An improved thermo-time domain reflectometry method for determination of ice contents in partially frozen soils

Measuring ice contents (θi) in partially frozen soils is important for both engineering and environmental applications. Thermo-time domain reflectometry (thermo-TDR) probes can be used to determine θi based on the relationship between θi and soil heat capacity (C). This approach, however, is accurate in partially frozen soils only at temperatures below −5 °C, and it performs poorly on clayey soils. In this study, we present and evaluate a soil thermal conductivity (λ)-based approach to determine θi with thermo-TDR probes. Bulk soil λ is described with a simplified de Vries model that relates λ to θi. From this model, θi is estimated using inverse modeling of thermo-TDR measured λ. Soil bulk density (ρb) and thermo-TDR measured liquid water content (θl) are also needed for both C-based and λ-based approaches. A theoretical analysis is performed to quantify the sensitivity of C-based and λ-based θi estimates to errors in these input parameters. The analysis indicates that the λ-based approach is less sensitive to errors in the inputs (C, λ, θl, and ρb) than is the C-based approach when the same or the same percentage errors occur. Further evaluations of the C-based and λ-based approaches are made using experimentally determined θi at different temperatures on eight soils with various textures, total water contents, and ρb. The results show that the λ-based thermo-TDR approach significantly improves the accuracy of θi measurements at temperatures ≤−5 °C. The root mean square errors of λ-based θi estimates are only half those of C-based θi. At temperatures of −1 and −2 °C, the λ-based thermo-TDR approach also provides reasonable θi, while the C-based approach fails. We conclude that the λ-based thermo-TDR method can reliably determine θi even at temperatures near the freezing point of water (0 °C).