An effective medium theory-based unified model for estimating thermal conductivity of unfrozen and frozen soils

Soil thermal conductivity (STC) is a crucial parameter in modeling land surface processes. However, the current STC models are developed separately for unfrozen and frozen soils, leading to inconsistent understanding. In this study, we propose a unified model based on the work of Ghanbarian and Daigle (2016) originally developed for unfrozen soils. The unified model comprises three parameters: critical volume fraction (ϕc), scaling exponent (t), and a compensating factor (α), and considers dry soil as the low-conductivity component (weighted by air volume fraction) and saturated soil as the high-conductivity component (weighted by volumetric liquid content for unfrozen state and total water content for frozen state). Specifically, ϕc represents a critical point where high-conductivity component begins to govern the behavior of effective STC, characterized by t. α allows for accurate calibration of saturated STC. Using a dataset of 90 unfrozen samples (693 measurements) and 74 frozen samples (255 measurements), pedotransfer functions (PTFs) for the three parameters were trained. The unified model successfully reproduces the sharp rise in STC at low moisture conditions during wetting and the increase during freezing. Compared to an empirical model (Côté and Konrad, 2005a) and a theoretical model (Tian et al., 2016), the unified model demonstrates higher predictive skill for unfrozen and frozen soils, achieving Nash-Sutcliffe efficiency coefficients of 0.96 and 0.90, respectively. This work contributes to a more consistent and comprehensive understanding of STC in cold environments and has the potential to be integrated into land surface models.