Soil water content inverse profiling from single TDR waveforms

An inverse procedure for the estimation of soil water content profiles along TDR probes is presented. A TDR metallic probe is considered as a transmission line, for which relevant partial derivatives equations apply. The direct problem consists in the integration of transmission line equations, providing V(x,t) along the line. To this aim, the unit length parameters of the transmission line must be known. In particular, unit length capacitance C(x) and transverse conductance G(x) depend on water content distribution along the probe θ(x) through relative permittivity εr(x) and bulk soil electrical conductivity σ(x), respectively. The inverse procedure consists in finding the water content distribution, and the relevant unit length parameters, giving rise to the best fit between the numerically simulated voltage image at the beginning of the line and the experimental voltage trace image measured by a cable tester. In order to reduce the ill-posedness of the inverse problem, unknown water content profiles are expressed by means of a four parameters functional form. The search for the best fitting parameters vector is carried out with a genetic algorithm. The proposed inverse procedure is successfully applied to the determination of vertical water content profiles along a soil sample in the laboratory by means of a single three rods metallic TDR probe. Water content profiles estimated either in steady flow conditions, or during controlled infiltration-evaporation transients are compared with independent water content measurements carried out by means of horizontal TDR probes at various depths, showing in all cases good agreement.