Excluding quartz content from the estimation of saturated soil thermal conductivity: Combined use of differential effective medium theory and geometric mean method

Saturated soil thermal conductivity (lambda(sat)) is the maximum soil thermal conductivity value of a given soil. Although it can be determined accurately with a heat pulse sensor, there are challenges to prepare fully saturated soil samples. Numerous models have been developed to estimate lambda(sat), and among these, the geometric mean method (GMM) generally performs well. The GMM requires soil mineral composition or quartz content information, which is unavailable for most soils. Earlier studies commonly used assumed that quartz content (f(quartz)) was equal to sand content (f(sand)) or to 0.5 x f(sand), which led to significant lambda(sat) estimation errors especially on coarse-textured soils. We derived a novel method to estimate lambda(sat) from soil porosity (phi) based on a combination of the GMM and differential effective medium theory (DEM). The new DEM-GMM approach has a single parameter, cementation exponent (m). Using a calibration dataset of 43 soils, we determined best fit m values for soils in three groups: 1.66 for Group I (f(sand) < 0.4), 1.62 for Group II (0.4 <= f(sand) < 1) and m = -1.34 phi+1.70 for Group III (f(sand) = 1). Using best fit m values for different groups, the new model can estimate lambda(sat) values from phi. Independent validation results on another 46 soils showed that the new model outperformed the GMM method with the assumption that f(quartz) = f(sand) or f(quartz) = 0.5 x f(sand). The mean RMSE, Bias and R-2 values of the DEM-GMM approach were 0.202 W m(-1) K-1, 0.013 W m(-1) K-1 and 0.89, respectively, and corresponding values of the GMM with the two assumptions were 0.295 and 0.476 W m(-1) K-1, 0.056 and -0.28 W m(-1) K-1, 0.80 and 0.82, respectively. The robust performance of the DEM-GMM approach suggests that it can be incorporated into thermal conductivity models to accurately estimate the thermal conductivity of unsaturated soils.