measured using a soil thermal properties analyzer and the values of t_s and θ_c were estimated as a function of clay content. Thermal conductivity was also estimated using the Johansen model. By comparison with observations, the P-EMA model resulted in a root mean square error (RMSE) ranging from 0.029 to 0.158 W m⁻¹ K⁻¹, whereas the Johansen model had an RMSE ranging from 0.021 to 0.173 W m⁻¹ K⁻¹. Our results demonstrate that the P-EMA model has comparable accuracy to the widely used Johansen model to estimate the saturation-dependent soil thermal conductivity of undisturbed soils with minimal input parameters. Future studies should focus on better understanding the physical meaning of t_s and θ_c in the P-EMA model to improve our ability to model thermal conductivity in undisturbed soil from percolation principles.