Frequency-, temperature-, and texture-dependent dielectric model for frozen and thawed arctic mineral soils

In this paper, a physically based dielectric model for frozen and thawed Arctic mineral soils is developed to account for moisture, dry density, temperature, texture of the soil and wave frequency. The model is based on the dielectric data measured for the three soils collected in the Yamal tundra, with clay content varying from 9.1% to 41.3%. Earlier developed the generalized refractive mixing dielectric model (GRMDM) was used as a theoretical basis for processing the measured data. In the frame of GRMDM the bound water and unbound water are identified as intrinsic parts of soil water. The maximum amount of bound water is considered to be a one of the basic major parameter of the proposed model. The dependence of this parameter on the soil temperature, and texture is derived, using dielectric data for the measured soils. In the measured frequency range 0.05 to 15 GHz, both the dipole and ionic interfacial (Maxwell-Wagner) dielectric relaxations were identified. These relaxation parameters for both parts of the soil water were determined as a function of temperature in the range −30 to 25° C, using the measured soil dielectric spectra and the multi-relaxation theoretical formula for them. Besides, the relaxation parameters were found to be independent on the soil texture. Electric conductivities for both parts of the soil water were determined as a function of temperature and clay content in the same temperature range, using the measured soil dielectric spectra and the theoretical formula for them. The error of the predicted values of the complex relative permittivity (CRP) of soils relative to the measured ones was evaluated through normalized root mean square error (nRMSE). The nRMSE appeared to be 5.5%, and 17.2% for the real and imaginary parts of the CRP, respectively.