Critical review of the models used to determine soil water content using TDR-measured apparent permittivity

Time domain reflectometry (TDR) is the most widely used non-destructive, easily automated method to determine water content of soils and other porous media. However, it should be noted that two key steps are required for TDR applications: (1) Obtain and analyze TDR waveforms using travel-time analysis to determine apparent permittivity; (2) determine a new- or apply an existing relationship between the derived apparent permittivity and the volumetric water content of the porous medium of interest. Activities associated with the first key step were presented in a previous review of TDR applications in porous media including soils, plants, snow, food, and concrete (He et al., 2021, Advances in Agronomy, 83–155). This review focuses on the second step required by TDR applications to determine soil water content in both field and laboratory environments. Numerous mathematical models have been developed to enhance our ability to better estimate water content with TDR-measured apparent dielectric permittivity. When applied judiciously, TDR measurements can help to better understand processes such as coupled transport of water, solutes, and heat, measure the soil water balance and improve the efficiency of irrigation scheduling. However, there are important differences in the formulation, applicability, and accuracy of these models, and no systematic review has been previously undertaken. The objectives of this study are to (1) review and synthesize models relating TDR-measured apparent permittivity to water content in porous media, and (2) analyze the relationships between models. This review examines a total of 157 models that are categorized into 123 empirical models, 11 semi-empirical models, and 23 physical models, based on their development, underlying theories, phase configurations, applications to mineral or organic soils, and unfrozen or frozen conditions. Model limitations and perspectives are discussed and several unresolved questions are presented to highlight the need for further research in this rapidly expanding field.