Published in Soil Sci. Soc. Am. J. 68:25-31 (2004).
© 2004 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
DIVISION S-1—SOIL PHYSICS
A Variable-Volume TDR Probe for Measuring Water Content in Large Soil Volumes
C. F. Souzaa,
D. Or*,b and
E. E. Matsuraa
a Faculdade de Engenharia Agrícola, Univ. Estadual de Campinas, Campinas, SP, Brazil
b Univ. of Connecticut, Storrs, CT
* Corresponding author (dani{at}engr.uconn.edu).
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ABSTRACT
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Management of favorable conditions for plant growth within partially wet soil volumes under drip irrigation presents a measurement challenge. Typically, soil water status is determined from a single point measurement or several point measurements within the wet volume requiring various assumptions for quantitative interpretation of total water available for irrigation decisions. We propose a new coaxial time domain reflectometry (TDR) probe capable of measuring the total soil water storage within well-defined soil volumes (referred to as the variable volume coaxial probe, VVCP). The measurement volume is contained between an array of stainless steel conductors embedded in the soil and arranged in a coaxial configuration with variable spacing. The average water content in the spacing between the inner and outer circular arrays of conductors is determined from travel time analysis of VVCP waveforms. Laboratory and field tests of the VVCP established that waveforms and travel time analyses resulted in dielectric permittivities and water contents similar to those obtained with standard three-rod TDR probes. For uniform distribution of soil water VVCP measurements were independent of conductor spacing or soil volume. Variable volume coaxial probe-determined water balance within a partially wet soil volume was in excellent agreement with the amount of water applied from a point source indicating accurate and integrative volumetric measurement.
Abbreviations: EC, electrical conductivity • TDR, time domain reflectometry • TEM, transverse electromagnetic • VVCP, variable volume coaxial probe
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INTRODUCTION
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ADEQUATE ESTIMATION of average water content of wetted soil volumes is important for evaluation and management of drip irrigation systems. Measurements of the extent of wetted soil volumes are often made by either exhaustive soil sampling or deployment of a dense bank of sensors to monitor the spatial distribution of soil water content (Coelho and Or, 1997). Among presently available soil water monitoring techniques, TDR offers the most accurate and repeatable field method. Time domain reflectometry is capable of simultaneous measurement of water content and electrical conductivity within the same soil volume. The method capitalizes on the large disparity between the dielectric permittivities of water (
w = 81) and other soil constituents such as air (a = 1) and soil solid particles (s = 3–5). Consequently, measured bulk dielectric permittivity (b) is dominated by the water phase. The TDR method determines soil b from the travel time of a step electromagnetic pulse along a buried waveguide (TDR probe). Conventional TDR probes are comprised of two or three parallel metal rods completely embedded in the medium of interest (Topp et al., 1982). Zegelin et al. (1989) evaluated various probe designs and concluded that coaxial probe design was superior to two-wire probes with a balancing transformer.
Topp and Davis (1985) extended measurement capabilities from a small volume (point) to multiple depths enabling construction of a vertical water content profile. They designed a probe with step changes in rod diameter causing a step change in probe impedance and consequently a characteristic reflection marking the discontinuity location on the waveform. Travel times between reflections with known physical distances were used to determine water contents in the regions between discontinuities. Hook et al. (1992) designed a probe for profiling soil water with depth using two metal strips mounted on a plastic core where shorting diodes defined the various segments along the probe. Redman and DeRyck (1994) measured the soil water content profile with depth using a probe comprised of a polyvinyl chloride (PVC) access tube with two metal rods attached to its exterior. Another profiling probe was designed by Ferré et al. (1998) using two short rods placed within two parallel access tubes. Small diameter wires lead to the top of the measurement interval, limiting the sensitivity of the probe to the medium above the region of interest.
Extension of TDR measurement capabilities to enable water content sensing within large and well-defined soil volumes are desirable for management of drip irrigation systems due to the nonuniform wetting and highly dynamic changes in soil water status within active plant rooting zones. Coelho and Or (1997) discussed aspects of wetted volume sensing as compared with point measurements and highlighted their importance for proper management and establishment of automatic irrigation threshold values under nonuniform wetting conditions induced by drip irrigation. The primary objective of this study was to develop and test a new TDR probe design termed the variable volume coaxial probe (VVCP) for sensing water content in large and partially wet soil volumes.
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THEORY
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We designed a new TDR probe for measurement of average volumetric water content (or water storage) in a large soil volume confined within a coaxial transmission line formed by concentric arrangement of VVCP conductors (stainless steel rods). The use of transmission lines for dielectric measurements is well-established (Bussey, 1980) using a variety of waveguides ranging from simple parallel wires to fully coaxial designs (Zegelin et al., 1989). The coaxial design has the advantage that the electrical field is confined between the inner and outer conductors, and it propagates in a transverse electromagnetic (TEM) mode, which is the simplest form of guided wave propagation. Consequently, the measurement is confined to the volume that fills the coaxial gap between inner and outer conductors. Such a design has been used in numerous studies such as to measure dielectric properties of rocks (Kraft, 1987), and by the National Bureau of Standards to measure the dielectric properties of soils and agricultural materials (Bussey, 1980).
The VVCP design is shown schematically in Fig. 1
. The transmission line consists of a primary 2-m long coaxial cable (RG-58; 50 ohms) leading from the cable tester to the probe head. From the probe head six coaxial cables (RG-174/U; 50 ohms, 0.6 m) connect the shield of the primary coaxial cable to six stainless steel conductors (each of length 0.26 m and 3 mm in diameter) that form the outer conductors of the VVCP. Six identical rods are connected to the conductor of the primary coaxial cable and form the array of the VVCP inner conductors. The VVCP outer conductor array (comprised of six rods) is inserted at equal spacing around the perimeter of the cylindrical measurement volume, and the VVCP inner conductor is formed by concentric arrangement of the other six rods. The flexible rod arrangement facilitates soil water content measurement within different soil volumes and greatly simplifies conductor's installation in which each rod is inserted individually into the soil (by following marks on the surface or using a simple template). The diameters of VVCP inner and outer conductor arrays are denoted in Fig. 1 as a and b, respectively.
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Fig. 1. A scheme of the proposed variable volume coaxial probe (VVCP) made of two arrays of 0.26-m stainless steel rods embedded in partially wet soil in a coaxial configuration with a and b as the inner and outer diameters of the coaxial VVCP, respectively. Note that the inner six rods are connected by equal length and flexible conductors to the core of the VVCP primary coaxial cable, whereas the outer six rods are connected to the shield on the cable.
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The spatial sensitivity of measurement plays a key role in the performance of the proposed VVCP design due to the combination of nonuniform water content distribution within the measurement volume (expected under drip irrigation) and the nonuniform electromagnetic energy density between the conductor arrays. A theoretical analysis of this problem is beyond the scope of this feasibility study (interested readers are referred to Knight, 1992 and Knight et al., 1997). Based on Knight's (1992) small perturbation analysis for coaxial probe design, we imposed a practical constraint on the VVCP ratio of a/b > 0.1 to reduce the so-called "skin effect" or concentration of most measurement sensitivity within a soil cylinder surrounding the inner conductor array. We also limited our evaluation to either uniform water content distribution (for basic comparison with standard probe designs), or to nonuniform water distribution from a point source located at the center of the VVCP inner conductor array to maintain coaxial symmetry. A drawback of these constraints is the use of a large value of the inner radius "a" resulting in an unmeasured soil volume confined within the inner conductor array (just below the dripper). The consequences of such tradeoffs were evaluated experimentally as discussed below.
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MATERIALS AND METHODS
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Two types of experiments were conducted in the laboratory. First, we studied the electromagnetic performance of the new coaxial probe; subsequently we used the VVCP to determine average water content for uniform and nonuniform water content distributions.
Electromagnetic Performance of the VVCP
The characteristic impedance (Z0 [ohm]) of the VVCP was used to evaluate the electromagnetic performance of the probe as compared with an ideal coaxial design. The impedance of a transmission line is a function of its geometry (spacing and diameters of conductors) and the dielectric constant of the medium surrounding the probe. The characteristic impedance for an ideal coaxial transmission line is (Kraus, 1984):
 | [1] |
where b is the dielectric constant of a material surrounding the transmission line, a and b are the diameter of the inner and outer conductors, respectively. In practice, one can measure Z0 from the reflection coefficient 
ref measured when the probe is filled with a uniform material of known dielectric constant b (Zegelin et al., 1989):
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where ZU is the load impedance (
50 ohms for Tektronix 1502B cable tester [Tektronix Inc., Beaverton, OR]), V1 is the voltage of the measured waveform in the medium, and V0 is the initial voltage of the waveform before travel in the medium (see Fig. 2
for details). We conducted two different tests of the VVCP characteristic impedance comparing Z0 for different combinations of a and b experimentally (Eq. [2]) with geometrically predicted values (Eq. [1]) as summarized in Table 1.
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Fig. 2. Two typical time domain reflectometry (TDR) waveforms obtained with the variable volume coaxial probe (VVCP) placed in soil saturated with tap water (electrical conductivity [EC] = 0.01 dS m–1) and with salt solution (resulting in bulk EC of 2 dS m–1). The variables t1 and t2 mark the first and second reflections used for travel time analysis of the waveform. The values V0 and V1 are used for the calculation of EC (see text for detail).
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Additionally, we compared the shape and several other characteristics of VVCP waveforms with those obtained from standard three-rod TDR probe under similar conditions.
Measurements of Changes in Soil Water Content
Measurements of soil water content under uniform and nonuniform wetting patterns were conducted in a Millville silt loam soil (Or and Hanks, 1992), in the laboratory, and in the field. The air-dried soil was sieved (through a 2-mm sieve) and packed in a large cylindrical container (with diameter of 0.50 m and height of 0.50 m). The soil bulk density in all experiments was about 1.30 Mg m–3. A Mariotte device was used to uniformly wet the soil surface by ponding, and later by supplying water to a dripper with a flow rate of 2 L h–1 to induce a nonuniform (radial) wetting pattern. Changes in water content were monitored through measurement of soil b using a Tektronix 1502B cable tester (Tektronix Inc., Beaverton, OR) equipped with a RS 232 computer interface. Time domain reflectometry waveform collected from either the VVCP or standard three-rod probe (with rod length equal to that of the VVCP rods L = 0.26 m) were analyzed to infer water contents were performed automatically using a computer program (WinTDR, 1999). The Topp et al. (1980) equation was used to calculate volumetric water content, 
, from TDR measured b.
Uniform Soil Water Content
Starting with a saturated soil, we allowed the water content to decrease gradually and measured subsequent changes in soil water content using the VVCP and a three-rod probe during 35 d. The top surface of the container was divided into 64 grid cells (0.0025 m2 each), and a three-rod probe (rod length of 0.26 m) was sequentially inserted into the soil in the center of each cell to obtain a "point" value of water content. The resulting 64-point measurements were averaged and compared with VVCP volume-averaged measurements for the same conditions. These latter measurements were obtained by inserting the VVCP in a prescribed coaxial arrangement considering different volume combinations by varying a and b values.
Nonuniform Soil Water Content
The soil surface was wetted using a dripper with a flow rate of 2 L h–1. In the laboratory experiments we applied the following discrete water volumes of 1, 2, 3, 4, and 8 L at 1-d intervals. The dripper was placed in the center of the inner coaxial array "a" of the VVCP. Additionally, we conducted a field experiment within a drip-irrigated corn (Zea mays L.) field by applying 20 L of water in a single event (located in the center of the VVCP). Soil water dynamics was monitored using the VVCP at 8-h intervals in the laboratory, and 1-d intervals in the field. Details of the various combinations and monitoring volumes are presented in Table 2.
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RESULTS AND DISCUSSION
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Electromagnetic Performance of the VVCP
Waveforms Measured with the VVCP
Figure 2 depicts a waveform collected using the VVCP with inner spacing a = 0.04 and outer spacing b = 0.30 m embedded in saturated soil. The reflection coefficient as a function of TDR signal travel distance is shown. The points t1 and t2 correspond to signal reflections at probe entry (soil surface) and probe end, respectively. The propagation velocity is determined from these features, and subsequently used to determine the bulk dielectric constant of the medium. The inferred water content from the attached waveform is 0.39 m3 m–3, which in good agreement with standard three-rod probe measured water content of 0.40 m3 m–3. Concurrent measurements of electrical conductivity (EC) rely on VVCP waveform attenuation as a function of bulk EC and VVCP characteristic impedance. A sample of waveform measured in soil saturated with salt solution with bulk EC of 2.08 dS m–1 is depicted in Fig. 2.
VVCP Characteristic Impedance
Comparisons between geometrically calculated (Eq. [1]), and measured (Eq. [2]) characteristic impedance for different VVCP configurations (volumes) are summarized in Table 1. The results show an increase in characteristic impedance value (measured and calculated) with increasing diameter ratio b/a, which is also proportional to measured soil volume. The increase in characteristic impedance with larger probe volumes may cause an increase in signal attenuation and adversely impact waveform analysis for travel time (water content). Combination #6 (a = 0.04 and b = 0.40 m) with a/b = 0.1 resulted in the highest measured characteristic impedance (Z0 = 205 ohms) that was close to 197 ohms for the three-rod probe with a/b = 0.12 (see bottom row in Table 1).
The geometric equation for the characteristic impedance of a coaxial transmission line (Eq. [1]) predicts that a plot of Z0 vs. ln(b/a) is a line with a slope of 60 and intercept of zero. The results of our first test (Test 1) yielded the theoretically correct slope of 60, however, there was a constant offset (of about 60 ohms) that was attributed to an incorrect reference (V0) determination in an earlier version of the WinTDR program. This was corrected and subsequent measurements resulted in reasonable correspondence with theoretical values as depicted in Fig. 3
(Test 2) and shown in the last column of Table 1. In summary, characteristic impedance measurements suggest that the VVCP electromagnetic performance is similar to an idealized coaxial transmission line for most combinations of a and b tested.
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Fig. 3. Variable volume coaxial probe (VVCP) characteristic impedance Z0 as a function of probe geometry (expressed as ln[b/a]). The full symbols are experimental results of Test 1 measurements (with faulty V0 reference), the empty symbols are Test 2 measurements, and the line is the predicted characteristic impedance for a perfect coaxial probe (Eq. [1]).
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Soil Water Content Measurements for Uniform Spatial Distribution
Temporal variations in soil water content for uniform soil wetting (Fig. 4)
, clearly show the agreement between the VVCP and a standard three-rod probe. Deviations between the two probes become noticeable only at water contents below 0.09 m3 m–3. Note that the results represent averages over several VVCP configurations (Table 2) that became progressively difficult to vary as the soil became drier. In some instances repeated installation resulted in small air gaps that could perhaps explain some of the discrepancies shown in Fig. 4. Such repeated installations were made for evaluation purposes only and do not reflect the intended use of the VVCP in which a single configuration encompassing a target soil volume is likely to be used for prolonged periods of monitoring. The correspondence between the two sets of measurements during water redistribution phase confirm that VVCP water content measurements in a uniformly wet soil are indistinguishable from those obtained with standard three-rod probe.
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Fig. 4. Measured soil water content dynamics for uniformly wet soil using variable volume coaxial probe (VVCP) and multiple readings from standard three-rod time domain reflectometry probe (first measurement in saturated soil).
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Soil Water Content Measurements for Nonuniform Spatial Distribution
Laboratory Measurements
For this series of experiments, water was applied to the soil surface from a single emitter (flow rate of 2 L h–1) to induce a radial distribution pattern of water content. Figure 5 summarizes measurements of soil water dynamics during a 40-h period with incremental addition of water as indicated on the x-axis. Application times were 0.5, 1, 1.5, 2, and 4 h for the cumulative volumes of 1, 2, 3, 4, and 8 L. The results reflect the dynamic process of water redistribution between application events. Nonuniform water content spatial distribution under drip irrigation affects VVCP measurements as progressively larger soil volumes are interrogated by the probe from the C1 configuration (
3 L of soil) to the C5 configuration (47 L of soil, see Table 2). As the soil volume sensed by the VVCP increased, the volume-averaged water content measured was lower because of the larger fraction of dry soil included in the progressively larger measurement volume.
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Fig. 5. Measured water dynamics in different soil volumes after application of 1, 2, 3, 4, and 8 L of water.
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To evaluate the mass balance between water applied and soil water volume sensed by the VVCP under nonuniform spatial distribution, we have chosen to use measurements taken with the C5 configuration (the largest and most inclusive soil volume measured). The resulting average water contents and equivalent volumes of water sensed (the product of volumetric water content and soil volume) after application of 1, 2, 3, 4, and 8 L of water are shown in Table 3. All water volume calculations were corrected for the residual water content (r = 0.02 m3 m–3). The soil surface was covered with plastic sheet to reduce evaporative losses during the experiments. The results in Table 3 show good agreement between water volume applied and measured in the soil. The small and constant discrepancy observed between VVCP-measured and applied water volumes of about 0.07 L is attributed to the unmeasured soil volume in the core of the VVCP probe (i.e., soil volume enclosed by inner conductor as can be seen in Fig. 1b). This difference requires a small correction that can be applied at the onset of the experiment or monitoring period (an estimate of the soil volume and porosity can provide an upper bound for the maximum amount of water stored in this immeasurable volume).
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Table 3. Volumetric water content and soil water volume measured by VVCP in the C5 configuration (Soil volume = 47 L; Residual water content [r] = 0.02 m3 m–3).
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Field Conditions
The dynamics of water redistribution and evapotranspiration in a wetted soil volume in the field experiment was monitored during four consecutive days after application of 20 L of water from a dripper. The results depicted in Fig. 6
show that total water storage in the partially wetted soil volume decreased with elapsed time since the end of irrigation. It can also be seen that increasing the measurement volume results in lower average soil water content as expected from incorporation of larger proportions of drier soil into the measurement soil volume. From geometrical considerations, it is evident that a given wet soil volume contained in progressively larger cylindrical measurement volumes sensed by the different VVCP configurations would result in progressively lower values of average water content as seen in Fig. 6. The field results confirm our laboratory findings and show that VVCP measurements are reliable and can be used for field measurement of partially wet soil volumes. Comparisons with volume averaged three-rod measurements obtained from three locations (same depth as VVCP of 0.26 m) show that the water content volume averaging by the VVCP was similar to averaging obtained by these multiple measurements by three-rod probe.
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Fig. 6. Temporal changes in average soil water content in different soil volumes measured by VVCP (square symbols) and standard three-rod probe (circle, average of three measurements) under field conditions during 4 d after application of 20 L of water from a dripper.
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Both laboratory and field experimental results described in this section clearly demonstrate that for water application from a point source located at the center of the VVCP, radial variations in water content distribution did not have a significant impact on the capability of VVCP to measure total water stored within the soil volume defined by the coaxial arrays. The apparent lack of sensitivity to radial spatial variations in water content (and in bulk dielectric constant) may be attributed to the relatively high a/b ratios used that reduced skin effects and extreme sensitivity observed in other studies (Annan, 1977; Knight et al., 1997). Additionally, the use of large a values (large inner diameters) may have reduced large radial gradients in water content near the point source in favor of more gradual radial variations with small spatial sensitivity as predicted by the perturbation analysis of Knight (1992). These conclusions however, are limited to a point source located at the VVCP axial-symmetry, for nonsymmetrical point sources, issues of spatial sensitivity are likely to become more significant.
Potential Applications of the VVCP
We envision several potential applications for the proposed VVCP. The primary application is the use of a single probe to monitor changes in water and solute mass emitted from a point source within relatively large soil volumes. This leads to practical applications involving integration of soil water status in crop rooting zones that are nonuniformly wetted by drip and micro irrigation. In addition to monitoring applications, the VVCP offers unique capabilities as a controller for maintaining predetermined water storage or average water content within a given measurement volume (defined by the VVCP deployment volume). This capability could be useful for a developing orchard with young trees (or vines) whose rooting volumes evolve with time and require different amounts and volumes of water and fertilizer with time.
The VVCP may be suitable for lateral profiling of soil water distribution around a point source by using various coaxial configurations to differentiate soil water conditions at different radial slices or soil volumes. We speculate that other applications in the wood and construction industry requiring determination of water content in large volumes of porous media (wood, concrete, etc.) could benefit from the availability of a probe capable of interrogating such large volumes. Finally, we anticipate that the VVCP could play an important role as an experimental platform for testing theoretical models for spatial sensitivity functions and volume averaging under a wide range of configurations (for example predictive models developed by Knight, 1992 and others).
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SUMMARY AND CONCLUSIONS
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We designed and tested of a new TDR probe (termed VVCP) for measurement of water content and electrical conductivity in partially wetted soil volumes. Coelho and Or (1997) emphasized the need for such volume averaging measurement capability for irrigation management in partially wetted soil volumes such as by drip irrigation. The VVCP is comprised of 12 stainless steel rods (3 mm diam.) arranged in the measurement volume in a coaxial transmission line configuration with six rods forming the outer shell, and the other six rods forming the inner coaxial core.
Experimental results show consistent relationships among measured water content by VVCP and by standard three-rod TDR probes at different soil volumes, and they exhibit similar dynamic responses. The following conclusions may be drawn from the results: (i) waveforms measured with the VVCP were similar to those obtained with standard three-rod probes; (ii) measured characteristic impedance of the VVCP for different combinations was similar to geometrically calculated values for an ideal coaxial probe; (iii) the VVCP was capable of maintaining a water balance to within <90% for uncorrected measurements, and could easily be improved to nearly 98% considering the unmeasured core of the coaxial probe; (iv) an important attribute of the proposed VVCP is the determination of volume-averaged water content and its dynamics around a dripper using a single measurement. No other method presently used for drip irrigation management can provide such information (neutron probe cannot measure near the surface, other TDR applications require multiple probes and averaging). Our conclusions suggest that future research should focus on evaluation of VVCP for other soil types and variable water content contrasts (e.g., drip irrigation in a relatively wet soil).
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ACKNOWLEDGMENTS
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This research was supported in part by Grant 98/04931-7 and 98/13819-6 from Fapesp– Fundação de Amparo à Pesquisa do Estado de São Paulo–Brazil. Special thanks to Alberto Colombo, Markus Tuller, Teamrat Ghezzehei, Scott Jones, Bill Mace, and Vaughn Thacker for their able assistance during various phases of the study. The support of Utah State University (USU) and the Israel-US Binational Agricultural Research and Development Fund (BARD) through grant no. IS-2839-97 is gratefully acknowledged.
Received for publication February 5, 2002.
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REFERENCES
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ABSTRACT
INTRODUCTION
