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a National Agricultural Research Center for Kyushu Okinawa Region, Nishigoshi, Kumamoto 861-1192, Japan
b Faculty of Agriculture, Yamagata University, Tsuruoka, Yamagata 997-8555, Japan
c Biotron Institute, Kyushu University, Hakozaki, Fukuoka 812-8581, Japan
* Corresponding author (teruhito{at}affrc.go.jp)
Received 16 May 2002.
ABSTRACT
Various types of soil physical properties are affected by texture and structure. Our objective was to determine aggregate structure effect on the soil dielectric property of an Andisol measured by time domain reflectometry (TDR). The relationships between volumetric water content (
) and dielectric permittivity (
) for both a wet-sieved aggregate and its crushed sample were examined and compared. In the – relationship for 0.1- to 2.0-mm-diam. wet-sieved aggregates, the gradient of the – curve moderately changed at a volumetric water content (critical water content), although this property disappeared when we crushed the aggregate structure. Furthermore, the critical value corresponded to the water content of the plateau in a bimodal-type water retention curve. We suggest that effects of aggregate structure on a soil's dielectric property are involved in the aggregate sizes, the configuration of water in aggregates, the processes of water filling in intra- and interaggregate pores, and the low value of bound water adsorbed on soil surfaces.
Abbreviations: RMSE, root mean square error • TDR, time domain reflectometry
TIME DOMAIN REFLECTOMETRY has become a popular method of soil water measurement since Topp et al. (1980) showed the unique relationship between volumetric water content () and dielectric permittivity () for mineral soils:
 | [1] |
Moreover, the TDR research has been followed by numerous studies to examine many factors affecting the dielectric properties of soil, such as water content and its status as bound or free water, soil texture (Dasberg and Hopman, 1992; Dirksen and Dasberg, 1993), organic matter (Topp et al., 1980; Herkelrath et al., 1991), soil bulk density (Dirksen and Dasberg, 1993; Jacobsen and Schjønning, 1993), electromagnetic measurement frequency (Campbell, 1990; Heimovaara, 1996), temperature (Wraith and Or, 1999), salinity (Persson and Berndtsson, 1998), particle shape (Jones and Friedman, 2000), and particle-size distribution (Robinson and Friedman, 2001).
Natural soils may be characterized by soil structure and texture. Many soil physical properties have been determined in relation to soil structure and texture. Volcanic soils are very unique soils in aggregate structure, with well-defined and stable intra- and inter-aggregate voids. Therefore, these soils commonly have low natural bulk density, high porosity, relatively large specific surface areas, and large water holding capacities. These characteristics contribute to various kinds of physical properties, including water retention, water transmission, and/or thermal conditions (Maeda et al., 1977).
It is well known that the – relationship for volcanic soils deviates significantly from Eq. [1] because of high porosity (Weitz et al.,1997; Miyamoto and Annaka,1998; Tomer et al.,1999; Miyamoto and Chikushi, 2000). Miyamoto and Annaka (1998) measured the – relationship for an aggregated Andisol and found that in the relationship there exists a volumetric water content at which the slope of the – relationship (i.e., the change of dielectric permittivity per unit change of volumetric water content) moderately changes (Fig. 1). They referred to this volumetric water content as a critical water content and suggested that this is the result of the soil structure effect on the dielectric properties of Andisols. Similar results of the – relationship for an Andisol were reported by Fukumoto and Tanaka (1995) and Haraguchi (1999). Despite the definite characteristic in the – relationship for Andisols, little concern has been given to it. Thus, there has been no clarification of why the – relationship for Andisols has the critical volumetric water content at which the slope of the – relationship apparently changes.
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– relationships for wet-sieved aggregates were examined and compared with the – relationships for crushed aggregate samples. Furthermore, a water retention curve was employed to evaluate volumetric water content at the point where the slope of the – relationship moderately changes. MATERIALS AND METHODS
Aggregate Soils
Sample soils were from an experimental field at the National Agricultural Research Center for Kyushu Okinawa Region in Kumamoto, Japan. The species of soil was Andisol (Hydric Pachic Melanudands). The soil was passed through a 2-mm sieve and air-dried.
A clod of the soil was prepared into four aggregates as follows. A nest of five sieves was placed in a holder and suspended in a container of water. The mesh sizes of the sieves were 2.0, 1.0, 0.5, 0.25, and 0.1 mm. The sample clod was put on the top sieve of the nest, and then the nest was alternately moved up and down for a vertical distance of 38 mm at a rate 30 cycles min-1 for 40 min. The residues of each sieve were used as aggregate samples to determine the – relationship. Thus, size fractions of the aggregates were 1.0 to 2.0, 0.5 to 1.0, 0.25 to 0.5, and 0.1 to 0.25 mm in diameter. Besides the four fractions of wet aggregates, air-dried soil passed through a 0.1-mm sieve was also used for obtaining the – relationship for comparison. Physical properties for soil samples used in this study are shown in Table 1. Water content at air dryness or -1555 kPa (shown in Table 1) were used as that of bound water.
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– Relationships– relationships, each soil sample was packed uniformly into a transparent acrylic box, 0.06 m high, 0.08 m wide, and 0.15 m long. Through the box wall we could observe water behavior in the box. Two stainless-steel parallel rods (3-mm diameter, 0.14-m rod length, and 0.03-m spacing between rod centers) were set horizontally in the box as a wave-guide. The rod ends were connected to TDR cable testers (Tektronix 1502B; Tektronix, Beaverton, OR) through shielded TV-antenna wire, an impedance-matching transformer, and a 50-
coaxial cable. In the calibration experiment with aggregate soil, a series of data were obtained in a soil water drying process step by step to establish the equilibrium of water distribution in soil for each measuring step. The experiment was repeated twice with the same procedure. For each step, <30 mL of water was lost in the soil samples during evaporation period of 12 h to 3 d. The time required for one run of the experiment was 6 to 8 wk. The measurement of was conducted using the WinTDR98 waveform analysis software (Or et al., 1997), which enabled the automated TDR control, data acquisition, and waveform analysis. Water contents were measured by weighing the soil samples gravimetrically using an electronic balance.
After the calibration experiments for aggregated soil samples, the aggregate was crushed with a mortar and pestle and passed through a 0.1-mm sieve. For the crushed samples, the calibration procedure was also conducted as mentioned above under the soil water wetting process. This is because the bulk density of the soil samples cannot be held constant since the shrinkage of the crushed samples occurs under the soil water drying process. For each water content step, the corresponding soil and distilled water were thoroughly mixed, and then kept the water content constant. After curing for at least 24 h, at which time the soil moisture was uniformly redistributed, the moist soil was packed into the acrylic box in small increments. The measurements of and were conducted as mentioned above.
Measurement of Water Retention Curve
The aggregated soils were packed into a soil sample cylinder (51 mm in diameter and 25 or 50 mm high) with the same soil bulk density as the soil sample for measuring the – relationship. For aggregated soils, the water retention curves were determined by a suction column method (e.g., Jamison, 1958) in the high matric potential (>-3.1 kPa) range. By using the same soil sample column the equilibrium soil wetness in the range between -1555 and -3.1 kPa was measured by the pressure plate method (Klute, 1986). To determine the water retention curve more precisely for the 1.0- to 2.0-mm aggregate size, an additional measurement was conducted using a soil column (25.5 mm in diameter and 100 mm high) by the suction column method. After soil water equilibrium, the soil column was divided into 10 sections 10 mm high, and the water content of each section was measured. The equilibrium soil wetness in the lower matric potential (<-1555 kPa) range was also obtained by the vapor equilibrium method (Klute, 1986).
For Andisols, the water retention curve has often shown a prominent bimodal-type feature. Thus, the measured retention data were fitted by using a bimodal retention function consisting of a linear superposition of van Genuchten (1980)-type retention models (Durner, 1994).
 | [2] |
- r)/(s - r), with r and s the residual and saturated water content (cm3 cm-3), respectively, is the volumetric water content, 
is the soil water pressure head (cm), wi are the weighting factors for the least squares optimization, 
i (cm-1) and n are curve-fitting parameters, and mi is related to ni as mi = 1 - 1/ni. k is the number of modes and equals 2 for a bimodal type. Se is considered a cumulative distribution function of a capillary pore size with a distribution function f(), which may be expressed by the equation (Durner, 1994). Pore-size distributions are estimated using the following equation,
 | [3] |
The parameters of the bimodal retention function are optimized by the objective function
 | [4] |
s, r, ni, mi, wi}T is the parameter vector, N is the number of () data, 
i are the weighting factors, and i and 
(i,P) are the measured and estimated water contents at i, respectively. The nonlinear parameter estimation code Soil HYdraulic Properties FITting (SHYPFIT) (Durner, 1995) was used to obtain parameter values for bimodal moisture retention curves in this study.
Application of the Dielectric Mixing Model
The mixing model is useful for understanding the dependency of the dielectric permittivity on the water content and soil physical properties (Dirksen and Dasberg, 1993). Some mixing models based on physical theory have been proposed to describe the – relationship accounting for soil physical properties (De Loor, 1964, 1990; Birchak et al., 1974). Among various kinds of mixing models, the Maxwell–De Loor model has been chosen for convenience since the model does not include any geometrical fitting parameter. Dobson et al. (1985) rewrote this basic model for a four-component system.
 | [5] |
is porosity, s, a, fw, and bw are the dielectric permittivities of soil solid, air, free water, and bound water, respectively, and bw is a volumetric water content of bound water. This equation cannot be applied for calculating the – relationships in a moisture range of <bw. Hence, the following equation was used for evaluating ( < bw).
 | [6] |
When applying the four-component mixing model, we need to estimate the volume fraction of bound water, bw, and its relative dielectric permittivity, bw. Dirksen and Dasberg (1993) evaluated bw from hygroscopic water content (air dryness), and they assumed bw equaled the relative dielectric permittivity of ice (3.2). Dobson et al. (1985) found good agreement between theory and experiment in the range of 20 to 40 of bw, but this was the case for more than a monomolecular water layer on a soil particle surface. Since there is little information concerning the dielectric property of water inside aggregates, we conveniently treated bw and bw as parameters of the mixing model. Hence we tried to calculate for three cases of the dielectric mixing model: (i) bw = hygroscopic water content and bw = 3.2 (Case 1), (ii) bw = water content at -1555 kPa and bw = 3.2 (Case 2), and (iii) bw = water content at -1555 kPa and bw = 40.0 (Case 3). Relative dielectric permittivities of free water, soil material, and air were assumed fw = 80.4, s = 5.0, and a = 1.0, respectively. For the three different cases, the fitness of dielectric mixing model to the measured data was evaluated by the root mean square error (RMSE), defined as
 | [7] |
obs and cal are the measured and estimated dielectric permittivities. RESULTS
– Relationships for Aggregates
Figure 2 shows the – relationships for aggregate soils and their crushed samples. The relationships were obtained in the moisture range of 0.02 to 0.7 cm3 cm-3. Contrary to aggregated soils, the moisture ranges for crushed soils were from 0.07 to around 0.45 cm3 cm-3, beyond which values the uniformity of soil packing became difficult to determine as the degree of wetness increased. Thus, the – relationships for aggregate soils were compared with those for crushed soils in the same moisture range.
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– relationships were on a moderately rising tendency to a critical value, but beyond that, value steeply developed with . Thus, the – relationships can be separated into two differently characterized regions at the point of critical water content. On the other hand, for the crushed aggregate, such critical water content disappeared. Moreover, when we compared the – relationships of aggregates and crushed samples, it was found that the smaller the aggregate, the smaller the difference in the – relationships between aggregates and crushed samples. To validate the results we examined the linear regression lines and their 95% confidence intervals for the 1.0- to 2.0-mm aggregate size (Fig. 2a) within the limited moisture range 0.24 to 0.42 m3 m-3. The regression functions were
 | [8] |
range between 0.24 and 0.35,
 | [9] |
range between 0.35 and 0.42, and
 | [10] |
range between 0.24 and 0.4. Figure 2a (inset) shows there is a significant difference in between the aggregate and crushed sample around the critical water content.
The calculated result for Case 1 gave a satisfactory fit to the measured data for wet-sieved aggregates. However, in aggregate soils, the calculated curve deviated from the measured data for the range of between 0.2 and 0.45. The deviation from the calculated curve was the largest at the critical volumetric water content, around = 0.35. However, the calculated result for Case 2 was mostly underestimated in the – relationships for aggregates. For Case 3, the calculated result fitted the measured data for aggregates in the moisture range under critical water content, but it deviated for the range over the critical water content (Table 2).
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– relationships for aggregates with a diameter <0.1 mm. The measured data were plotted with smoothed-curve relationships. Even though the aggregate structure was destroyed for crushed soil, the – relationships were similar to those of uncrushed aggregates. Contrary to the results for coarser aggregates, no critical water content at which the slope changes abruptly was found. Moreover, the dielectric mixing model of Case 1 fit best with the experimental result.
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– curves for the coarser aggregates were obtained by differentiating the cubic spline function which connected each measured data of – relationships for aggregate soils (Fig. 4). The values of the gradient varied largely at the high moisture range ( > 0.55). The d/d level was low in the low moisture range (0.08 < < 0.3) and was high in the high moisture range (0.4 < < 0.65). These results indicate that the sensitivity of apparent dielectric permittivity of aggregate soil to water content depends highly on moisture range.
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changed moderately with matric potential. However, plotting of measured contents drew water retention curves similar to the curves for the coarser aggregates in a matric potential range of less than -1555 kPa. These measured data fit well with curves of the bimodal van Genuchten model proposed by Durner (1994).
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0.4 m3 m-3) at which d/d becomes a peak in Fig. 4 corresponded to the water content in the plateau of water retention curve from -1555 to -100 kPa (Fig. 5). Such a matric potential range agreed with the pore radius range between two peaks of pore-size distribution (Fig. 6). DISCUSSION
Relationship between Dielectric Property and Water Retention Characteristic for Aggregates
There might be skepticism about the existence of a sharp water content change in the sample when measuring soil water characteristic curve in the high moisture range. In such a case, transient water movement is still proceeding. However, in this study, the measurements of the aggregated soil sample were conducted under equilibrium conditions. Definite deviation of water content profile such that only the top of the sample was dried or only the bottom of the sample was still wet could not be observed, although the actual water content profile could not be determined inside the sample. Therefore, the TDR measurement in the center of the sample probably represents the average water conditions of the sample.
The dielectric property of aggregate soil relates to the soil structure. In the – relationship for aggregate soils, the – line gradient moderately changed at the critical water content, although this property disappeared when we crushed the aggregate structure (Fig. 2). On the other hand, the critical water content was in the mild gradient section of the water retention curve between two steep slopes (Fig. 5). These results suggest that the water retention characteristic for aggregate soils could affect dielectric property measurement.
Aggregate structure is composed of two pore systems of textural and structural pores. In these pore systems, textural and structural pores contribute to soil water retention in low and high moisture ranges, respectively. The presence of a plateau zone in the soil water retention curves suggested that these contributions could be relatively independent (Fig. 5). Across the plateau level of water content, textural and structural pores have different water retention characteristics. These differences may also affect the – relationships for aggregated soils.
Aggregate Size Effect on – Relationships
The effect of aggregate structure on dielectric property depends on the sizes of aggregates. For coarser aggregates, the – relationships were separated into two different regions at critical water content (Fig. 2). On the other hand, for finer aggregates, such a critical water content could not be detected (Fig. 3). These different results can be related to the pore-size distributions. For coarser aggregates, the two clear peaks of pore size density made it possible to divide pore space into two distinguishable pore systems. On the other hand, for finer aggregates, although two peaks of pore size density also appeared, the density distribution was continuous, and no particular pore radius was found at which pore size density became close to zero between two peaks (Fig. 6). An abrupt change of water-configuration in pores, and thus , may not occur in finer aggregates.
Furthermore, it was found that the difference in the – relationships between coarser aggregate and crushed samples also showed the aggregate size dependency (Fig. 2). This size dependency also is translated to the pore-size distributions. The left-hand peak of pore size density, corresponding to structural pores, moved toward the right-hand side with decreasing aggregate size. On the other hand, the right-hand peak still remained at almost the same position, even in the case of the small aggregate size (Fig. 6). That is, the ratio of structural pore size to the texture pore size decreased with decreasing aggregate size. Since the structural pores were almost filled with air at the moisture range around critical water content (Fig. 4), the air volume in the structural pores must have caused the aggregate size dependency on the difference in the – relationships between coarser aggregate and crushed samples.
Gradient of – Curve
The gradient of the – curve is considered as representing the contribution of water content to the apparent dielectric permittivity of soil. The d/d values of Topp's equation increased with and reached 100 at the highest moisture. This result indicates that the contribution of water content to is enhanced with . Contrary to this, the relationship between and d/d for aggregate soils was quite different from Topp's equation and was partitioned into two moisture ranges—high and low constant d/d values at higher and lower moisture ranges, respectively. In particular, the d/d values remained constant for the water content range less than the critical value. These different results between aggregate and nonaggregate soils may be caused by aggregate structure. That is, while the water is held inside aggregates, the water distribution in the soil can change partially inside aggregates with increasing . After textural pores are almost saturated, structural pores begin to fill with water, and in turn the water distribution changes to become more homogeneous than when the water is held inside aggregates (Fig. 7). Friedman (1998) showed from the calculated results that once the water phase was encapsulated within the solid and gaseous phase, the d/d values remained low, and vice versa. Hence, once pores inside aggregates become saturated, the rapid increase in can be expected.
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– Curves for Aggregates (Annan, 1977; Ferré et al., 1996; Sakaki et al.,1998). Moreover, it also must be considered whether or not the system can be macroscopically treated as a continuum. Del Río and Whitaker (2000) developed the volume-averaged equations for the individual phase in the two-phase systems and used them to define the condition of local electrodynamic equilibrium. They pointed out that the mixed system cannot be treated as a continuum macroscopically when the characteristic length for each phase is not small enough compared with the averaging volume. As the aggregate size becomes large, the air phase surrounding aggregates may need to be treated as an individual phase. Hence, the external air phase apparently encapsulates the aggregates. According to the calculated results by Friedman (1998), who used the three-phase composite spheres model for the six possible three phase arrangements, the external air or solid phase cell encapsulating the water cell has a significant effect in reducing . By increasing the aggregate size, the effects of the structural pores may become more prominent.
Dielectric Property of Water Held in Textural Pores of Aggregates
The dielectric property of water held in textural pores of aggregates can be also considered as another reason why the measured values of for aggregates were lower than those of the crushed soil, and the difference between them was largest at the critical water content (Fig. 2). That is, the dielectric property of water held in textural pores is not close to that of bulk water, but to that of bound water. According to the calculation, Case 3 resulted in the most satisfactory fit to the measured data for aggregate soils in the moisture range under critical water content (Table 2). This result suggests that the water inside aggregates is not adsorbed so strongly as is the case with the monomolecular layer, but it is still affected by the aggregate structure. Ito (1962) examined the physical properties of adsorbed water on soil from its dielectric phenomena. He reported that the matric potential at which the property of film water can be assumed to be the same as that of bulk water ranges from -100 to -50 kPa. In an Andisol, it could be also considered that the water content corresponding to the potential less than -100 kPa can affect the estimation of dielectric property of aggregates.
CONCLUSION
The – curve for Andisol soils includes a critical point where d/d changes moderately. This critical water content corresponds to the water content in the plateau of the bimodal-type water retention curve. This dielectric property disappeared when we crushed the aggregate structure. We speculated that the causes of this dielectric property for aggregate soils are based on the aggregate size effects, the configuration of water in aggregates, the processes of water filling in inter- or intraaggregate pores, and the effect of a low value of bound water adsorbed on soil surfaces on the bulk estimation. This speculation may help us to understand the reason why the calibrated results of the – relationship for Andisol soils may not coincide with the Topp et al. (1980) curve.
ACKNOWLEDGMENTS
We will express our thankfulness to Dr. W. Durner for helping us with the determination parameters of the bimodal retention function.
REFERENCES
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