Accuracy of frequency domain analysis scenarios for the determination of complex dielectric permittivity

Abstract

Frequency domain analysis of time domain reflectometry waveforms has been shown to be useful for more accurate water content determination, water content determination in saline soils, and determination of such difficult to measure soil properties as specific surface area and soil solution conductivity. Earlier frequency domain analysis approaches to determine frequency‐dependent dielectric properties of soils have used a variety of methods. In this paper, these methods for the determination of dielectric permittivity were compared using the Shuffled Complex Evolution Metropolis algorithm (SCEM‐UA). SCEM‐UA is a global optimization method that allows the simultaneous determination of optimal Debye parameters, which describe the dielectric permittivity as a function of frequency, and their confidence intervals. The analysis of numerically generated measurements with added instrumental noise showed that analysis of network analyzer measurements in the frequency domain potentially has the highest accuracy for determination of dielectric permittivity. Furthermore, the analysis of time domain reflectometry waveforms in the time domain was found to be more accurate than analysis of these waveforms in the frequency domain. Analysis of real network analyzer measurements in the time and frequency domain showed that both analysis scenarios allowed reasonably accurate estimates of the Debye parameters with the SCEM‐UA algorithm, even when the true value of a parameter falls beyond the limits of the frequency bandwidth. However, frequency domain analysis of ethanol measurements showed that results were susceptible to model errors caused by nonideal probe behavior. These errors were larger for three‐wire probes than for seven‐wire probes. This study shows that the accuracy of the dielectric permittivity determination can be improved by reducing the model error. This can be achieved by the use of more accurate models, such as multiscatter functions, and by using more advanced probes, such as coaxial cells. The results also imply that future research on dielectric properties of soils should focus more on the use of network analyzers instead of cable testers, since model errors are more obvious in the frequency domain. The SCEM‐UA algorithm proved to be a valuable tool in frequency domain analysis because reported problems with parameter identification and initialization of the optimization are circumvented with this global optimization algorithm.