Canadian Field Soils IV: Modeling Thermal Conductivity at Dryness and Saturation

Abstract

The thermal conductivity data of 40 Canadian soils at dryness $(\lambda _{\mathrm{dry}})$ and at full saturation $(\lambda _{\mathrm{sat}})$ were used to verify 13 predictive models, i.e., four mechanistic, four semi-empirical and five empirical equations. The performance of each model, for $\lambda _{\mathrm{dry}}$ and $\lambda _{\mathrm{sat}}$, was evaluated using a standard deviation (SD) formula. Among the mechanistic models applied to dry soils, the closest $\lambda _{\mathrm{dry}}$ estimates were obtained by MaxRTCM $(\textit{SD} = \pm ~0.018\,\hbox { Wm}^{-1}\cdot \hbox {K}^{-1})$, followed by de Vries and a series-parallel model ($\hbox {S-}{\vert }{\vert }$). Among the semi-empirical equations (deVries-ave, Advanced Geometric Mean Model (A-GMM), Chaudhary and Bhandari (C–B) and Chen’s equation), the closest $\lambda _{\mathrm{dry}}$ estimates were obtained by the C–B model $(\pm ~0.022\,\hbox { Wm}^{-1}\cdot \hbox {K}^{-1})$. Among the empirical equations, the top $\lambda _{\mathrm{dry}}$ estimates were given by CDry-40 $(\pm ~0.021\,\hbox { Wm}^{-1}\cdot \hbox {K}^{-1}$ and $\pm ~0.018\,\hbox { Wm}^{-1}\cdot \hbox {K}^{-1}$ for18-coarse and 22-fine soils, respectively). In addition, $\lambda _{\mathrm{dry}}$ and $\lambda _{\mathrm{sat}}$ models were applied to the $\lambda _{\mathrm{sat}}$ database of 21 other soils. From all the models tested, only the maxRTCM and the CDry-40 models provided the closest $\lambda _{\mathrm{dry}}$ estimates for the 40 Canadian soils as well as the 21 soils. The best $\lambda _{\mathrm{sat}}$ estimates for the 40-Canadian soils and the 21 soils were given by the A-GMM and the $\hbox {S-}{\vert }{\vert }$ model.

Appendix

See Table 12.

Table 12 Selected soil minerals and their approximate $\lambda _{\mathrm{min}}$ values