Modelling the relative permittivity of soils using soil hygroscopic water content

A model describing the increase in the relative permittivity of water with distance from the soil mineral surface is presented. The model assumes an exponential increase in the value of permittivity with increasing distance from the mineral surface; arguments are presented supporting this approach. The volume of bound water (within the bandwidth of time domain reflectometry, (TDR) 0.01–1 GHz) is considered to be equivalent to the soil hygroscopic water content. The refractive index mixing equation is used as a geometric base into which the model is incorporated. The new equation is tested using measurements of permittivity collected from two drying undisturbed soil cores that contained ∼10% hygroscopic water. The RMSE of predicted permittivity as a function of water content was found to decrease from ∼3.5 to less than 1. The model was further tested on data previously presented in the literature and found to correspond reasonably well.