Temperature- and texture-dependent dielectric model for frozen and thawed mineral soils at a frequency of 1.4 GHz

Abstract A single-frequency dielectric model at 1.4 GHz for frozen mineral soils was developed, with the temperature and gravimetric clay content varying from − 1 to − 30°C and from 9.1 to 41.3%, respectively. The model is based on the refractive mixing dielectric model and the dielectric data measured for the three typical soils collected in the Yamal tundra. The refractive mixing dielectric model was applied to fit the measured dielectric data as a function of soil moisture at a number of fixed temperatures. As a result, the parameters of the developed model were derived as a function of temperature and texture. This set of parameters consists of the maximum gravimetric fraction of unfrozen bound water and the values of the complex refractive indexes relating to soil solids, unfrozen bound water, and moistened ice. The developed model for frozen mineral soils in conjunction with the previously developed by us dielectric model for thawed mineral soils is considered as an integral dielectric model which is applicable for permittivity calculations of soil in both thawed and frozen states. The developed integral dielectric model for frozen and thawed mineral soils was validated using the dielectric data for five measured soils, and the statistical errors were estimated in terms of the root mean square error and the determination coefficient. In addition, the only known in the literature dielectric model for frozen soils suggested by Zhang was validated based on dielectric data for soils measured in this research. The comparative analysis proved substantially better accuracy of predictions in the case of the developed model as compared to those related to the Zhang model.