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Enhancing modelled water content by dielectric permittivity n stony soils.

Introduction

Several methods of soil-water measurement are currently used with a diversity of accuracy, repeatability, and cost of installation. Although time domain reflectometry (TDR) is increasingly being replaced for irrigation management by methodologies that are cheaper and easier to use, it remains important for accurate monitoring of soil water in time and space for research purposes, especially in hydrological modelling. Numerous studies have been published with a variety of objectives, from calibration and modification of the TDR method under local conditions to assessment of new probes, or comparisons with the other methods (Arsoy et al. 2013; Chung et al. 2013 ; Coppola et al. 2013 ; Fatas et al. 2013; Laloy et al. 2014; Fan et al. 2015; Noh et al. 2015; Wu et al. 2015). Electrical resistivity tomography (ERT) is an emerging and promising method. It has shown accuracy in soil-water detection similar to TDR and with easier application and comparable cost of installation (Calamita et al. 2012; Fan et al. 2015); however, the spatial accuracy of ETR in the vertical dimension is distinctly less than that of TDR.

Time domain reflectometry exploits the dielectric properties of the medium under study and is essentially a guided wave technology that has been widely used in electrical engineering for detection of cable breakages (Yu and Yu 2011). Several studies have shown that the dielectric permittivity of a porous media ([K.sub.a]) primarily depends on its water content (Lundien 1971; Cihlar and Ulaby 1974; Hoekstra and Delaney 1974; Selig and Mansukhani 1975; Okrasinski et al. 1978; Topp et al. 1980). Relatively simple but reliable measurement of dielectric permittivity in the frequency domain of 1 MHz to 1 GHz is an applicable and effective means of soil-water content measurement (Topp et al. 1982). Several methods were discussed by Selig and Mansukhani (1975) for [K.sub.a] measurement. In applications, the water content, [[theta].sub.v], is related to [K.sub.a] through use of an empirical equation (Topp et al. 1980). The wide applicability of the Topp equation to most mineral soils has been verified by many researchers, leading to a suggestion that it has potential for acceptance for general usage (Coppola et al. 2013) with the caution that soil-specific calibration equations may significantly deviate from the universal equation for various reasons.

Dirksen and Dasberg (1993) examined changes in [K.sub.a] for particular [[theta].sub.v] values in 11 soils with different mineral and clay contents. They showed that the coefficients of the Topp equation cannot be considered constant for all soil types. Deviations from the Topp equation appear to be due to the low bulk density and thus higher air volume fraction at the same [[theta].sub.v] associated with fine-textured soils rather than to tightly bound water with low dielectric permittivity. Furthermore, Malicki et al. (1996) showed that bulk density, and thus porosity, substantially affects the relationship between [K.sub.a] and [[theta].sub.v]. They presented two equivalent, empirical, normalised calibration functions, one accounting for bulk density and the other for porosity to reduce the root-mean-square error (RMSE) of the moistures determined by TDR. Cataldo et al. (2009) consider that the individualisation of an optimal calibration function for each of the materials under investigation is a key means to improve the accuracy of the results. Bittelli et al. (2008) noted that TDR always overestimated soil water content (SWC) in clay soils compared with standard, oven-dry gravimetric measurements, in the moisture range <20% of soil saturation. They derived a new calibration curve to replace the existing calibration curves, including the widely used Topp equation. Therefore, the results obtained through experimental measurements and different procedures used to extrapolate empirical calibration curves are not readily comparable and need adjustment to local conditions. Arsoy et al. (2013) proposed an artificial neural network to incorporate dry bulk density, specific gravity and fines content to minimise errors caused by use of a universal TDR equation. Hignett and Evett (2008) caution that the sensors used for SWC measurements generate results that are barely related to authentic field settings if employed for unsuitable purposes. Numerous studies have indicated that the performance of SWC sensors, which have achieved widespread use and provide instant measurements, should be assessed before being used in specific soils (Varble and Chavez 2011). The reliability of the TDR method for measuring water content in stony soils, as prevalent at our study site, is rarely reported in the literature. Coppola et al. (2013) obtained good relationships between TDR-measured and observed [[theta].sub.v] for different stone fractions. They used stones 2-5 mm to prepare homogeneous soil mixtures with different stone fractions, which were different from the non-homogeneous mixtures of our soils.

A potential error arises when long cables are used because cable length affects the waveform of a given probe owing to the degraded rise time of the reflected pulse in longer cables (Tektronix 1987). Logsdon (2000) and Thomsen et al. (2000) showed that long cables influence the [K.sub.a] reading of the TDR Therefore, when using long cables, the effect of cable length on the [K.sub.a], and thus the associated water content, must be determined before data collection.

At our study site, determination of soil-water balance was essential in an investigation of artificial recharge of groundwater in a 30-m-deep well dug in a stony soil, and necessitated the use of this technique. Therefore, calibration of the TDR probes and connector cables was of utmost importance for collecting a reliable dataset. The main aim was to measure soil-water content in stony, deep profiles. The specific objectives of this study were (i) to test the available calibration equations for accurately deriving [[theta].sub.v] from [K.sub.a] in a coarse-textured, stony soil and to develop new equations to improve the accuracy; (ii) to examine the effect of selected capture windows, probe type and cable length on the measurement error and to provide an improved calibration equation that reduces additional errors; and (iii) to determine the practical implications for the TDR method in these soil types.

Materials and methods

The Gareh Bygone Plain (28[degrees]35'-28[degrees]41'N, 53[degrees]53'-53[degrees]57'E) is south of the Zagros Mountains, southern Iran. It is a debris cone and an alluvial fan formed by eroded material delivered from the Agha Jari Formation (inter-bedded sandstones, siltstones and marls) and the Bakhtyari Formation (mainly conglomerate). Therefore, the colluvial and alluvial soils formed in that landscape are characterised as multi-layered stony soils and classified according to Soil Taxonomy (Soil Survey Staff 2010) as Torriorthents, Haplocalcids and partly Haplocambids (Kowsar and Pakparvar 2003).

Soil sampling

Soil samples were taken from an experimental well 30 m deep, located at 28[degrees]36'37"N and 53[degrees]56'02"E in a recharge basin of a floodwater-spreading system. Details of the study area are given in Pakparvar et al. (2014). The profile of the well consists of multiple layers with distinct features, but commonly consists of three main layers having different amount of stones: a top layer of recently deposited sediment (loam); and two types of subsurface layers, sandy loam and sand (Table 1). These two subsurface layers are repeated throughout the vadose zone. Three representative, disturbed samples, each 50 kg, were taken from depths of 0-10, 10-109 and 109-150cm (layers 1-3, respectively) (Fig. 1).

Experimental setup

Bulk soils were air-dried and their SWC was measured gravimetrically. From each sample, 2 kg was used to determine particle-size distribution. This was done by the hydrometer method combined with sieve analysis to characterise the range of particle diameters from 0.002 to 2 mm (Gee and Or 2002). The particle density of the samples was determined by measuring the mass and the water displacement.

The remaining material from each layer (1-3), including gravel and stones, was divided into three homogenised subsamples (as replications) and placed into plastic polyvinyl chloride (PVC) containers (30 cm height and 50 cm diameter) up to the height of 22 cm. The bottom ends of the containers had been removed and covered with a plastic mesh. Bulk densities were measured by considering the air-dry weight of the bulk sample and the volume of the soil-filled part of the containers. A 20-cm-long, 3-rod uncoated metal waveguide (home-made) with rod spacing of 2.1cm between the outer and central rods and a 15-cm-long, 2-rod probe with a waveguide connector and rod spacing of 5.0 cm (Fig. 2a) were used with a main TDR device (TRASE System 6050X1; Soilmoisture Equipment Corp., Goleta, CA, USA). The probes were inserted vertically and the heads of the probes were buried so that the free end of the rod was at the bottom of container with a distance of 1.0 cm to avoid direct contact between the end of the rod and the plastic mesh. The size of the stone fraction in studied soils was mostly (97%) <5.0 cm (Table 1); therefore, the spacing of the 2-rod waveguide connector was enough wide to incorporate the stone fractions.

The 3-rod waveguide had less spacing than a portion of the stone fractions and it was employed to assess the error in moisture measurements that arises from the narrow spacing of this probe compared with 2-rod probe. Both probes were inserted vertically into each container to a depth of 25 cm. Each container was placed in a drum filled with water to a height of 2 cm above the soil surface to ensure that the water replaced the air in the soil and to minimise air entrapment. However, real saturation would need zero entrapped air, so the resulting soil was considered practically saturated, in which the majority of pores are filled with water. The containers were left until the soil showed a shiny surface. The water jacket was then drained from the drums. Gravimetric SWC was calculated based on the air-dry soil and weights before and after saturation. Then, bulk densities were used to determine the [[theta].sub.v] at saturation. Thereafter, dielectric permittivity, [K.sub.a], and [[theta].sub.v] of both sensors with capture windows of 10, 20 and 40 nanoseconds (ns) were recorded and the containers were weighed until the change in [[theta].sub.v] was <0.01 [m.sup.3] [m.sup.-3], which occurred after 81 days. The TDR-measured [[theta].sub.v] ranged from 0.032 to 0.385 [m.sup.3] [m.sup.-3] during the period in which the range of soil water content started from the saturation and finished at its minimum level in the laboratory. Air temperature was held constant at ~22[degrees]C throughout the experiment.

In order to minimise the errors incurred from the stoniness, the same three subsamples mentioned above were sieved to remove particles >2 mm. Air-dry gravimetric SWC was measured, and then the [K.sub.a] by TDR and the observed [[theta].sub.v] for the sieved subsamples were measured. The samples were packed into the PVC tubes of 30 cm height and 15 cm diameter up to the height of 22 cm, and a 20-cm-long, 3-rod uncoated metal waveguide (home-made) with a 2.1-cm spacing between the outer and central rod was inserted vertically into each tube. The same depth of insertion was chosen used in the previous experiment. Bulk densities were set to 1.30, 1.45 and 1.60 g [cm.sup.-3] for the samples of layers 1-3, respectively. Owing to the smaller sample size, saturation was achieved by connecting two Mariotte bottles to the lower ends of the tubes until the soils showed shiny surfaces (Fig. 2b). Measurements of [K.sub.a] and 9V for the capture windows of 10 and 20 ns and changes in tube weights were then recorded. The volumetric water content was measured via the conventional gravimetric method. Measurements were continued until the final [[theta].sub.v] reached 0.01 [m.sup.3] [m.sup.-3] (14 readings ranging from 0.28 to 0.01 [m.sup.3] [m.sup.-3]).

To validate the effect of cable length on the [[theta].sub.v] measurements, the previous trial was repeated without gravimetric measurements. Samples were again moistened and [K.sub.a] and [[theta].sub.v] were measured using the original 2-m-long probe cable connected with extension cables of 3, 5, 10, 15, 20, 25 and 30 m length (manufactured by the same company).

Data analyses

The Topp equation is traditionally used for mineral soils to convert the measured permittivity to [[theta].sub.v]:

[[theta].sub.v] = -5.3 x [10.sup.-2] + 2.92 x [10.sup.-2] [K.sub.a] - 5.5 x [10.sup.-4] [K.sup.2.sub.a] + 4.3 x [10.sup.-6] [K.sup.3.sub.a] (1)

Under field conditions, high stone content may be responsible for significant deviation of the soil moisture derived from Eqn 1. Thus, following the guidelines of Birchak et al. (1974) and Coppola et al. (2013), we distinguished the dielectric permittivity of different components of the soil mixture (i.e. fine soil, stones, air and water). A semi-empirical model proposed by Birchak et al. (1974) to relate the bulk (the mixture of different components) dielectric permittivity ([K.sub.ab]) to the volumetric fraction of soil components, [V.sub.i], and the corresponding dielectric permittivity, [K.sub.ai], was used. The model may be written as:

[K.sup.[beta].sub.ab] = [[summation].sup.N.sub.i=1] [V.sub.i] [K.sup.[beta].sub.ai] (2)

The component [beta] in Eqn 2 is an empirical constant summarising the geometry of the medium in the applied electric field. A value of [beta] = 0.5 has been proposed for homogeneous soils (Birchak et al. 1974; Ledieu et al. 1986). Coppola et al. (2013) found an average value of [beta] = 0.55 for different stone fractions. In a stony soil, by neglecting the effect of the bound water and separating the individual contribution of the fine soil particles ([V.sub.s]) and the stones ([V.sub.st]), Eqn 2 might be expanded as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

where [phi], [[theta].sub.v] and [V.sub.st] are the soil porosity, volumetric water content and stoniness, respectively, referred to the bulk soil (fine soil plus stones); and [K.sub.ast], [K.sub.as], [K.sub.aa], and [K.sub.aw] are the dielectric permittivity for stones, fine soil particles, air and water, respectively. By assigning the pre-determined parameters, the TDR [K.sub.ab] field measurements can be converted to the corrected [[theta].sub.b] ([V.sub.st]) as follows (Coppola et al. 2013):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

In this study, the porosity of bulk soils ([phi]) was determined based on bulk density and particle densities, [V.sub.st] was measured by sieving for three soil layers, and dielectric permittivity values of water and air ([K.sub.aw], [K.sub.aa]) were measured by TDR as 98 and 1, respectively. The [K.sub.as] was set to 4.3 as reported by Wraith and Or (1999) for a soil texture of loamy sand similar to our soil, and the [K.sub.ast] as 7.3 as measured by Coppola et al. (2013) for types of calcareous stones similar to those in our soils. A set of paired [[theta].sub.v] values (observed and calculated by Eqn 4) was used for optimisation of [beta] by least-square method with solver add-in in Microsoft Excel.

In the following sections, the TDR-based [[theta].sub.v] values estimated by Eqns 1 and 4 as [[theta].sub.vTp] and [[theta].sub.vmx] (subscript Tp for the Topp equation, subscript mx for mixture equation), respectively, are used.

Validation of the results

In the stony soils, improvement in [[theta].sub.v] estimation due to the inclusion of the soil-stone mixture in Eqn 4 was assessed based on the comparison between [[theta].sub.vTp] and [[theta].sub.vmx]. In the stone-free soils, two-thirds of the data were used to generate the new [[theta].sub.v]-[K.sub.a] relationships and the rest were used to evaluate the generated relationships against the Topp equation. Polynomial equations were fitted to our experimental results.

Statistical Indices for the model validation

Pearson's correlation coefficient (r) and coefficient of determination ([r.sup.2]) describe the degree of collinearity between simulated and measured data (Moriasi et al. 2007). The correlation coefficient, which ranges from -1 to 1, is an index of the degree of linearity between the observed and simulated data. If r = 0, no linear relationship exists. If r = 1 or -1, a perfect positive or negative linear relationship exists. Similarly, [r.sup.2] describes the proportion of the variance in measured data explained by the model; [r.sup.2] ranges from 0 to 1, with higher values indicating less error variance (Santhi et al. 2001; Van Liew et al. 2007). Although r and [r.sup.2] have been widely used for model evaluation, these statistics are over-sensitive to high extreme values (outliers) and insensitive to the additive and proportional differences between the model predictions and the measured data (Legates and McCabe 1999). The graphic results were also quantified by calculating the RMSE, which supplies a measurement of a scatter around the 1:1 line. For an ideal prediction, its value should be close to 0. According to Singh et al. (2004), RMSE values less than half the standard deviation of the measured data may be considered low. Because we worked with two estimated data series (uncorrected and corrected for stone data series), characterised by different standard deviations, we opted for a normalised statistic, the ratio of RMSE to observation standard deviation (RSR) (Moriasi et al. 2007). The RSR is calculated as the ratio of the RMSE and standard deviation of measured data. Thus, it includes a normalisation factor, so that the resulting statistic can apply to different data series. RSR varies from the optimal value of 0, which indicates zero RMSE or residual variation and therefore perfect model simulation, to a large positive value. The lower the RSR, and the lower the RMSE, the better the model simulation performance. The RSR is calculated according to the following equation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

where [O.sub.i] and [S.sub.i] are the observed and the simulated values, [[bar.O].sub.i] is the mean of the observed data, and N is the total number of observations. Model performance is categorised by Moriasi et al. (2007) in terms of the RSR values as very good, good, satisfactory and unsatisfactory for the RSR = 0.0-0.5, 0.5-0.6, 0.6-0.7 and >0.7, respectively.

Results and discussion

Soils with original stoniness

Soils with original stone volumes showed estimated v. observed [[theta].sub.v] with a declining deviation from layers 1 to 3 for [[theta].sub.vTp] ([r.sup.2] = 0.71, 0.88 and 0.91) and [[theta].sub.vmx] ([r.sup.2] = 0.71, 0.91 and 0.93) (corresponding to layers 1-3, respectively). Textural classes of the soil layers are in the order of fine to coarse (loam, sandy loam and sand, respectively) showing the least deviation in the coarser soil textures (Fig. 3). A ranking of narrower scattering of the points around the fitted lines by the two methods is shown for Fig. 3c-a, which infers better agreement between observed and estimated [[theta].sub.v] for both methods in coarser soils. This fact is also reflected in higher [r.sup.2] and lower RMSE of Fig. 3c than of Fig. 3a and b. Better agreement in Fig. 3c is shown for [[theta].sub.v] < 0.07 [m.sup.3] [m.sup.-3] than with the higher [[theta].sub.v], and this may indicate that the soil water bound by micropores of coarse-textured soils is better detected by the dielectric permittivity method. The number of points in the [[theta].sub.v] > ~0.1 interval is significantly less in Fig. 3c than in Fig. 3a and b, which is due to a lower air-entry value in sand compared with the finer textures, leading to sooner depletion of water from the macropores. Many researchers have considered the effect of soil texture on the reliability of the TDR measurements (Dirksen and Dasberg 1993; Jacobsen and Schjonning 1993; Ponizovsky et al. 1999; Gong et al. 2003; Bittelli et al. 2008; Stangl et ai 2009). As a general conclusion, a higher amount of fine particles (clay-sized), which leads to a lower bulk density of soils, causes a higher deviation in the TDR v. gravimetrically measured SWC. Considering the effect of stones by separating the different fractions, as reflected in Eqn 4, resulted in quite similar [r.sup.2] in [[theta].sub.vmx] and [[theta].sub.vTp]; however, a noticeable decline in RSR and RMSE of [[theta].sub.vmx] v. [[theta].sub.vTp] (Table 2) indicates a better performance of the mixture model compared with the conventional Topp equation in estimation of [[theta].sub.v]. Similar [r.sup.2] implies insensitivity of this statistic to the relative differences between the model predictions and measured data, whereas the RMSE and RSR are capable of demonstrating proportional disparities.

The capture windows and the probe types used in the stony soils showed diverse effects on the estimation of [[theta].sub.v] (Table 2). However, the capture window 20 ns showed a minor improvement in [[theta].sub.v] estimation compared with 10 ns, and major improvements were found when using 15-cm, 2-rod (connector) probe type compared with the 20-cm, 3-rod (buriable) type. The proportional spacing of the 15-cm, 2-rod type to the stone sizes is the main reason for its better results. Additionally, the added strength and shorter length of the rods of the connector type help to minimise lateral deformations of probe rods during insertion into the stony soil, compared with the 3-rod probes. Furthermore, a procedure of primarily zero set in TDR measurement, needed for connector type, might lead to more precisely measured [K.sub.a].

Therefore, the RSR and RMSE resulting from the capture window 20 ns and the 15-cm, 2-rod (connector) probe type were used to make the final comparisons (Fig. 3). The RMSE values of the mixture equation (0.04, 0.03 and 0.02 [m.sup.3] [m.sup.-3], respectively, for layers 1-3) showed improvements compared with the Topp equation (0.07, 0.10 and 0.09, respectively, for layers 1-3), implying that the final error in [[theta].sub.v] estimation was 2-4% when considering the stones by employing the mixture model. The RMSE values of the mixture equation were equal to or less than half of the standard deviation of the observed [[theta].sub.v] (Table 2), which might be considered low. The same conclusion was drawn from the RSR values, showing lower RSR of the mixture equation (0.87, 0.32 and 0.71) than the Topp equation (1.34, 1.07 and 3.05) corresponding to soil layers 1-3, respectively. However, despite the improvement gained by applying the mixture equation, the model performance was still defined as unsatisfactory (RSR >0.7), at least for layers 1 and 3, but very good (RSR <0.5) for soil layer 2.

Coppola et al. (2013) also obtained an improvement in the [[theta].sub.v] estimation for bulk soil by employing Eqn 4, with better agreement between the observed [[theta].sub.v] and [[theta].sub.vmx] than [[theta].sub.vTp] (RSR = 1.13 and 2.94 for [[theta].sub.vmx] and [[theta].sub.vTp], respectively). However, their resultant RSR was beyond the satisfactory level of model performance (RSR >0.7). The distinction between our soils and theirs was the stone size and configuration. Those authors used stones of 2-5 mm size to prepare different stone fractions, leading to homogeneous mixtures, whereas the fragmental soils of our study were collected from the research site where a heterogeneous mixture of stones in size and shape were naturally distributed. This difference in stoniness is reflected in their lower mean error of 0.004, compared with our final error of 0.02-0.04, indicating the better performance of Eqn 4 in stony soils with homogeneous stone distribution.

Stone-free soils

The second experiment, in which the stones were removed, resulted in calibration curves to be applied for precise water-content estimation in individual soil layers. As shown in Fig. 4, the plotted points are very close to the regression lines, leading to [r.sup.2] > 0.99 and RMSE = 0.002 [m.sup.3] [m.sup.-3] for the three soil layers.

The calibration equations (presented in Table 3) in this study are needed to minimise the error in water content detection to as low as 1%, because minor changes in soil water content in arid landscapes are significant, due to lack of accessible water. In addition, insertion of the TDR probes into the original stony layers is practically impossible with the occasional presence of large stones; therefore, we suggest making lateral holes filled with original fine soil to place TDR probes for long-term monitoring. However, this might create non-homogeneity in the soil domain, the effect of which would depend on the diameter of the filling and how the filled material is different from the surrounding soil. The effect of this non-homogeneity is being studied and will be addressed in a separate paper. Furthermore, as our data show, the main shortcoming of the built-in Topp equation in the stone-free soils is the failure to estimate accurately [[theta].sub.v] < 0.05 [m.sup.3] [m.sup.-3].

Calibration of TDR at a low [[theta].sub.v] was attempted by Skierucha et al. (2008). They stated that the convolution effects caused an increase in reflection time and consequently an increase in the measured values of permittivity. This is especially evident for low dielectric permittivity and the corresponding low [[theta].sub.v] values. For soil-water content values >0.2 [m.sup.3] [m.sup.-3], the gravimetrically measured data were close to the Topp standard calibration equation. As an alternative to the Topp equation, a new set of coefficients for this equation that relate [K.sub.a] to gravimetrically measured [[theta].sub.v] was established (Fig. 4). The low [[theta].sub.v], which is expected in our profiles in an arid area with only a few rain and flooding events per year, can be effectively obtained by these new equations (Table 3).

A comparison between the [[theta].sub.v] estimated by the new equations and the equation of Topp et al. (1980) is presented in Table 4. In all soil types, the RMSE of the new equation was lower than that of the Topp equation. The measured [K.sub.a] in the capture windows of 20 ns also resulted in a better estimation of [[theta].sub.v] with a lower RMSE than that of the 10 ns windows. The capture windows of 40 ns showed erroneous data in some measurements; therefore, they are not presented. Estimation of the minimum [[theta].sub.v] by the new equation was closer to the gravimetrically measured [[theta].sub.v] than that by the Topp equation in all soil types. The RMSE for the new equation was 0.002 [m.sup.3] [m.sup.-3] for all soil layers.

Validation of the model performance of the new equations prepared for stone-free soils was achieved by separating the whole dataset (soil samples of the three layers) into two groups, one for calibration and the other for validation. Several pairs were generated by combination of layers (Table 5); for instance, in the first pair, the soil samples of layer 1 were selected as the calibration set, and the samples of layers 2 and 3 as validation. As shown in Table 5, the best results were obtained by using the soil samples of layer 3 as calibration and layers 1 and 2 as validation (RMSE = 0.020) or inversely, layers 1 and 2 as calibration and layer 3 as validation (RMSE = 0.021).

Effect of extension cables length

The effect of extension-cable length was minor on the TDR-measured [[theta].sub.v] (<0.01 [m.sup.3] [m.sup.-3]) for cables of lengths 3 and 5 m. Increasing the length caused a linear decrease in [K.sub.a] and [[theta].sub.v]. In addition, deviations from the standard cable length 2 m became larger as the water content increased (Fig. 5). A set of linear regression equations was generated for the three soil layers to correct [K.sub.a] for cable length. An increase in the cable length caused a non-linear decrease in the [K.sub.a] reading, which fits into a third-order polynomial equation. The coefficients for the correction factor for [K.sub.a] readings of any cable length >5 m are presented in Table 6.

These equations can be used for any cable length <30 m. For instance, the [K.sub.a] reading with extension cable of 27 m length for soil type 1 results in a correction factor of 1.048, which should be multiplied by the TDR reading to find the correct [K.sub.a].

Heimovaara (1993) reported that a 0.1-m-long probe could be used with a cable <15 m without losing distinct reflections from the beginning and end of the probe. Comparable results are obtained by using probes >0.2 m with cables up to 24 m long. Short probes (0.05 m) or longer cables cannot be used when measuring dry soils owing to the indistinguishable reflections (Heimovaara 1993). This occurs through an increased rise time of the voltage pulse from the cable filtering of the high-frequency components. Shorter probes with longer cables than those described above can be applied if a TDR instrument with a higher bandwidth is used (Noborio 2001). Our results, which have shown a deviation in the measured [K.sub.a] values with cable length >10 m as opposed to those of standard 2-m cables, do not completely correspond with the findings of Heimovaara (1993). Our probes had similar specifications to those of Heimovaara (1993), but we used a TRASE system, which is different from that used by Heimovaara (1993) (1502B/C). The accuracy of the reading unit to produce and transmit the exact frequency, the accuracy of timing, and the quality of manufacturing of the cables might have caused the difference. Therefore, calibration of the cables before the application seems mandatory. It is also suggested by Logsdon (2000) that for soils of high surface area, the TDR calibration should be carried out with the combination of coaxial cable length and equipment that will be used on-site, or calibration should be performed on-site.

Conclusions

Application of the TDR technique for measuring SWC is widely accepted for laboratory and on-site experimental purposes. Although some results of use and calibration of TDR in stony soils can be found in the literature, its applicability in soil with naturally distributed stone fragments has been rarely investigated. In the present study, a multilayer profile was sampled and the natural distribution of soils was duplicated in the laboratory. The main objective was to assess the role of stones in measured and simulated water contents, as well as the effects of extension cable on the reliability of the results. The robustness of a simulated water-content determination of stony soils may only be ascertained if the parallel measurements are accurate and precise. To this end, stoniness of the soil should be considered in the in-situ TDR-based water content measurements.

For proper comparison of the measured and simulated water content of stony soils, the in-situ TDR-based water content measurements on the fine fraction of the bulk soils should include the effect of stoniness. The latter could be accounted for in the in-situ TDR measurements by converting the bulk dielectric permittivity to the bulk water content and explicitly considering the role of the volumetric fraction of stone. This approach can be applied to convert the in-situ measured dielectric permittivity to [[theta].sub.v] of the bulk soil based on the determined stoniness. The 15-cm, 2-rod (connector) probe type and capture windows of 20 ns resulted in better performance than the 20-cm, 3-rod (buriable) probe type and capture windows 10 ns (with final RMSE of 0.02-0.04 [m.sup.3] [m.sup.-3]).

The calibration equations prepared for the finer (stone-free) part of the soils might lead to a perfect match between observed and simulated water content for the soils in our study area (RMSE = ~0.002 [m.sup.3] [m.sup.-3]). The worth of the calibrated equations becomes obvious when the low water content (e.g. <0.05 [m.sup.3] [m.sup.-3]) in the studied soils is important.

Noticeable effects of cable length on measured [K.sub.a] were found for cables >10 m. Accurate [K.sub.a] values (corrected for extension cable length) can be obtained if the suggested regression equations reported in this study were employed.

For application of the TDR method in layered soils with large-sized stone fractions, two options exist according to the approach of this study. First, if it is possible to insert the probe properly into the undisturbed soil, use the expensive connector probe type, which is designed for this purpose. The strong metal rods have minimal lateral deformation when hammered during the insertion. In this case, the measured [K.sub.a] is the [K.sub.a] of bulk soil (including the stones) and the corrected [[theta].sub.v] can be found based on the stone fraction and its dielectric permittivity by employing Eqn 4 and its power (determined in this study).

Second, if the probe cannot be inserted properly because of practical difficulties in slotting the probes, it may cause the rods not to be inserted in a parallel fashion, and there will be inadequate contact between the rods and the soil particles, resulting in insufficient media for transmission. In this case, it might be decided instead to work with the disturbed soil, and the buriable probe type could be employed. Then, it is recommended to excavate the desired horizontal hole with enough space lengthwise in the undisturbed soil profile, filling the hole with soil of similar texture, and inserting the probes inside the hole. Thereafter, the hole, including the probe, might be covered with insulating material to prevent atmospheric moisture from interfering with the SWC measurement. In this circumstance, the calibration equations for the local (stone-free) soil can be used to find the accurate water content of the fine part and then convert it to the water content of bulk soil (including the stone fraction). The homogeneity between the measured [[theta].sub.v] of filler soil and the [[theta].sub.v] of bulk soil must be ascertained in a separate investigation. However, for monitoring purposes, after an equilibrium has occurred between the filler material and the bulk stony soil, even though the estimated [[theta].sub.v] of filler is not exactly equal to the [[theta].sub.v] of bulk soil, the temporal changes in [[theta].sub.v] include a systematic error and can be corrected. Therefore, the temporal changes in [[theta].sub.v] measured for the soil inside the lateral hole can be assigned to the bulk soil of the same depth.

Acknowledgement

We thank Mr. Amin Rahmani from the Nogarayan Andisheh Company for helping in TDR probe production.

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http://dx.doi.org/10.1071/SR15154

M. Pakparvar (A,B,C), W. Cornelis (B), D. Gabriels (B), Z. Mansouri (A), and S. A. Kowsar (A)

(A) Fars Agricultural and Natural Resources Research & Education Center, Shiraz, I.R. Iran.

(B) UNESCO Chair on Eremology, Soil Management Department, Faculty of Bioscience Engineering, Ghent University, Ghent 9000, Belgium.

(C) Corresponding author. Email: m.pakparvar@areo.ir

Table 1. Particle size distribution (%) of the sampled layers

Textural class <2 mm is calculated based on no stone percentage.
Textural class (USDA): L, loam; SL, sandy loam; S, sand

Depth       >50    25-50    10-25    2-10     >2     0.05-2
(cm)        mm       mm       mm      mm      mm       mm

0 10        0.0     0.0      4.3      2.4     6.7     35.7
10-109      1.0     3.3      10.2     7.6    22.1     67.0
109-150     3.0     12.7     15.6    21.5    52.8     91.4

Depth      0.002-0.05   <0.02   Textural
(cm)           mm        mm      class

0 10          45.5      18.8       L
10-109        15.0      17.0       SL
109-150       6.1        2.5       S

Table 2. Statistical indices for model performance evaluation in
stony samples

L, Loam; SL, sandy loam; S, sand; [V.sub.st], stone (particles >2 mm)
fraction; [phi], porosity; s.d., standard deviation of observed water
contend data; CW, capture window of time in TDR measurement. TDR
probe type: 1, buriable waveguide with three 20-cm-long rods; 2,
connector waveguide with two 15-cm-long rods. RMSE, Root-mean-square
error; RSR, ratio of RMSE to observation standard deviation; Mix,
mixture equation defined as Eqn 4; Topp, Topp et al. (1980) equation
(Eqn 1); [beta], empirical constant summarising the geometry of the
medium in the mixture equation

Soil    Textural   [V.sub.st]   [phi]   s.d.
layer    class        (%)

1          L          6.7       0.49    0.08

2          SL         22.1      0.43    0.09

3          S          52.8      0.36    0.07

                             RSR         RMSE ([m.sup.3]   [beta]
                                           [m.sup.-3])

Soil    CW      TDR     Mix      Topp     Mix      Topp
layer   (ns)   probe

1        10      1      1.24     1.29     0.06     0.06     0.48
                 2      0.89     1.35     0.04     0.07
         20      1      1.42     1.34     0.07     0.07
                 2      0.87     1.34     0.04     0.07
2        10      1      0.44     0.69     0.04     0.06     0.47
                 2      0.41     1.11     0.04     0.10
         20      1      0.29     0.72     0.03     0.06
                 2      0.32     1.07     0.03     0.10
3        10      1      2.11     1.20     0.06     0.04     0.47
                 2      0.78     3.00     0.03     0.09
         20      1      1.96     3.79     0.06     0.11
                 2      0.71     3.05     0.02     0.09

Table 3. Layer specific calibration equations for estimation of
volumetric soil water content ([[theta].sub.v],) in stone-free samples

y, Estimated [[theta].sub.v]; x, measured [K.sub.a] by TDR

            y = a + bx + [cx.sup.2] = [dx.sup.3]      [r.sup.2]   RMSE
Soil
layer       a          b           c          d

1       -2.35E-04   8.08E-03   -1.05E-01   2.85E-01     0.992     0.002
2       -1.69E-04   6.10E-03   -8.73E-01   2.24E-01     0.991     0.002
3       -1.95E-04   6.81E-03   -9.04E-02   2.47E-01     0.997     0.002

Table 4. Statistics of soil water content in sieved soil samples

CW, Capture window of time in TDR measurement; [[theta].sub.v],
volumetric soil water content; s.d., standard deviation; RMSE, root-
mean-square error; Topp equation, from Topp et al. (1980)

                                              [[theta].sub.v]
                                                 ([m.sup.3]
Soil                    CW                       [m.sup.-3])
type                   (ns)   Min.    Max.     Mean      s.d.     RMSE

1      Observed               0.016   0.363    0.161     0.106
       Topp equation    10    0.044   0.375    0.165     0.104    0.005
                        20    0.050   0.365    0.171     0.102    0.005
       New equation     10    0.010   0.368    0.161     0.106    0.004
                        20    0.010   0.366    0.161     0.106    0.002
2      Observed               0.012   0.377    0.129     0.110
       Topp equation    10    0.022   0.377    0.129     0.111    0.007
                        20    0.020   0.369    0.129     0.109    0.009
       New equation     10    0.019   0.361    0.149     0.105    0.002
                        20    0.014   0.367    0.155     0.105    0.002
3      Observed               0.009   0.333    0.122     0.102
       Topp equation    10    0.041   0.329    0.122     0.093    0.009
                        20    0.047   0.331    0.128     0.092    0.009
       New equation     10    0.011   0.325    0.117     0.099    0.008
                        20    0.010   0.332    0.122     0.102    0.002

Table 5. Calibration equations for the stone-free samples used in
validation

Cal., Sample set used for calibration; Val., sample set used for
validation; y, estimated volumetric soil water content
([[theta].sub.v]); x, measured [K.sub.a] by TDR; RMSE, root-mean-
square error. The equations Topp (Topp et al. 1980) and this study
are the regression equations prepared based on soil layer sample sets

Eqn     Soil layers          y = a + bx+ [cx.sup.2] + [dx.sup.3]
        sample set

         Cal.   Val.       a            b           c            d

Topp                   -5.30E-02    2.92E-02    -5.50E-04    4.30E-06
This      1     2, 3   -2.85E-01    1.05E-01    -8.08E-03    2.35E-04
study     2     1, 3   -2.24E-01    8.27E-02    -6.10E-03    1.69E-04
          3     1, 2   -2.47E-01    9.04E-02    -6.81E-03    1.95E-04
         2, 3     1    -1.97E-01    7.23E-02    -4.90E-03    1.00E-04
         1, 2     3    -1.73E-01    6.28E-02    -3.73E-03    1.00E-04
         1, 3     2    -2.85E-01    I.05E-01    -8.08E-03    2.40E-04

Eqn      Soil layers     [r.sup.2]    RMSE
          sample set

          Cal.   Val.

Topp                        0.97      0.027
This       1     2, 3       0.96      0.032
study      2     1, 3       0.97      0.025
           3     1, 2       0.96      0.020
          2, 3     1        0.54      0.096
          1, 2     3        0.98      0.021
          1, 3     2        0.96      0.044

Table 6. Regression coefficients for correction of dielectric
permittivity ([K.sub.a]) readings for any cable length >5 m

y, Correction factor for [K.sub.a]; x, cable length (m)

           y = a + bx + [cx.sup.2] + [dx.sup.3]
Soil
types      a          b          c          d       [r.sup.2]

1       9.97E-1    1.31E-3    -1.37E-4   5.85E-6      0.986
2        1.02     -6.81E-3    4.68E-4    -5.26E-6     0.987
3        1.01     -3.41E-03   2.03E-4    -7.14E-8     0.990
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Author:Pakparvar, M.; Cornelis, W.; Gabriels, D.; Mansouri, Z.; Kowsar, S.A.
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Date:May 1, 2016
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