Waveform analysis for short time domain reflectometry (TDR) probes to obtain calibrated moisture measurements from partial vertical sensor insertions

Abstract

Time Domain Reflectometry (TDR) probes are extensively used for measuring soil moisture in agricultural and environmental water management applications. Short ($<$ 15 cm) commercial TDR probes provide accurate soil moisture measurements when installed correctly in the soil. Ground and aerial robots have recently been designed to measure soil moisture autonomously, but ensuring proper sensor insertion is challenging. Incomplete sensor insertions in the soil can lead to air gaps and underestimation of soil moisture due to differences in the dielectric permittivity between air (ε $=$ 1) and water (ε $=$ 80). A new TDR waveform calibration methodology was developed by modifying the waveform analysis approach by Schwartz et al. (2014). The objective was to calculate the apparent permittivity of the soil knowing the length exposed to air during automated sensor insertions. This method was validated using different liquid media and soil with different moisture conditions (ranging from air-dry to full saturation), showing accurate permittivity calculations within the manufacturer-specified accuracy range. The method was applied to field data collected from an aerial vehicle payload designed to measure soil moisture. The model successfully reduced the percent error in 8 out of 11 incomplete robotic sensor insertions and validated the values obtained by the drone payload in three complete sensor insertions. The study demonstrated that the sensor must be inserted at least 50% into the medium for reliable waveform analysis. This research enhances the reliability of automated soil moisture measurements using robotic technologies.