An implicit model for soil thermal conductivity and matric potential

Soil thermal conductivity (λ) is affected by the energy status of water and is closely related to soil matric potential (h). In this study, a soil water retention curve and a soil thermal conductivity curve were linked via the critical point that separated the adsorption water and capillary water regimes. Based on existing water retention curve and a thermal conductivity curve models, we derived a new implicit mathematical formulation of the λ-h relationship. The λ-h relationship was valid for the entire water content range at room temperature. The new model parameter values for adsorption, capillarity and soil thermal conduction were optimized, and a linear relationship between critical water content and maximum adsorption capacity was established by fitting the SWRC and STCC models to measurements from eight soils. Laboratory evaluations using λ and h measurements on a loam soil and a clay loam soil showed that the new model well described observed values with coefficients of determination greater than 0.97. The implicit model can quantify λ-h behaviors for various soil textures over the entire water content range.