Evaluation of five composite dielectric mixing models for understanding relationships between effective permittivity and unfrozen water content

• Five multi-phase composite dielectric mixing models to estimate unfrozen water content were evaluated
• Sensitivity analysis and applicability of these models were examined
• The de Loor model, discrete and confocal model are appropriate for frozen soil studies
• The power law and sphere model have limited applicability

Accurate estimation of unfrozen/liquid water content (θl) of soils with time domain reflectometry (TDR) is important for understanding freezing and thawing processes and hydrology in cold regions. Empirical equations and composite dielectric mixing models are the two most commonly used methods to estimate water content in unfrozen soils from TDR-measured soil effective permittivity (εeff). However, empirical equations derived from unfrozen soil data always overestimate θl in frozen soils and few studies were found to examine the validity of composite dielectric mixing models for measuring θl. Therefore, the objective of this study was to evaluate the sensitivities and applicability of composite dielectric mixing models for modeling the εeff(θl) relationship. Five multi-phase, composite dielectric mixing models (i.e., power law model, de Loor model, Sihvola discrete model, Sihvola confocal model, and Sphere model) were evaluated with published dataset consisting of independently measured εeff and θl on the same samples. The results show that: (1) the power law model and de Loor models are independent of configurations of dielectric mixtures; (2) the Sihvola discrete model depends on the host medium and independent on the configurations of the other components; (3) different dielectric mixing models may end up with the similar εeff(θl) relationships by parameter adjusting to represent the same problem; and (4) the de Loor model, and Sihvola discrete and confocal models are most appropriate for modeling the εeff(θl) relationship of frozen soils based on the published dataset. This study will significantly contribute to the application of TDR method for liquid water measurement in frozen soils and facilitate the understanding of freezing/thawing processes.