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DIVISION S-1-SOIL PHYSICS

Time Domain Reflectometry Probe for Simultaneous Measurement of Soil Matric Potential and Water Content

^a Department of Agronomy, Iowa State University, Ames, IA 50011-1010 USA
^b Greenhouse and Processing Crops Research Centre, Agriculture and Agri-Food Canada, Harrow, ON Canada N0R 1G0

rhorton{at}iastate.edu

	ABSTRACT

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results and discussion Conclusions REFERENCES

 
Simultaneous measurement of matric potential, , and water content, , is demanded in many disciplines. Time domain reflectometry (TDR) has been routinely used to measure water content and electrical conductivity of soil. Previous efforts to combine TDR probes with porous materials functioning as tensiometers were successful, but these probes were still constrained by characteristics of tensiometers, such as the need to supply water and measuring ranges > -85kPa. A new – TDR probe was developed to overcome shortcomings of the previous work. A portion of the TDR rod was embedded in a dental plaster (gypsum), whose matric potential equilibrated with surrounding soil. The rest of the TDR rod was inserted into the soil. The TDR technique was used to determine dielectric constants, , of both the gypsum and the soil. The new – TDR probes were tested in clay loam soil using a pressure-plate apparatus to produce – relationships of the gypsum and the soil for -1000 -10 kPa. Changes in of the gypsum corresponded well to applied pressures for -1000 -30 kPa, but values did not noticeably change for > -30 kPa. Values of of the soil corresponded well to the whole range tested. The new probes accurately measure and of soil when soil water content gradually decreases or increases. The newly developed – TDR probe requires no more maintenance than ordinary TDR probes and requires no additional instrumentation.

Abbreviations: TDR, time domain reflectometry

	INTRODUCTION

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results and discussion Conclusions REFERENCES

 
A SOIL WATER characteristic curve—the relationship between water content, (m³ m^-3), and matric potential, (kPa)—is one of the most important parameters to study water flow in soil. A pressure-plate apparatus, combined with the oven-drying soil method, is popularly used to establish water characteristic curves in the laboratory. However, in situ determination of water characteristic curves is difficult. Measuring soil water content may be relatively easy in both destructive (e.g., sampling soils) and nondestructive (e.g., TDR, neutron scattering method) manners. Matric potential of soil is often measured with a tensiometer in situ; however, its measuring range is limited to > -85 kPa (Cassel and Klute, 1986). Thermocouple psychrometry can be used for a wide range of but is very sensitive to temperature changes (Rawlins and Campbell, 1986); thus, it may not be suitable for routine field measurements. Measuring water, thermal, or electrical properties of a constructed porous medium equilibrated with surrounding soil is another attempt to indirectly measure the matric potential of soil. For specific ranges of water potential, the heat-dissipation method, the filter-paper method, or the gypsum block electrical-resistance method may be used in the laboratory and the field (Campbell and Gee, 1986).

Time domain reflectometry is routinely used to measure water content and electrical conductivity both in the laboratory and the field (Dalton et al., 1984; Nadler et al., 1991; Noborio et al., 1994; Heimovaara et al., 1995). For simultaneous measurement of and of soil with a TDR probe, Baumgartner et al. (1994) and Whalley et al. (1994) attached porous materials functioning as tensiometers to the end of hollow electrodes of the TDR probe. However, their probe configuration has the same constraints as tensiometers, that is, the need to supply water to tensiometers and the limited measuring range for > -85 kPa.

To estimate values by measuring the dielectric constant, , or water content of an equilibrated porous material, TDR techniques have been applied to a commercial product (e.g., Equitensiometer, Delta-T Devices, Cambridge, England) and to a TDR probe in ceramic discs described by Or and Wraith (1999a). When both and need to be measured, an additional probe is required to measure . There is a need to develop a probe that simultaneously measures wide ranges of and in situ.

In this paper, we present a design of a new TDR probe that simultaneously measures and . A portion of the TDR probe is embedded in a porous material, and the rest is inserted into a surrounding soil. This unique configuration of the probe enables the simultaneous measures of for the porous material and for the soil, side by side, in almost the same sampling volume. The new – TDR probes are tested in clay loam soil.

	Materials and methods

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results and discussion Conclusions REFERENCES

 
Probe Design
The impedance of a transmission line (i.e., a probe) is a function of the spacing and diameter of rods in addition to the dielectric constant of the medium in which the probe is installed. If there are differences in impedance along the transmission line length due to different diameters or spacing of rods being connected in series, one can detect different reflections in TDR waveforms from the interfaces where the two different diameters or spacing of the rods are connected (Davis, 1975; Topp and Davis, 1985). The impedance, Z (), for a two-rod type transmission line can be approximated (Kraus, 1984) using Eq. [1]:

(1)

where is the dielectric constant of a material surrounding the transmission line, s is the spacing of the rods, and d is the radius of the rods.

To distinguish reflections from the interface between different diameters and spacings of rods, the impedance differences should be large enough in a full range of soil water contents, that is, dielectric constants. The two-rod transmission line or probe consisted of two stainless-steel rods (1.6-mm diam. and 25 mm apart) in which a portion was covered with copper tubes with larger outer diameters (3.2-mm diam., 50 mm long, and 5 mm apart) (Fig. 1) . The copper tubes were soldered to the stainless-steel rods at the both ends of the copper tubes. The copper tubes were then embedded in dental plaster (Lab Plaster, Bayer Corp., South Bend, IN) following Phene et al. (1971). Lab Plaster's main constituent is gypsum. The powder plaster was mixed with deionized water in a ratio of 47 mL of water to 100 g of the Lab Plaster. The slurry of the plaster was poured into a plastic cast in which the copper portion of the two rods was placed at the center of the cast.

View larger version (27K): [in this window] [in a new window]   Fig. 1 Schematic of the – TDR probe

According to Eq. [1], the stainless-steel portion of the transmission line in dry and wet soil yield Z = 238 and 75 , respectively, whereas the copper portion in dry and wet gypsum results in Z = 58 and 25 , respectively. The dielectric constant of dry and wet soil was assumed to be 3 and 30 (Topp et al., 1980), respectively, and that of dry gypsum was assumed to be 5.6 (Curtis and Defandorf, 1929). The dielectric constant of wet gypsum was assumed to be the same as that of wet soil. The diameters and spacings of rods were selected to provide distinguishable diffraction of TDR waves at the interface between gypsum and soil for all combinations of water contents of gypsum and soil. A 75- coaxial cable (RG-187/A, Alpha Wire, Elizabeth, NJ) was connected to the end of the copper tubes. The 75- coaxial cable provided a distinguishable reflection from the beginning of the probe in the full range of water contents of gypsum, especially when the gypsum was dry. Two – TDR probes were constructed and tested.

Calibration
The – TDR probes were embedded in Harps clay loam (fine-loamy, mixed, superactive, mesic Typic Caliaquoll; 37% sand, 35% silt, and 28% clay) in a pressure-plate apparatus. A layer 1.3 cm thick of air-dried Harps clay loam was placed in a PVC cylinder (15.2-cm diam. and 5.0 cm high) on a pressure plate, then two probes were horizontally placed on the soil. Additional air-dried soil filled gaps between the probes and the cylinder. The extra 1.3-cm thickness of soil covered the probes on top. Using Eq. [4] and [5] of Petersen et al. (1995), who modified Knight's work (1992), the 1.3-cm-thick soil was sufficient to involve 95% of the total electromagnetic energy provided by a TDR cable tester. The soil and the probes were saturated with deionized water for 1 d and placed in a pressure chamber. Nine different pressures were applied to the system in a constant temperature room (20°C). After the soil and gypsum were assumed to be equilibrated with each applied pressure (equilibration times ranged from 2 to 16 d), the pressure chamber was opened, and TDR waveforms were collected using a 1502 TDR cable tester (Tektronix Inc., Beaverton, OR) connected to a 21X datalogger (Campbell Scientific, Logan, UT) for control and data storage. Acquired TDR waveforms were transferred to a computer and analyzed using a procedure similar to that of Baker and Allmaras (1990). Waveform acquisition from the cable tester was duplicated for each pressure applied. Additional soil columns (4.75-cm i.d. and 5 cm high) were placed on the same pressure plate for determining equilibrated soil water content for each applied pressure.

Dielectric constants of gypsum and soil were determined (Baker and Allmaras, 1990) in Eq. [2] as

(2)

where is the dielectric constant of gypsum or soil, L_a is an apparent probe length on a cable tester (m), and L is a probe length (m). Apparent probe lengths for gypsum and soil were represented by L_a,g and L_a,s, respectively, as in Fig. 2 . The TDR-measured dielectric constant, , of the gypsum was related to matric potential, (kPa), with an equation (Eq. [3]) similar to that of van Genuchten (1980):

(3)

where _s and _r are dielectric constants at saturation and residual water contents, respectively, and , n, and m are calibration constants. The relationship between the TDR-measured dielectric constant, , and the volumetric water content of soil, (m³ m^-3), was established (Eq. [4]) (Yu et al., 1997) with:

(4)

where a, b, and c are calibration constants.

View larger version (23K): [in this window] [in a new window]   Fig. 2 Examples of TDR waveforms from Probe 1 in a clay loam soil with different matric potentials. Apparent probe lengths for the gypsum and the soil are represented by La,g and La,s, respectively

	Results and discussion

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results and discussion Conclusions REFERENCES

 
Examples of waveforms from Probe 1 are shown for = -10, -100, and -1000 kPa in Fig. 2. Reflections from the beginning and end of the probe, in addition to the reflection from the interface between gypsum and soil, were consistently distinguishable in the whole pressure range we tested. Waveforms from Probe 2 were very similar to Probe 1 (data not shown).

Changes in the dielectric constant of the gypsum and the soil corresponding to external pressures applied are shown in Fig. 3 . Dielectric constants of the gypsum and the soil were determined using Eq. [2] with apparent probe lengths L_a,g for the gypsum and L_a,s for the soil as shown in Fig. 2. The observed – relationship for the gypsum was almost identical for the two – TDR probes. The – relationship for the gypsum was established using Eq. [3] with data from these two probes. Fitted parameters were _r = 3.158, _s = 21.452, = 0.0207, n = 3.150, and m = 0.228. The correlation coefficient was r² = 0.998. If the – relationship for the gypsum differed from soil to soil, it would be necessary to confine the electromagnetic energy by enclosing the gypsum with a wire screen (e.g., Wraith and Baker, 1991). The observed – for the soil was similar for the two probes, but differed by as much as = 0.85, which is equivalent to = 0.016 m³ m^-3. This difference may be within the acceptable error range. Changes in for the gypsum were sensitive enough to detect a change for -1000 -30 kPa, but almost insensitive for > -30 kPa. These characteristics of the gypsum used were similar to those of the gypsum reported by Bourget et al. (1958) and those of the ceramic discs used by Or and Wraith (1999a). In contrast, a nylon block (Bourget et al., 1958) and a porous material used for a heat-dissipation sensor (Reece, 1996) are sensitive at -1 -100 kPa, but lose sensitivity at > -100 kPa. A porous material having a semi-log linear relationship between and in a wide range of matric potential, perhaps 0 to -1500 kPa, may be ideal.

View larger version (23K): [in this window] [in a new window]   Fig. 3 Calibration of the TDR-measured dielectric constant of the gypsum and the soil against matric potential for the – TDR probes. Bars indicate ± one standard deviation of measurement. For the gypsum, a calibration curve was established with r2 = 0.998 using fitted parameters, r = 3.158, s = 21.452, = 0.0207, n = 3.150, and m = 0.228

Advantages of measurement using TDR may be extended to the – calibration of the gypsum because there is little effect of temperature and salinity on or determination (Topp et al., 1980). Unlike other methods for measuring , such as thermocouple psychrometry and the gypsum block-resistance method (Campbell and Gee, 1986), we can expect temperature independence in the – relationship because Halbertsma et al. (1995) reported that a fine-textured soil showed little effect of temperature on TDR-measured . Others, however, reported temperature dependency of in fine-textured soils (Pepin et al., 1995; Wraith and Or, 1999b). Or and Wraith (1999b) proposed a mechanistic model for the temperature dependency of soil . Thus, we may need temperature compensation for the gypsum, which has tight pore-size distribution, when the probe is exposed to large temperature differences such as occur in surface soil. Although salinity effects on TDR-measured are not completely understood (Ren et al., 1999), the – relationship should be consistent when the calibration is made under fixed conditions, that is, the gypsum block is always moistened with a saturated solution of dissolved gypsum (Gardner, 1986).

Hysteresis in the gypsum, however, may influence the calibration. Tanner and Hanks (1952) and Bourget et al. (1958) found hysteresis when they measured electrical resistance between electrodes in a gypsum block as a function of matric potential. Although hysteresis between TDR-measured and was negligible (Topp et al., 1980; Horino and Maruyama, 1993), there may be hysteresis between and in the gypsum because the hysteresis between and in other porous media (e.g., soil) has been evident (Royer and Vachaud, 1975; Watson et al., 1975).

A calibration curve for the clay loam was made by fitting the volumetric water content and the TDR-measured dielectric constant to Eq. [4]. Calibration constants were then determined as a = -0.0340, b = 0.0458, and c = 0.718, with r² = 0.987 (Fig. 4A) . The calibration curve was determined using data collected by Probes 1 and 2. Water content measured using TDR with Eq. [2] and [4] agreed well with gravimetrically determined , for > 0.12 m³ m^-3. For 0.05 < 0.12 m³ m^-3, however, TDR overestimated . This overestimation may not be attributed to the special configuration of our probe design because Ren et al. (1999) reported the same trend using a 4-cm long three-rod probe in the same soil. When the general calibration curve (Topp et al., 1980) was used instead of Eq. [4], the middle range of water contents was well estimated, but performance was poor near saturation and in dryer regions (Fig. 4A). Using calibration curves for matric potential (Eq. [3], Fig. 3) and for water content (Eq. [4], Fig. 4A) estimated using the – TDR probes, water characteristic curves for the clay loam were comparable to those determined by the conventional pressure-plate apparatus (Fig. 4B). Deviation from the data collected by the conventional method was found at > -20 kPa and –500 < < -200 kPa, due to calibration errors for the – relationship of the gypsum and the - relationship of the clay loam, respectively.

View larger version (23K): [in this window] [in a new window]   Fig. 4 (A) Relationship between TDR-determined dielectric constant and gravimetrically-determined water content. The calibration curve was determined using only the data obtained by Probes 1 and 2. (B) Comparison of water characteristic curves for the clay loam determined by the – TDR probes with that determined by the conventional-pressure apparatus

View larger version (23K): [in this window] [in a new window]   Fig. 5 Response time of the dielectric constant of the gypsum and the soil during (A) desorption from saturation to = -100 kPa followed by (B) water absorption

	Conclusions

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results and discussion Conclusions REFERENCES

 
A new – TDR probe that simultaneously measures matric potential and water content of soil was developed and tested in the laboratory. Like previously reported devices using gypsum as a porous medium, our new probes showed the similar response of changes with an effective range of -30 kPa. Water content measured by these probes agreed with gravimetrically determined using a soil-specific calibration. The response time was similar to other devices using gypsum as a porous medium. This new TDR probe can be used to simultaneously monitor and in the field. More research is needed to find (i) ideal porous materials with a wide range of water retention and a fast response to the water status of the surrounding soil, and (ii) temperature and hysteresis effects on the – relationship of the porous materials.Wraith Or 1999

	ACKNOWLEDGMENTS

 
The authors thank Dr. Massimo Sementilli, Windsor, Ontario, Canada, for providing the sample of dental plaster; Mr. Don Pahlman, Greenhouse and Processing Crops Research Centre, Agriculture and Agri-Food Canada, for technical assistance; and the Raymond and Mary Baker Trust for financial support.

	NOTES

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results and discussion Conclusions REFERENCES

 
Journal Paper no. J-18077 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa, Projects no. 3262 and 3287, and supported by Hatch Act and State of Iowa.

Received for publication September 21, 1998.

	REFERENCES

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results and discussion Conclusions REFERENCES

 

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