Determination of Soil Ice Content with Thermo-Time Domain Reflectometry: A Thermal Conductivity Based Approach.

Measuring ice content (θ_i) in partially frozen soil is challenging in both engineering and environmental sciences. The thermo-time domain reflectometry (thermo-TDR) technique has been applied to determine θ_i based on the linear relationship between θ_i and soil heat capacity (C). This approach, however, can only be applied to partially frozen soils at temperatures below -5°C, and performed poorly in clayey soils. In this study, we present a thermal conductivity (λ) based approach for determining θ_i using thermo-TDR measured λ and liquid water content. Parameter λ is described using the simplified de Vries model that relates λ to θ_i, particle size distribution, bulk density, and liquid water content, and θ_i is estimated using inverse modeling from thermo-TDR measured λ and liquid water content. A sensitivity analysis using a hypothetical soil indicated that the λ-based approach performed better than the C-based approach. Laboratory evaluation on three soils showed that at temperatures lower than -5°C, the root mean square errors (RMSE) of θ_i estimates were 0.05 and 0.09 m³ m^-3 for C-based and λ-based approaches, respectively.  Further evaluations on four soils at -2°C indicated that the λ-based approach gave θ_i data with RMSE of 0.07 m³ m^-3, and the C-based approach failed to give appropriate θ_i data. We concluded that the λ-based approach Thermo-TDR method could provide reliable θ_i data even at temperatures near the freezing point.