Obtaining the Spatial Distribution of Water Content along a TDR Probe Using the SCEM-UA Bayesian Inverse Modeling Scheme

Abstract

Time domain reflectometry (TDR) has become one of the standard methods for the measurement of the temporal and spatial distribution of water saturation in soils. Current waveform analysis methodology gives a measurement of the average water content along the length of the TDR probe. Close inspection of TDR waveforms shows that heterogeneity in water content along the probe can be seen in the TDR waveform. We present a comprehensive approach to TDR waveform analysis that gives a quantitative estimate of the dielectric permittivity profile along the length of the probe and, therefore, the distribution of water content. The approach is based on the combination of a multisection scatter function model for the TDR measurement system with the shuffled complex evolution Metropolis algorithm (SCEM-UA). This combined approach allows for the estimation of the 40 parameters in the transmission line model using a series of simple calibration measurements. The proof of concept is given with measurements in a layered system consisting of air and water. Finally, TDR waveforms from layered soil samples were analyzed to estimate the distribution of the water content along the length of the probe. Results show that the proposed method provides much more reproducible results than obtained with the traditional travel time method. Because the proposed method can be fully automated, it increases the applicability of the TDR method, especially in applications where detailed (real-time) data are required on heterogeneous infiltration.