Laboratory characterization of a commercial capacitance sensor for estimating permittivity and inferring soil water content

Ring-capacitor sensors are used widely for real-time estimation of volumetric soil water content theta from measured resonant frequency f(r), which is directly affected by the bulk soil permittivity e. However, the relationship fr( e) requires improved quantification. We conducted laboratory experiments to characterize the response of the Sentek EnviroSMART sensor system for a full range of e values from air to water and a range of temperatures. Water-dioxane mixtures were placed into a solvent-resistant container equipped with custom tools for heating and mixing the fluid, removing air bubbles from sensitive surfaces, measuring permittivity in situ, and creating an axisymmetric metal disturbance to the electric field. Total capacitance C was measured using a vector network analyzer (VNA) connected to one sensor, while four other sensors provided replicated fr readings. The measured temperature response of free water permittivity was linear with a negative slope, which is qualitatively consistent with theory. A precise nonlinear relationship between e and normalized fr was derived. The instrumental error in e was RMSE epsilon = 0.226 ( for < epsilon < 43), which corresponds to a measurement precision in theta(epsilon) derived from Topp's equation of RMSE theta= 0.0034 m(3) m(-3). Axisymmetric numerical simulations of the electric field supplemented the experimental results. The characteristic length scale for the distance measured radially from the access tube is 12.5 mm, meaning that 80 and 95% of the signal are sensed within approximately 20 and 37 mm of the access tube, respectively. The results are crucial for scientific applications of the investigated sensor type to environmental media.