A bimodal model for thermal conductivity as a function of matric potential incorporating adsorption and capillarity

• The BoT model is proposed to describe the λ(pF) relationship by incorporating adsorption and capillarity. • The BoT model outperforms existing λ(pF) models. • BoT model parameters have physical meanings and are linked to key water content values. • Pedo-transfer functions are established to estimate BoT model parameters. Estimating soil thermal conductivity (λ) in relation to soil water matric potential ( h ) is important to understand energy transfer, water movement, and ecological processes in soils. However, there is a lack of universally applicable λ( h ) relationships that characterize soil thermal behavior across the full h range, particularly for soils with diverse textural classes and varying bulk density. In this study, we present the Boltzman-Tani (BoT) model, a physically based and continuous framework that captures the bimodal pattern of λ (pF, the common logarithm of | h| ) relationship over the entire h range by incorporating both adsorption and capillarity. The BoT model parameters pF ads and pF cap , which mark the inflection points in the adsorption and capillary domains, respectively, have clear physical meanings and are linked to key soil thermal and hydraulic properties, i.e., critical and hydraulic continuity water contents. We evaluate the BoT model using a λ(pF) dataset comprising 246 observations from 18 soil samples, representing a wide range of texture and bulk density. The BOT model outperforms two existing models: the unified exponential model and the two-segment power model, achieving the least root mean square error (0.043 W m −1 K −1 ) and mean error (0.033 W m −1 K −1 ), the lowest Akaike Information Criterion (−82.2), and the highest coefficient of determination (0.983). The changes in λ are driven by variations in the adsorption and capillary components, with adsorptive force dominating at higher pF and capillary force becoming more influential at lower pF, validating the model’s theoretical framework. Furthermore, we develop pedo-transfer functions to estimate the BoT model parameters from soil texture and bulk density, which facilitates its broader and practical application such as soil-climate feedback and optimizing land management. Future work should focus on validating the model with larger, independent datasets and exploring its integration with advanced machine learning techniques to expand its predictive capabilities.