The S11 scatter function of a coaxial probe in the frequency domain is shown to be an accurate model for predicting waveforms of a seven‐wire coaxial probe in the time domain. Reproducibility of discrete Fourier analyses carried out on waveforms measured with the Tektronix 1502b cable tester (Tektronix, Incorporated, Beaverton, Oregon) indicated a frequency band width ranging from 20 kHz to approximately 1.5 GHz. The frequency dependent complex dielectric permittivity can be calculated from measured waveforms by inverting the S11 scatter function. Results indicate that a seven‐wire coaxial probe, connected to a 1‐m RG214 coaxial cable, emulates a coaxial tube for frequencies up to 150 MHz. Application of the frequency domain model to time domain reflectometry waveforms shows that the apparent dielectric permittivity calculated from the travel time in the probe is very dependent on the relaxation frequency of the material in which the probe is embedded. For materials with low relaxation frequencies the apparent dielectric permittivity is much lower than the static permittivity. Inversion of the frequency domain model allows for solving the frequency dependent complex dielectric permittivity of soils from measured waveforms.
Time domain reflectometry (TDR) can be used to study temporal variations in volumetric soil water content (θ) and bulk soil electrical conductivity (σa). The variations in σa are associated with changes in θ and the soil water composition. Laboratory and field experiments were conducted to verify if TDR can be used to monitor the temporal variation in the soil water composition between solution sampling occasions. Effects of cable length and temperature on the σa measurement were evaluated. Including the series resistance of the cable and connectors in the analysis improves measurements at high electrical conductivity levels. The temperature factor of the bulk soil appears to be similar to the temperature factor of soil extracts. Laboratory experiments showed that the theoretical model giving σa as function of θ and the electrical conductivity of the soil solution (σw) combined with the water retention function was capable of describing σw measured on soil solution extracted with ceramic cup solution samplers under static water flow conditions. After optimization of a single parameter, the model was able to describe σw values of the soil solution obtained in the laboratory, whereas literature values were sufficient for field data. Concentrations of a number of solutes in a field data set spanning 3 yr were positively correlated with σw. Site‐specific regressions between solute concentration and σw combined with automated TDR measurements of σa and θ enable a more meaningful interpretation of the temporal variation of the concentration of major solutes present in the soil solution between sampling occasions.
Time domain reflectometry (TDR) is accepted as a valuable tool for measuring soil water content and bulk soil electrical conductivity. The accuracy of TDR measurements depends on the quality and type of probes, as well as on the length of cable used. The objective of this study was to test the effects of different triple‐wire TDR probe dimensions and cable lengths on the measurements. Additional measurements were done in order to test the performance of small triple‐wire probes in soils with a wide range of water contents. Measurements in air and in water showed that the position of the first reflection from the connection between cable and probe is influenced by the dielectric medium. This problem was solved by using the zero of the cable tester as a time reference, and calibrating the TDR probes before measurements. The major effect of increasing cable lengths is that the rise time of the TDR voltage pulse increases, spreading each reflection across a larger time interval, which influences the accuracy of the wave form analysis and causes a possible underestimation of the apparent dielectric permittivity in dry soils. As a result, it is not possible to use short probes with long cable lengths. Smaller spacing of the wires results in steeper reflections from the end of the probe. Small triple‐wire probes are convenient in laboratory applications. Large triple‐wire probes are convenient for automated field applications in which long lengths of cable are required.
Research on the spatial and temporal dynamics of soil water has long been impeded by the lack of an automated technique for the measurement of soil water content. A computer controlled time domain reflectometry (TDR) system is described which gives the possibility of making a large number of measurements at different sites at predetermined time intervals. The developed system operates on 12 V dc and has the capability to monitor water contents at 36 sites. The algorithm used for the automatic analysis of the measurements is also presented. It is based on the calculation of the travel time of the TDR signal between the beginning and the end of a three-wire probe.
[1] A series of primary drainage experiments was carried out in order to investigate nonequilibrium capillarity effects in two-phase flow through porous media. Experiments were performed with tetrachloroethylene (PCE) and water as immiscible fluids in a sand column 21 cm long. Four drainage experiments were performed by applying large pressures on the nonwetting phase at the inlet boundary: 20, 30, 35, 38 kPa. Our results showed that the nonequilibrium local fluids pressure difference-saturation curves are above the capillary pressure saturation curve. Moreover, the nonequilibrium pressure difference showed a nonmonotonic behavior with an overshoot that was more pronounced at higher injection pressures. The dynamic capillarity coefficient was calculated from measured local pressures and saturations (the scale of sensor devices, 0.7 cm). Its value was found to vary between 1.3 Â 10 5 to 2 Â 10 5 Pa s. Within the saturation range of 0.50 > S w > 0.85, no clear dependency of the dynamic coefficient on the wetting saturation was observed. Also, no dependency of the dynamic capillarity coefficient on the applied boundary pressure was found. Averaged values of ½ at the length scales of 11 and 18 cm were also estimated from averaged pressures and saturations. The upscaled dynamic coefficient was found to vary between 0.5 Â 10 6 and 1.2 Â 10 6 Pa s at the average window size of 11 cm. This is one order of magnitude larger than the local-scale coefficient. Larger values were found for the length scale of 18 cm: 1.5 Â 10 6 and 2.5 Â 10 6 Pa s. This suggests that the value of dynamic coefficient increases with the scale of observation.
Measured spatial patterns of water uptake were found to be related to measured throughfall patterns around trees, especially in dry months. To simulate these lateral feedback mechanisms, the one-dimensional soil water model SWlF was modified to a quasi-three-dimensional model allowing preferential water uptake from wet sites. Input-output relations, linking soil physical input parameters to simulation results, showed that soil water contents at field capacity and those after a dry period in summer could be used to parametrize the soil physical characteristics. To assess parameter values for the 2.5-ha research area, soil water contents were mapped using data from vertically installed time domain reflectometry sensors. Model results indicated that the spatial distributions of yearly water uptake and percolation fluxes were strongly affected by throughfall patterns, whereas soil water contents primarily depended on soil physical properties. Results also indicated that refined model parametrization can improve the reliability of model predictions of soil water dynamics at specific sites.
Although time domain reflectometry (TDR) is becoming accepted as an important tool for the measurement of soil water content and bulk soil electrical conductivity, a major part of the method is based on empirical relationships. An improved understanding of dielectric measurements on soils may give more insight into soil properties other than soil water content and bulk soil electrical conductivity. Frequency domain analysis of TDR waveforms enables the measurement of the frequency dependent complex dielectric permittivity of soils. The frequency dependent complex dielectric permittivity of soils can be described with a four‐component complex dielectric mixing model based on the volumetric mixing of the refractive indices of the soil components. The four soil components in the model are air, solids, bound water, and free water. Results indicate that the apparent dielectric permittivity obtained from the travel time of the TDR pulse in the soil is the dielectric permittivity at the highest measurement frequency of the cable tester, probe, and soil system. The model based on the volumetric mixing of real permittivities underestimates the measurements in situations with high values of the imaginary part of the dielectric permittivity. Because the model based on the mixing of the complex dielectric permittivities can describe the data, we conclude that the apparent dielectric permittivity is influenced by the imaginary parts in the dielectric, permittivities of the soil components. Combination of the four‐component complex dielectric mixing model with the complex dielectric permittivity obtained from the frequency domain analysis of TDR waveforms gives a tool for modeling the bulk soil electrical conductivity by separating the conductivity of the soil water into a bound water conductivity and a free water conductivity.
Measurements on a seven-wire coaxial probe carried out with a cable tester in the time domain are compared with measurements carried out with a network analyzer in the frequency domain. Results are compared in the frequency domain and in the time domain. The frequency domain results of the time domain measurements are less smooth than the direct frequency domain measurements, but similar trends can be observed. The measurements carried out with the cable tester (Tektronix 1502B) clearly have a frequency content well above 3 GHz for measurements in air but with a very low signal-to-noise ratio for the higher frequencies. The useful frequency band for measurements carried out with a seven-wire probe depends on the dielectric properties of the material being measured. The higher the complex dielectric permittivity, the lower the useful frequency band. Methods are presented for calibrating seven-wire coaxial probes and measuring the frequency-dependent dielectric properties of soil samples using a combination of frequency and time domain analyses. The approach does not depend on a choice of frequency bandwidth. A Debye relaxation curve is capable of describing the frequency domain dielectric permittivity of sandy soils containing a soil solution with an electrical conductivity of approximately 0.4 S m -•. Results indicate an effective bandwidth of at least 0-1 GHz for sandy soils. IntroductionTime domain reflectometry (TDR) has obtained a reputation as a versatile and reliable technique for the measurement of soil water content and bulk electrical conductivity. This measurement technique quantifies the modification of an electromagnetic pulse by a soil owing to water and electrical conductivity. In order to obtain an improved understanding of the measurement technique and possibly extend the application of TDR to other topics Heimovaara [1994] presented an analysis technique which allows the dielectric permittivity as a function of frequency to be obtained from TDR waveforms. The frequency-dependent dielectric permittivity of soils was also measured by Campbell [1990] with a network analyzer directly in the frequency domain.Modern cable testers currently used in soil science are rugged, portable, battery-powered instruments and are therefore practical field instruments. Network analyzers, besides being more expensive, are not particularly suited for field use. However, network analyzers have superior frequency domain capabilities. This paper presents a comparison between measurements carried out with a Tektronix 1502B cable tester (Tektronix, Beaverton, Oregon) and a Hewlett Packard 8753A
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