Tangent line/second-order bounded mean oscillation waveform analysis for short TDR probe

Tangent line (TL) methods and the second-order bounded mean oscillation (BMO) method have been proposed for determining the reflection positions of time domain reflectometry (TDR) waveforms, especially for short-probe TDR sensors. However, the accuracy of TL methods is limited by the multi-reflection effects of the short-probe TDR sensor, and an automatic implementation of the second-order BMO is challenging because of the superimposition of the TDR waveforms. In this study, we combined a TL method with second-order BMO to develop a tangent line/second-order bounded mean oscillation (TL-BMO) method. Laboratory and field data were used to evaluate the TL-BMO method. Separate tests were performed on laboratory data to compare the TL-BMO method with the TL method and the second-order BMO method. For selected waveforms, the TL-BMO was more accurate than the TL method (the RMSE of TL-BMO was 0.0197 m³ m⁻³ and the RMSE of the TL method was 0.1071 m³ m⁻³). The TL-BMO was able to avoid calculation errors associated with automatic analysis by the second-order BMO (RMSE of TL-BMO automatic analysis was 0.0199 m³ m⁻³ and the RMSE of second-order BMO automatic analysis was 0.1414 m³ m⁻³). For analyzing field measurements, the TL-BMO method was able to determine soil water contents accurately during a 3-wk-long measurement period. Conclusively, the new TL-BMO method was more accurate than the TL method, and it demonstrated the stability necessary for automatic analysis of short-probe TDR sensors.