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

Soil thermal conductivity (lambda) 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(theta)$\lambda ( \theta )$) using data from 38 undisturbed soil samples collected across the state of Kansas. The P-EMA model has four parameters including a scaling exponent (ts), critical water content (theta c), and thermal conductivities at oven-dry (lambda dry) and full saturation (lambda sat) conditions. To estimate the lambda-theta$\lambda - \theta $ curve, the values of lambda dry and lambda sat were measured using a soil thermal properties analyzer and the values of ts and theta 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 ts and theta c in the P-EMA model to improve our ability to model thermal conductivity in undisturbed soil from percolation principles. Soil thermal conductivity was estimated using the percolation-based effective-medium approximation (P-EMA) model.We used a dataset of soil thermal properties measured in 38 undisturbed soil samples.The P-EMA model resulted in a root mean square error ranging from 0.029 to 0.158 W m-1 K-1, which was similar to the widely used Johansen model.