The determination of soil water content by time domain reflectometry (TDR) involves the measurement of the propagation velocity of a radio frequency (RF) pulse in soil and the conversion of this measurement to an estimate of soil water content. The objective of this study was to quantify errors in this conversion. A comprehensive error analysis can only be carried out if a well‐defined measurement procedure is followed. We define and recommend such a procedure and identify the physical origin and the magnitude of each of the error sources in the procedure. Total measurement errors are calculated as the root mean square sum of each of the individual errors. We express propagation velocity measurements in terms of time intervals, that is, the travel time of an RF pulse in soil (T) relative to that in air (Tair). Our measurement and error calculation procedure is based on an analysis of our own and published data for nonclay soils, which reveals that in all cases, there is a linear relation between T/Tair and volumetric water content (θv) with a mutually independent slope and intercept. A theoretical explanation for this observation is presented. We show that the dominant measurement error source is the transition time of the TDR reflection, which in turn is a function of θv. Absolute measurement errors range from 0.015 to 0.028 m3 m‐3 if the T/Tair vs. θv intercept is known and increase to 0.023 to 0.034 m3 m‐3 if a nominal value (1.55) is used. We recommend that a T/Tair vs. θv slope value of 0.1193 (5% less than theory) be used for measurements in nonclay agricultural soils. This leads to little loss in accuracy. Measurement resolution is primarily a function of the time base error of the TDR instrument and can be as good as 0.0018 m3 m‐3.
With the recent development of improved time domain reflectometry (TDR) probe design, measurement systems, and calibration procedures, it is now possible to detect and quantify the effect of temperature on the soil apparent dielectric constant (Ka). We investigated measurement errors in Ka associated with soil temperature variations and compared measured changes in Ka with those predicted by a dielectric mixing model. After confirming the accuracy and resolution of our measurement system with a series of measurements on distilled water, we measured changes in Ka with temperature for a range of soil types, including sand, loam, and peat, at soil water contents (θv) ranging from 0.09 to 0.81 m3 m−3. The measured variation with temperature in the dielectric constant of distilled water (0.322°C−1) was very close to that reported in the literature (0.356°C−1). In soils, changes in Ka with temperature were highest at high water contents. For soils near saturation, the overall changes observed in Ka with temperature were lower than those predicted by the dielectric mixing model by 17% for sand, 24% for loam, and 39% for peat. These results suggest that the temperature dependence of the dielectric constant of water in a soil matrix is lower than that of bulk water. Absolute water content errors increased linearly with the size of the water fraction, ranging from 8.75 × 10−5 m3 m−3°C−1 at 0.05 m3 m−3 soil water content to 1.40 × 10−3 m3 m−3°C−1 at 0.80 m3 m−3 soil water content. To obtain the highest measurement accuracy, particularly at higher θv, we suggest that a temperature correction of 0.00175θv °C−1 be employed.
There is a growing interest in the use of Inertial Measurement Unit (IMU)-based systems that employ gyroscopes for gait analysis. We describe an improved IMU-based gait analysis processing method that uses gyroscope angular rate reversal to identify the start of each gait cycle during walking. In validation tests with six subjects with Parkinson disease (PD), including those with severe shuffling gait patterns, and seven controls, the probability of True-Positive event detection and False-Positive event detection was 100% and 0%, respectively. Stride time validation tests using high-speed cameras yielded a standard deviation of 6.6 ms for controls and 11.8 ms for those with PD. These data demonstrate that the use of our angular rate reversal algorithm leads to improvements over previous gyroscope-based gait analysis systems. Highly accurate and reliable stride time measurements enabled us to detect subtle changes in stride time variability following a Parkinson's exercise class. We found unacceptable measurement accuracy for stride length when using the Aminian et al gyro-based biomechanical algorithm, with errors as high as 30% in PD subjects. An alternative method, using synchronized infrared timing gates to measure velocity, combined with accurate mean stride time from our angular rate reversal algorithm, more accurately calculates mean stride length.
The determination of soil water content by time domain reflectometry (TDR) involves two steps: the measurement of the propagation velocity of an electromagnetic pulse along a transmission line and the conversion of this measurement to an estimate of soil water content. The objective of this study was to identify and quantify errors associated with propagation velocity measurements. We developed new TDR techniques, involving the use of remotely switched diodes and differential wave form detection, that can be used to quantify and minimize propagation velocity errors. These errors are presented in terms of time interval errors. We show that the dominant time interval error term relates to the transition time of reflected pulses and that absolute time interval errors cannot be assumed to be <200 ps. We identify the presence of dissolved ions and the use of long cables as major sources of additional transition time errors. For transition times >2 ns, the time interval error caused by transition time effects can be estimated as the root mean square sum of the basic 200‐ps error and an error equal to 10% of the transition time. We show that although instrument time base errors are the main source of precision errors, they are less important in determining the absolute accuracy of propagation velocity measurements. We show that system costs can be reduced without compromising accuracy by using 75 Ω coaxial cable, which is not only inexpensive but is superior to standard 50 Ω cable.
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