Soil Science Society of America Journal 63:777-781 (1999)
© 1999 Soil Science Society of America
DIVISION S-1-SOIL PHYSICS
A Dielectric–Water Content Relationship for Sandy Volcanic Soils in New Zealand
M.D. Tomera,
B.E. Clothierb,
I. Vogelerb and
S. Greenb
a New Zealand Forest Research Institute Ltd., Private Bag 3020, Rotorua, New Zealand (sponsoring organization)
b HortResearch, Ltd., Private Bag 11-030, Palmerston North, New Zealand
mark.tomer{at}forestresearch.co.nz
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ABSTRACT
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To measure soil water content (
) by time domain reflectometry (TDR), one must know the relationship between the soil's dielectric constant (Ka) and . Our objective was to determine Ka– calibrations for sandy volcanic soils on the North Island of New Zealand. We collected samples from 24 horizons and 6 soil profiles. The soils were sandy loam and loamy sand textured, with bulk densities between 0.55 and 1.34 Mg m-3. Samples were air-dried and packed to their field bulk density in plastic boxes. Time domain reflectometry probes (100 mm long) were inserted, and TDR waveforms were recorded and analyzed. Water contents were increased in approximate steps of 0.05 m3 m-3 volume to the liquid limit, which varied between 0.33 and 0.57 m3 m-3. Samples were then submerged to obtain water contents as great as 0.646 m3 m-3. Measured water contents were greater that those predicted by the Topp equation, but the differences varied according to soil texture. Pooled data from 17 of the samples provided a third-order polynomial calibration with an R2 of 0.977 and root mean square error (RMSE) of 0.026 m3 m-3. A third-order mixing model and a linear Ka– expression gave greater mean errors. Although the calibration applied to a range of sandy volcanic soils, there were also two small groups of samples that showed distinct calibrations. These were coarser tephras, with at least 75% of particles >0.125 mm diam. by mass, and with bulk densities >1.0 Mg m-3.
Abbreviations: RSME, root square mean error • TDR, time domain reflectometry
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INTRODUCTION
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TIME DOMAIN REFLECTOMETRY has become a popular method of soil water measurement. This is partly because, for a broad range of mineral soils, a single calibration can be applied to calculate a soil's volumetric water content from its dielectric constant. This relationship, known as the Topp equation (Topp et al., 1980), is empirical and of the form
 | (1) |
Although this equation has been described as widely applicable for mineral soils (Roth et al., 1992), calibrations for individual soils may be required. Indeed, Topp et al. (1980) found that organic material and vermiculite did not follow Eq. [1]. Subsequent studies have confirmed that organic soils do not follow the Topp equation (Herkelrath et al., 1991; Pepin et al., 1991; Roth et al., 1992). Besides organic matter, bulk density has also been identified as an influence on the Ka– relationship (Jacobsen and Schjønning, 1993). Effects of soil temperature (Pepin et al., 1995) and salinity (White et al., 1994) on measurement of Ka have also been demonstrated. Soil-specific calibrations are now commonly recommended, including the use of field data to determine effects of small-scale heterogeneities (Timlin and Pachepsky, 1996).
Although soil-specific calibrations are desirable, they are not simple to perform. Hence, efforts to characterize the Ka– relationship with regard to soil properties have continued. Calibrations can directly include properties such as organic matter and bulk density in the Ka– relationship. Jacobsen and Schjønning (1993) found that calibrations were slightly improved by including linear terms for bulk density, organic mater content, and clay content; however, these terms did not eliminate significant differences among individual soils included in the study. Dasberg and Hopmans (1992) showed that a fine-textured soil required a specific calibration; this was attributed to greater amounts of water that are bound (adsorbed) on particle surfaces, resulting in a muted dielectric response.
The soil dielectric constant is not only affected by relative fractions of bound and free water (largely determined by surface area), but also by the shape of the soil particles and the shape of the water inclusions around the particles (Hallikainen et al., 1985). Volcanic soils are unique in regard to these factors for two reasons. First, particle shapes are shard-like or vesicular, due to their molten, vitric origin. This contributes to the low density, large porosity, and large water holding capacities of these soils, and it also affects the shape of water inclusions. Second, volcanic ash soils, even though sandy or loam textured, will also have relatively large surface areas, due again to shapes of soil particles and to the presence of allophanic clays, which have large surface areas and a high affinity for water (Aomine and Otsuka, 1968). Therefore, water stored in a volcanic soil can be expected to show an atypical dielectric response, due in sum to the soil's low bulk density, relatively large surface area, and water's partial occlusion by particle structures.
The objective of this study was to determine Ka– relationships for a range of soils developed from airfall tephras across New Zealand's North Island. We considered three forms of the Ka– relationship, including the third-order polynomial expressed by Eq. [1]. The second form was a dielectric mixing model (Dobson et al., 1985), a semi-empirical method that treats the soil as a multiphase system. Effects of soil solids, water, and air on the soil dielectric are modeled by
 | (2) |
In this equation, 
is porosity, 
s, a,and w are the dielectric constants of soil solids, air, and water, and 
, valued between 0.5 and 0.46 (Roth et al., 1990), is a geometric factor that determines the shape of the function. The third form of the Ka– relationship was described by Hook and Livingston (1996), who showed a linear relationship to determine from K0.5a. They recommended a slope of 0.1193, and an average intercept (value of
) of 1.55, but they found that their method applied poorly to a selected clay soil.
Few studies have examined dielectric behavior of volcanic soils. Vogeler et al. (1996) showed that a New Zealand loess soil of low density and mixed volcanic origin had Ka– relationship such that for a given Ka value, the corresponding was 
0.1 m3 m-3 greater than that predicted by Eq.[1]. Weitz et al. (1997) reported that Ka– relationships of two tropical soils of volcanic origin were best defined using a three-phase mixing model.
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Methods
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Twenty-four soil samples were collected from six soil profiles of differing volcanic origins on North Island of New Zealand. The distribution sampling locations (Fig. 1)
provided good geographic coverage of the volcanic region of New Zealand's North Island. In terms of soil classification, Profiles 1 through 5 are Typic Udivitrands, assuming they have andic properties. We did not obtain glass counts or acid oxalate–extractable Al and Fe data for these soils. Profiles 3 and 4 do not meet density requirements of the first qualifying option for andic properties, and they would be least likely of these five profiles to meet andic requirements. If they fail criteria based on glass content and extractable Al and Fe, then: (i) Profile 3 would be a Vitrandic Eutrochrept if a smaller part of the profile were to meet these criteria, or an Arenic Eutrochrept if not; and (ii) Profile 4 would be a Vitrandic Eutrochrept based on coarse fragment composition. Profile 6 does not meet the thickness nor the density criteria for Andisols, and they could be either a Vitrandic or Dystric Eutrochrept, depending on glass and acid oxalate–extraction criteria.
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Fig. 1 Map of North Island, New Zealand showing approximate locations of sampled profiles. The dashed line shows the general extent of volcanic soils (Molloy, 1988). Profiles 1 and 2 were in Whakarewarewa Forest, near Rotorua. Profile 3 was on the Whangaehu river floodplain, 20 km south of Mount Ruapehu. Profile 4 was 5 km west of Kawerau, Profile 5 was 5 km southwest of Whangamata, and Profile 6 was 20 km north of Napier. Profile 7 is that sampled by Vogeler et al. 1996, where the soil is an ash-influenced loess
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The samples were air-dried and passed through a 2-mm sieve. Gravel contents were generally small, but four samples contained >5% gravel by mass. Gravels smaller than 5 mm were recombined with the fine fraction to better represent field conditions. Subsamples of the air-dried soils were oven dried at 105° for 24 h to determine their water contents. The air-dry samples were packed to the field bulk density into plastic boxes with internal dimensions of 80 by 80 by 150 mm (0.96 L), the mass of soil packed into a box was calculated from the density, box volume, and air-dry water content. The boxes were perforated above and below, and a fine nylon gauze was used to line them and keep the soil in place. A 2-wire TDR waveguide, with wires 1 mm in diameter, 10 mm apart, and 100 mm long (miniprobes; Midwest Special Services, St Paul, MN)1
(Spaans and Baker, 1993), was inserted into the soil through an opening in the end of the box that fit the probe's head. A TDR waveform (one per sample) was captured with a Tektronix 1502B cable tester (Beaverton, OR), recorded on a laptop computer, and analyzed to determine Ka by a derivative-based method (Timlin and Pachepsky, 1996).
The box was weighed. The soil was then emptied into a tub, and 50 mL of water was mixed into the sample. Although sample mixing eliminates field heterogeneity as a source of variation in the data, it does help ensure a uniform distribution of water within the sample. The sample was again repacked into the plastic box, covered, and allowed to equilibrate for several hours before remeasurement and reweighing. This procedure was repeated until the sample reached its liquid limit, at which the soil would flow into the box and settle at an increased density. This condition was avoided. The liquid limit varied between 0.33 and 0.52 m3 m-3 amongst the samples. Because greater water contents are sometimes observed in the field, the samples were then dried to less than the liquid limit, repacked at the correct density, and inundated in water for 24 h. The perforations at the bottom of the box allowed saturation to occur from below. A final measurement was then taken to give a data point near saturation. All TDR measurements were taken at room temperature, 16°C. The samples were then subjected to particle-size analysis using hydrometer and sieve analyses (Gee and Bauder, 1986) and total C analysis by a dry combustion method (Nelson and Sommers, 1996).
Calibration data were examined, and groupings were made according to texture, density, C content, and site. Regressions were by least squares techniques for the third-order polynomial (–Ka) and linear 
forms. The fit of the linear –K0.5a relationship was determined with a minimal "intercept" value of 1.4 forced into the regressions, because of the low density of these soils (Hook and Livingston, 1996). Results were compared with a slope of 0.1193. Third-order mixing models were applied with s, a, and w values of 4, 1, and 82, respectively (Dobson et al., 1985), and with values varying between 0.5 and 0.46 to determine an optimal fit. Porosity () was calculated for each sample using bulk density data and an assumed particle density of 2.40 (Cook et al., 1994). Goodness of fit of the calibrations was determined by the RMSE, defined as
 | (3) |
in which N is the number of observations, and obs and pred are the measured and predicted water contents.
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Results and discussion
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Soil Characteristics
Characterization data for all samples (Table 1)
shows that bulk densities varied between 0.55 and 1.45 Mg m-3. The two samples from Profile 6 had mixed-loess parent materials and, therefore, had the greatest bulk densities. Samples purely derived from airfall tephra had a maximum bulk density of 1.24 Mg m-3. The samples include deposits from at least 10 volcanic eruptions, with the Taupo ash being included in five of the profiles. The Lake Taupo eruption of 1800 years ago was the largest in written history, and deposits from this eruption are found in soils throughout the central North Island (Molloy, 1988). The soils were sandy textured, with between 65 and 95% sand, and only one sample (#24) contained >10% clay. Carbon contents were variable, ranging between 3 and 51 g kg-1. Soil pH values were in the 5 to 6 range (data not shown), and thus, the inorganic component of the total C was small.
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Table 1 Location, parent materials, ages, and characterization data for soils used to establish Ka–0 calibrations. Groupings of samples are indicated in the last column and identified according to the equation numbers for Ka–0 relationships given in the text
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Calibration Data
Data plots showed the samples could be stratified into textural groups. The largest group included 17 samples, which were dominantly sandy loam textured, consisting of all samples from Profiles 1, 2, and 5, two samples from Profile 3, and one sample each from Profiles 4 and 6. These samples are numbered 1 through 10, 13, 14, 16, and 20 through 23 in Table 1. Pooled data from this group of samples (Fig. 2)
showed a third-order polynomial Ka– relationship, found to be
 | (4) |
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Fig. 2 Ka– calibration data for 17 of the 24 samples (circles) and data from Vogeler et al., 1996 (squares). The best fit, third-order polynomial (Eq. [4]) is also shown, along with the Topp equation (Eq. [1])
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This equation had an R2 of 0.977 and an RMSE of 0.026 m3 m-3 and was valid for water contents up to 0.646 m3 m-3. This relationship closely matched that of a low density (0.84 Mg m-3), volcanic-influenced silt loam loess from Profile 7 (Fig. 1), which was reported on by Vogeler et al. (1996) (see Fig. 2). Results indicate a single Ka– relationship can be generally applied to a range of sandy volcanic soils in New Zealand, and perhaps to finer textures if the Vogeler et al. (1996) results are extendable (Fig. 2). The precision of Eq. [4] could not be improved by including bulk density, C content, or median particle size as independent variables. However, smaller groupings of samples, according to site, could be used to reduce the RMSE to 0.019 m3 m-3. Using Eq. [1] to measure water contents in these soils would lead to inaccurate inferences of hydraulic conductivity, water potential, and plant available water that could be made from those measurements. But, because the two lines (Fig. 2) are of similar shape, relative changes in water content can be accurately estimated using Eq. [1] (i.e., <0.01 m3 m-3 difference between Eq. [1] and [4] for Ka changes of five units, except near saturation).
The dielectric mixing model for these 17 samples was best-fit using an value of 0.46, and it had an RMSE of 0.034 m3 m-3. In comparison, Weitz et al. (1997) found an value of 0.47 gave RMSEs between 0.022 and 0.045 m3 m-3 for intact samples from surface and subsurface horizons of two soil profiles. In addition a plot of –K0.5a data for this group of samples did not show a linear trend. Rather, we observed a deviation from a linear trend similar to that shown for a clay loam by Hook and Livingston (1996). The maximum deviation from a line with 0.1193 slope was 0.08 m3 m-3 at 0.30 m3 m-3 water content (data not shown).
Seven of the samples did not fit the relationship given by Eq. [4]. One of these, the lower sample from Profile 6 (Sample 24), had mixed loess parent materials, and greater density (Table 1). It showed a Ka– relationship similar to the Topp equation (Eq. [1]). We conclude that this loess sample was largely derived from local sedimentary sources. The six remaining samples were grouped according to textural differences. Three sand-textured samples from Profile 4 (Samples 17–19) comprised one grouping, and three of the soils with large gravel contents (Samples 11, 12, and 15) formed the other. These two groups of samples showed Ka– relationships that fell between Eq. [1] and [4] (Fig. 3) . Both sample groups showed a muted dielectric response, but only at low water contents, a probable result of less surface area in these coarser soils. Regression fits to the data were
 | (5) |
for the sand-textured soils with an R2 of 0.984 and RMSE of 0.019 m3 m-3; and
 | (6) |
for the gravel soils with an R2 of 0.957 and a RMSE of 0.042 m3 m-3. Equation [5] was valid for water contents up to 0.428 m3 m-3, and Eq. [6] for water contents up to 0.531 m3 m-3. Dielectric mixing models for these groups of samples were best-fit with an value of 0.46 for the sand-textured soils
and of 0.5 for the gravel soils
. Data from these groups also did not fit a linear –K0.5a trend.
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Fig. 3 Ka– calibration data for two groups of coarser-textured samples, which consisted of three samples for each group. Best-fit calibration equations, Eq. [5] for the sand-textured soils (dotted line), and Eq. [6] for the gravel soils (dashed line), are also indicated. These groups show dielectric responses that are intermediate between the Topp equation (Eq. [1], lower solid line) and that of the finer ash soils (Eq. [4], upper solid line)
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The particle-size distribution and bulk density data showed how the sample groups were distinct from one another. The six coarser soils all had bulk densities >1.0 Mg m-3, and had <25% of their mass as particles smaller than 0.125 mm diam. This distinguished them from the finer samples that were captured by Eq. [4]. The coarsest samples (11, 12, and 15) were distinguished from the sand-textured samples (17–19) by their larger gravel contents (>8%), and by having 
20% of their mass as particles larger than 1.0 mm diam. These distinctions applied across all the samples, but we noted that Samples 14 and 16 were best fit by Eq. [4] despite having relatively coarse textures and high density. The clay content of Sample 14 and the C content of Sample 16 were among the largest observed (Table 1), and we believe this explains the muted dielectric response of these two samples.
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Conclusion
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We have shown a general Ka– relationship that may be applied to a range of sandy volcanic soils on New Zealand's North Island, that is valid for volumetric water contents up to 0.646 m3 m-3. Although the 17 samples that fit this relationship varied with regard to bulk density and C content, these data could not be used to improve the relationship's precision. A third-order polynomial expression provided a better fit to the data than a third-order mixing model, or a linear –K0.5a expression. We expect this relationship can be applied to other sandy volcanic soils, except for those coarser tephras with bulk densities >1.0 Mg m-3 and >75% of their mass as particles of >0.125 mm diam.
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ACKNOWLEDGMENTS
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Thanks to Jean Michel Carnus, Louise Barton, and Steve Pearce for assistance collecting samples, and to Michael Rosen, Chris McLay, and Shane McMahon for review of the draft manuscript. This work was funded by the Public Good Science Fund, administered by New Zealand's Foundation of Research, Science and Technology, under contract CO4409.
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NOTES
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1 No product endorsement implied. 
Received for publication September 7, 1998.
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REFERENCES
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TOP
ABSTRACT
INTRODUCTION
