Tangent Line/Second‐Order Bounded Mean Oscillation Waveform Analysis for Short TDR Probe

Abstract

Core Ideas • A new method for analyzing TDR waveforms is presented. • The method provides consistent results on waveforms obtained from short TDR probes. • The method is stable enough for automatic implementation on large sets of TDR waveforms. 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.