Published online 11 January 2008
Published in Soil Sci Soc Am J 72:11-15 (2008)
DOI: 10.2136/sssaj2007.0076
© 2008 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
SOIL PHYSICS
Electrical Spectra of Undisturbed Soil from a Crop Rotation Study
S. D. Logsdon*
National Soil Tilth Lab., 2110 University Blvd., Ames, IA 50011
* Corresponding author (sally.logsdon{at}ars.usda.gov).
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ABSTRACT
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Soil permittivity can be determined across a range of frequencies, but little is known about how the factors derived from the frequency spectra are related to soil pore structure or crop management. The purpose of this study was to test use of a 12-wire, quasi-coaxial probe for determining soil permittivity spectra, and to see if derived factors could be related to soil pores and crop management practices. Undisturbed soil cores were collected from two management fields, one with a 2-yr rotation and the other with a 6-yr rotation. Comparisons between the fields were based on 95% confidence intervals of the differences in the means for each factor tested. Similar analysis was used to compare cores with and without continuous macropores. The soil from the 6-yr rotation had significantly higher water content (
) after drainage to 100-cm pressure head, and had significantly lower air-filled porosity (AFP) after free core drainage. The cores with continuous macropores had a significantly higher natural log of saturated hydraulic conductivity and AFP after drainage to 100-cm pressure head, and significantly lower bulk density and square root of apparent permittivity at a higher frequency than cores without continuous macropores. The cores from soils with carbonates had higher electrical conductivity as a function of AFP than those from the soils without carbonates. Overall, soil macropore differences were more pronounced than differences in crop management practices. The 12-wire probe was useful for determining permittivity spectra on undisturbed soil.
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INTRODUCTION
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Many soil moisture sensors attempt to relate the apparent permittivity to soil water content. The electrical spectra have been determined either through inversion of time domain measurements (Feng et al., 1999) or measurements across a range of frequencies (Logsdon, 2005). Little is known about how the factors derived from the spectra are related to soil pore structure or management effects. Undisturbed samples must be used to determine soil pore structure effects, which is not possible for ground soil packed into a sample cell.
Permittivity properties across a range of frequencies are altered by relaxation processes under the alternating electrical fields. Polar molecules, such as water, reorient according to the alternating electrical field until the alternating frequency becomes too high, i.e., too fast for the molecules to respond. Free water has a high relaxation frequency (
17 GHz depending on temperature and salinity [Stogryn, 1971]), meaning that at this frequency, about half of the water molecules are no longer able to rotate. The relaxation frequency is lowered if the water molecules are hydrating solutes or are sorbed to colloids, with differences related to colloid surface properties such as charge density, position of the water molecule relative to the charge site on the colloid surface and the exchangeable cations, and degree of hydrophobicity.
Permittivity is complex, with real and imaginary components:
 | [1] |
where 
* is complex permittivity, ' is the real component of permittivity, i is the square root of –1, f is frequency, 
dc is the direct current electrical conductivity, v is the permittivity of a vacuum (8.854 x 10–12 F m–1), and R'' is the relaxation component of imaginary permittivity. Notice that there are two factors contributing to the imaginary component: a relaxation component and a component that increases as f decreases. The apparent permittivity, a, is derived from the combined imaginary component as well as the real component (Topp et al., 1980):
 | [2] |
There are other factors affecting the a at low f besides the free water relaxation at high f. In addition to the dc effects, there are ion migration effects within the water sorbed to the colloids (Hunt et al., 2006) that contributes to rotating polarization of the colloid under alternating current at lower frequencies. In addition, an interaction of a lossy (conducting) material with the electrodes results in electrode polarization effects (Schwan, 1966) that increase as sample size decreases. Many calculation procedures for converting measured electrical properties to permittivity are less accurate at frequencies higher than the transverse electromagnetic (TEM or single mode) range (Kraft, 1987; Heimovaara et al., 1996). The TEM range decreases as sample size increases, so the most accurate measurement range of electrical properties decreases as sample size increases. Small sample holders require homogenized, ground soil, which may not be representative of structured soil; therefore, larger samples are better for structured soil even with loss of the higher frequency range.
Measurements made by packing soil into a coaxial cell are affected by aggregate size because of poor contact for larger aggregates (Miyamoto et al., 2003; Blonquist et al., 2006; Logsdon, 2006). Also it is necessary to have a large-diameter inner conductor (about half the diameter of the outer conductor) to maintain the impedance close to 50 
for measurements with a vector network analyzer (empty sample holder). Pushing a small-diameter electrode (relative to aggregate size) through soil results in better contact than packing soil around an electrode (Whiteley and Dexter, 1982). Others have used a seven-wire quasi-coaxial probe (Heimovaara, 1994), but unless the inner wire has a very large diameter, the impedance of the empty sample holder will not be close to 50 . Souza et al. (2003) used six wires for the inner conductor as well as six wires for the outer conductor. Then the spacing can be maintained to achieve close to 50- impedance for the probe in air.
The purpose of this study was to determine if electrical spectra could be determined from undisturbed soil after inserting a 12-wire quasi-coaxial probe. A secondary objective was to determine if parameters determined from the complex electrical spectra could differentiate management or structural effects. A preliminary study (data not shown) had shown similar results for packed soil measured with the 12-wire probe and for the same soil packed into the coaxial cell used by Logsdon (2005).
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MATERIALS AND METHODS
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Two adjacent fields were compared in this study. Both had been converted from continuous corn (Zea mays L.) disk-harrow to no-till in 1995. One field had a 2-yr corn–soybean [Glycine max (L.) Merr] rotation, with both crops present each year. The other field had a 6-yr rotation (corn–soybean–corn–3 yr alfalfa [Medico sativa L.]) in contour strips, all crops present each year.
The loess soils present in these fields were (Fisher, unpublished data, 1970): Ida, a fine silty, mixed, superactive, calcareous, mesic Typic Udorthent; Dow, a fine silty, mixed, superactive, calcareous, mesic Typic Udorthent; Monona, a fine silty, mixed, superactive, mesic Typic Hapludoll; Napier, a fine silty, mixed, superactive, mesic Cumulic Hapludoll (well drained); and Kennebec, a fine silty, mixed, superactive, mesic Cumulic Hapludoll (moderately well drained). All are fine silty because they are developed in loess. All are superactive, indicating larger amounts of charged clays. Ida and Dow are similar, both being Entisols and calcareous, which increases the dc, especially at high water contents. The difference is that the Ida soil has <0.18 kg kg–1 clay and Dow has 0.18 to 0.24 kg kg–1 clay. They are developed from calcareous loess on side slope positions with D (9–14%) and a few E (14–18%) slopes. Monona is on summit and shoulder positions with B (2–5%), C (5–9%), and a few D slopes. Napier and Kennebec are cumulic, being located in toeslope positions, with Kennebec closer to the first-order streams. Napier is well drained with B and C slopes, whereas Kennebec is moderately well drained with A (0–2%) and B slopes. For this study, we paired by soil means within field management (Karlen and Colvin, 1992). As described in Karlen and Colvin (1992), for each soil, the difference between the management fields was calculated. Then the 95% confidence interval was determined for the five means, and the differences were considered significant if the confidence interval was all negative or all positive.
Undisturbed soil cores were collected in the fall of 2004. The cylinders were thin-walled stainless steel with 74-mm diameter and 76-mm length. Soil physical measurements included saturated hydraulic conductivity (Ks) by the falling-head method, air-filled porosity (AFPfd) and water content (fd) after free core drainage, water content (100) and air-filled porosity (AFP100) after desorption to 100-cm applied pressure head, bulk density (
b), and pore continuity as indicated by white paint (Ewing and Horton, personal communication, 2005) after completing all other measurements. After oven drying and cooling, white paint was poured into the undisturbed samples. The paint infiltrated only the macropores because the high viscosity did not permit the paint to enter the smaller soil pores. After the paint had set, the soil cores were examined to see if the paint had infiltrated to the bottom of the sample, indicating a continuous macropore. Enough soil was excavated from the bottom of the sample to make sure the paint had infiltrated through a macropore and not between the cylinder wall and the soil.
The 12 wires for our prototype probe (Fig. 1
) were originally 50-mm-long cylinders, connected to the BNC connector within a 9-mm-thick epoxy head. Only 38 mm of wire extended beyond the head. The wire diameter was 1 mm, the spacing of the inner six wires was 17 mm, and the spacing for the outer six wires was 53 mm. The electrical length had been calibrated by four fluids, as described by Logsdon (2005), and determined to be 0.1236 m. This was longer than the physical length, presumably due to the wires in the probe head, and due to electrical fringing beyond the probe. The wires in the head were longer than the head thickness because they were angled to meet the connections in the coaxial cable.
The 12-wire probe was inserted into each soil sample after desorption to 100 cm. In total, there were 72 cores. One fell apart with b the only determination; two others did not have electrical property measurements, one because of a dense, platey layer in the center of the sample, and the other because it fell apart. Water was added, equilibrated, and the electrical spectra measured again. For some of the samples that were drier after 100-cm drainage, measurements were made after a third equilibrated water content. The electrical spectra were measured with the Vector Network Analyzer (Agilent 8753E, Agilent Technologies, Santa Clara, CA). Output (complex reflection scattering parameter: S11*) was converted to complex impedance (Z*), complex electrical conductivity (*), and complex permittivity (*):
 | [3] |
where Zp is the probe impedance in air (calculated from probe dimensions):
 | [4] |
c is the speed of light, L is the electrical length (from calibration in a series of fluids [Logsdon, 2005]), m and k are outer and inner radii of coaxial cell, and a is defined in Eq. [2]. As for permittivity (Eq. [1]), ' and '' are the real and imaginary .
Then the longitudinal resonance frequency (fR, Heimovaara et al., 1996; Shang et al., 1999) was determined from the frequency at the first valley of the S11' (real component) and the square root of the a was determined at the fR:
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Remember that a (Eq. [2]) includes both real and imaginary components. The ' spectra were used to fit the dc, a characteristic frequency (fc, at slope change), and the final slope (exponent n) (Hunt et al., 2006):
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The b effects are often accounted for by empirical volumetric mixing models (Roth et al., 1990):
 | [7] |
where v is the volumetric fraction of the component, and the subscripts m, w, s, and p refer to mixture, water, soil, and air, respectively. The of water is assumed to be 76 to 80 (depending on temperature), soil solids around 4 to 10, and air is 1. The exponent x is usually assumed to be between 0.5 and 1. We fit x using w set to 76 and s set to 5. Sometimes a "bound" water fraction is included using assumed lower values derived at high frequencies. There are some difficulties with this approach. First, the components are not merely additive, but rather interacting (Jonscher, 1996; Sihvola, 1999; Hunt, 2001), especially water sorbed to colloid surfaces. The "sorbed" or "bound" water is not well characterized at the lower frequencies of the spectra, often being much greater than values for free water (rather than lower as for the higher frequencies, or higher than the dielectric relaxation for bound water, which varies with sample).
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RESULTS AND DISCUSSION
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The fitted exponent x from the mixing model (Eq. [7]) was 1, but there was a lot of scatter (Fig. 2
). Usually x is assumed to be 0.5 at higher frequencies, but data have shown that 1 is more appropriate at lower frequencies (Schaap et al., 2003). For the data from this study, cancellation of effects may have resulted in a fitted x of 1. The sorbed water permittivity values were probably >80 assumed from "free water," and the resonance frequencies were in the 100-MHz range (mid rather than high). The a was much larger than the ' for frequencies lower than around 100 MHz (Fig. 3
). Soil moisture sensors that determine the a at lower frequencies could result in higher than expected readings for soils with high-charge clays.
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Fig. 2. Measured apparent permittivity (a) at the resonance frequency (Eq. [5]) as a function of that predicted from a volumetric mixing model (Eq. [7]), best fit with an exponent of 1. The dashed line is the 1:1 line.
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Fig. 3. Sample permittivity spectra at three water contents for (a) real and imaginary components, and (b) calculated apparent permittivity.
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Pairing soil means and examining the 95% confidence intervals of the difference showed that the soils with continuous macropores (Table 1
) had a significantly higher natural log of Ks, higher AFP100, lower b, and lower a1/2 at 100-cm applied pressure head (even though the 100 was not significantly different, nor was AFPfd). None of the other physical or electrical factors were significantly different between cores with and without continuous macropores.
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Table 1. Significant differences for mean soil properties in cores containing continuous macropores (CMP) vs. those cores not containing continuous macropores.
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Comparing the 2-yr vs. the 6-yr rotation (Table 2
), soil cores from the 6-yr rotation had significantly higher 100, but AFP100 was not significantly different; however, the AFPfd after free core drainage was significantly less for the 6-yr rotation. No other physical or electrical properties were significantly different due to crop rotation.
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Table 2. Significant differences for mean soil properties for cores taken from corn–soybean (CS) rotation vs. those taken from corn–soybean–corn–3 yr alfalfa (CSCAAA) rotation.
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At a given AFP, the dc was higher for the Ida and Dow soils, which had carbonates, than for the soils without carbonates (Monona, Napier, and Kennebec), but there were some crossovers (Fig. 4
). A few Kennebec samples were located downslope from Dow soils, and calcareous cumulic soil from Dow could have washed over the Kennebec soil. Also, a few of the Monona samples showed higher dc, perhaps due to erosion down to the calcareous layer that occurred since the first-order soil survey was done in 1972.
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Fig. 4. Soil effects on electrical conductivity as a function of air-filled porosity grouped by soils with or without free CaCO3.
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There were some expected significant correlations among the physical properties (Table 3
), since AFP is calculated from b and . There were not many correlations between the natural log of Ks and other physical factors because of the variability. Similarly, there were expected significant correlations within the electrical properties (Table 4
). Interestingly, fc was not correlated with a1/2 at the fR or with , but was negatively correlated with '101/2. Correlations between physical and electrical properties (Table 5
) showed significant correlations between air or water and several of the electrical factors, as expected, but the correlations were stronger for '101/2 than for a1/2 or . It was not apparent why the strongest correlations of the natural log of Ks were with fc and the exponent n (from Eq. [6]), and a weak correlation with a1/2.
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CONCLUSIONS
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Although there were some significant soil physical and electrical property differences related to continuous pores, there were only two significant soil physical differences related to crop rotation (air-filled porosity after core drainage and water content after drainage to 100-cm pressure head). The electrical spectra were more sensitive to soil differences than crop management differences (Fig. 4). There were expected correlations among physical factors and among electrical factors, as well as some correlations between physical and electrical factors, but the r2 values were only between 0.05 and 0.67.
The spectra data were useful for interpreting apparent permittivity as well as the real component response at different frequencies. The apparent permittivity increased much more at lower frequencies than did the real permittivity. This is important since many soil moisture sensors are based on apparent permittivity, but the theory relating permittivity to soil water content is based on real permittivity. At 50 MHz, the apparent permittivity was >70% higher than the real permittivity for wet samples (Fig. 3), and at 10 MHz it was >150% higher. The new generation capacitance- and impedance-based soil moisture sensors operate at lower frequencies than traditional time domain reflectometry (unless long cables are used). The lower frequencies allow development of lower cost sensors, but the numbers will not be the same as high-frequency measurements. At the lower frequencies, the a will often vary with soil properties other than water, necessitating site-specific calibrations.
The 12-wire probe was useful for measuring electrical spectra in undisturbed soil. An improved 12-wire probe has been developed for future studies across a wider range of soils with different mineralogies and organic matter and salt contents.
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NOTES
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Mention of manufacturers' names is for information only and does not constitute endorsement by the USDA.
All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Permission for printing and for reprinting the material contained herein has been obtained by the publisher.
Received for publication February 21, 2007.
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ABSTRACT
INTRODUCTION
