A Soil Refractive Index (SRI) Model Characterizing the Functional Relationship Between Soil Moisture Content and Permittivity

The functional relationship between soil permittivity and soil water content serves as the theoretical foundation for electromagnetic wave-based techniques used to determine soil moisture levels. However, the response of permittivity to changes in soil water content varies significantly across different soil types. Current models that utilize soil permittivity to estimate soil water content are often based on empirical statistical relationships specific to particular soil types. Moreover, existing physical models are hindered by an excessive number of parameters, which can be difficult to measure or calculate. This study introduces a universal model, termed the Soil Refractive Index (SRI) model, to describe the relationship between soil permittivity and soil water content. The SRI model is derived from the propagation velocity of electromagnetic waves in various soil components and the functional relationship between electromagnetic wave velocity and relative permittivity. The SRI model expresses soil water content as a linear function of the square root of the relative permittivity for any soil type with the slope and intercept as the two undetermined parameters. The slope is primarily influenced by the relative permittivity of soil water, while the intercept is mainly affected by both the slope and the soil porosity. The applicability of the SRI model is validated through tested soil samples and comparison with previously published empirical statistical models. For dielectric lossless soil, the theoretical value of the slope is calculated to be 0.126. The intercept varies across different soil types and increases linearly with soil porosity. The SRI model provides a theoretical basis for calculating soil water content using permittivity across various soil types.