Correction of TDR-based soil water content measurements in conductive soils

Transcription

1 Available online at Geoderma 143 (2008) Correction of TDR-based soil water content measurements in conductive soils Marco Bittelli, Fiorenzo Salvatorelli, Paola Rossi Pisa Department of AgroEnvironmental Science and Technology, University of Bologna, Italy Received 13 February 2007; received in revised form 24 August 2007; accepted 28 October 2007 Abstract Time Domain Reflectometry (TDR) is a widespread technique for measurement of soil water content (SWC). The main assumption behind the use of Time Domain Reflectometry (TDR) is of negligible losses, therefore assuming that only the real part determines the value of the TDRmeasured apparent dielectric permittivity. This assumption does not hold for soils where surfaces are conductive (clay soils) or where high concentrations of electrolyte are present in the soil solution (saline soils) because under these conditions the contribution of the imaginary part becomes important. One of the main effects of dielectric losses on the TDR measurement is overestimation of SWC. In this study we present a methodology for separating the real and the imaginary part from the measurement of the apparent dielectric permittivity. This approach allows correction of the SWC overestimation, by using the TDR-measured electrical conductivity as indicator of dielectric losses. Oven-dry gravimetric soil water content was used as an independent method for soil water content assessment. The original SWC overestimation (in respect to the ovendry gravimetric based measurement) reached values of up to 20% of total soil saturation, after the correction the differences were reduced to a 3 5%. The methodology can be applied based on knowledge of measured permittivity and electrical conductivity only, making it readily applicable to field experiments Elsevier B.V. All rights reserved. Keywords: Time Domain Reflectometry; Clay soil; Dielectric permittivity; Soil water content; Electrical conductivity 1. Introduction Time Domain Reflectometry has become an established method for soil water content (SWC) measurement. TDR exploits the difference in dielectric permittivity values between the solid phase, air phase and liquid phase. At the TDR frequencies, pure liquid water has a dielectric permittivity of about 80 (depending on temperature and electrolyte solution), air has a dielectric permittivity of about 1 and the solid phase of about 4 to 16 (Hallikainen et al., 1985; Wraith and Or, 1999). This contrast makes the dielectric permittivity of soil very sensitive to variation in soil water content. The measurement of the bulk dielectric permittivity is then used to obtain the Corrresponding author. Department of AgroEnvironmental Science and Technology, University of Bologna, Viale Fanin, 44, Bologna, Italy. Tel.: ; fax: address: marco.bittelli@unibo.it (M. Bittelli). volumetric water content through calibration curves (Topp et al., 1980; Roth et al., 1990). The dielectric permittivity is described by a complex number, where the real part (ε r ) describes the energy stored in the dielectric material and the imaginary part (ε r ) describes the dielectric losses. When the dielectric losses are assumed to be negligible in the TDR bandwidth, the TDR-measured apparent relative permittivity (ε a ) represents the real part of the dielectric permittivity (ε a ε r ). However, when TDR measurements are performed on conductive materials such as clay or saline soils, the imaginary component cannot be neglected, since ε a is then determined by both the real and the imaginary parts. Several authors have reported that the contribution of the imaginary part to the measured apparent permittivity (ε a ) results in overestimation of SWC (Dalton, 1992; Bridge et al., 1996; Wyseure et al., 1997). Regarding the sources of the dielectric losses, Topp et al. (2000) pointed out that the dielectric losses and the conductive losses did not differ depending on the different /$ - see front matter 2007 Elsevier B.V. All rights reserved. doi: /j.geoderma

2 134 M. Bittelli et al. / Geoderma 143 (2008) sources of conductivity, whether from clay content or electrolytes in the soil solution, thereby addressing the problem by using the electrical conductivity of the bulk material as indicator of dielectric losses. The motivation for this study stemmed from results obtained from a TDR station measuring SWC on clay soils, installed to investigate the effects of SWC on shallow landslides. A preliminary experiment to investigate the use of two common TDR-systems, the Tektronix 1502C (Tektronix Inc., Beaverton, OR) and the TDR100 (Campbell Scientific Inc., Logan, UT) showed two problems, both related to energy dissipation in the highly conductive material. The first issue concerned the probe length: when using a 30 cm-long probe (Model CS610, Campbell Sci. Inc.) the collected waveforms were flat and did not allowed waveform analysis because the reflection at the end of the probe was not detectable. By reducing the probe length by half (therefore reducing the energy dissipation along the shorter transmission line), the second inflection was then identifiable and the TDRsystems could be successfully used to measure the travel time (details are provided in the Materials and methods section). The second issue regarded the SWC data itself: after installing the TDR-system (with the 0.15 m, shorted probes), analysis of the apparent dielectric permittivity and SWC computation revealed a considerable SWC overestimation. Fig. 1 shows the measured apparent dielectric permittivity, the TDR-measured SWC (the latter obtained by using the Topp et al. (1980) calibration curve) before any correction, and independent oven-dry gravimetric soil water content (oven-dry gravimetric measurements were converted to volumetric measurements by measuring the samples bulk density). TDR always overestimated SWC in respect to the standard oven-dry gravimetric measurements, up to 20% of soil saturation. During data analysis, it was soon clear that the problem was not the calibration curve, but the apparent dielectric permittivity values ε a, which resulted in overestimation of the water content measurement. The first possible option for addressing this issue would have been to derive a new calibration curve or new parameters for Fig. 1. Daily values of TDR-measured apparent dielectric permittivity, TDR-measured soil water content obtained by using the Topp et al. (1980) algorithm, and independent oven-dry measurements. The TDR-measured soil water content presented in this figure was obtained before any correction.

3 M. Bittelli et al. / Geoderma 143 (2008) existing calibrations curves, i.e., for the Topp et al. (1980) equation. Indeed, Bridge et al. (1996) proposed alternative calibration parameters for the Topp's polynomial for three clay soils from Queensland, Australia. However, the derivation of different calibration curves performed on few soils are site specific and do not address the causes of the larger ε a. Moreover, the modified calibration curves do not account for the effect of electrical conductivity on soil water content measurements. In this paper we present a methodology to correct TDRbased measurements in conductive soils based on the separation of the real part from the imaginary part in the TDR-measured apparent dielectric permittivity, allowing to use only ε r to compute the soil water content. 2. Theory 2.1. Dielectric permittivity The relative dielectric permittivity ε r is expressed as the ratio of the permittivity of the material ε (F m 1 ) and the permittivity of free space ε 0 ( Fm 1 ): e r ¼ e ð1þ e 0 The relative dielectric permittivity is a complex variable characterized by a real part (ε ) r and by an imaginary part (ε r ). The real part accounts for the energy stored in the dielectrics at a given frequency and temperature, while the imaginary part describes the dielectric losses or the energy dissipation. The complex dielectric permittivity ε is written as (Robinson et al., 2003): e r ¼ ev r j e rel W þ r dc ð2þ e 0 x where ε rel is the imaginary part of the relative dielectric permittivity due to relaxations, σ dc is the electrical conductivity at zero frequency (S m 1 ), ωp is the angular frequency (2π f )where f is frequency (Hz), and j ¼ ffiffiffiffiffiffi 1 is the imaginary number. Eq. (2) describes the two processes determining energy losses in wet, porous materials: dipoles relaxations and electrical conductivity. The first is due to the relaxation time required by a dipole to adjust to the orientation of the electromagnetic field, resulting in adsorption of energy by the dipole. The second is due to conduction arising from the material surfaces as a result of electric charges, and from electrolytes in the liquid phase Travel time analysis The velocity of an electromagnetic wave in free space (c) is expressed by the dielectric permittivity ε 0, and the magnetic permeability of free space μ 0 (4π 10 7 Hm 1 )as: c ¼ pffiffiffiffiffiffiffiffi 1 ð3þ A 0 e 0 while the velocity (v) of a wave in a dielectric material is given by: v ¼ p 1 ffiffiffiffiffi Ae ð4þ where μ is the magnetic permeability of the dielectric material. From a mechanical standpoint, the velocity v (m s 1 )ofan electromagnetic wave travelling through a probe of length L (m), is given by: v ¼ 2L ð5þ t where t is time (s). For the TDR measurement, the number 2 in front of the probe length is included, because the wave travels back and forth. It is convenient to define a ratio of the propagation velocity (v p ) in the material in respect to the propagation velocity in free space: v p ¼ v c ¼ q 1 ffiffiffiffiffiffiffi ¼ 2L ð6þ ct A A 0 e e 0 which reduces to: 1 pffiffiffiffiffiffiffiffi A r e r ¼ 2L ct where μ r is the relative magnetic permeability. For most soils μ r is equal to 1 (Roth et al., 1990), therefore Eq. (7) can be written as: 1 p ffiffiffiffi ¼ 2L ð8þ e r ct Rearranging leads to: e r ¼ ct 2 ð9þ 2L which is the equation used as a basis for TDR analysis to obtain the relative dielectric permittivity, where the travel time is measured, and the probe length and the wave velocity are known. The primary assumption of TDR-based measurements is that the imaginary part of the complex relative dielectric permittivity is negligible in comparison to the real part, thus: e r cev r ð10þ However, since dielectric losses are always present in a dielectric (although small), the TDR-measured relative dielectric permittivity was called apparent (ε a )(Topp et al., 1980). The assumption of negligible losses does not hold for soils where surfaces are highly conductive (clay soils) or where high concentrations of electrolyte are present in the soil solution (saline soils). The contribution of the not-accounted imaginary component to the measured apparent dielectric permittivity ε a, results into higher values of ε a (in respect to its real component only), and therefore into SWC overestimation (Wyseure et al., 1997; Topp et al., 2000) Separation of the real and imaginary part To take into the account the imaginary part, and separate its effect from the measured ε a, the velocity of propagation can be described as (von Hippel, 1954): 1 v p ¼ vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi " rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi# ð11þ u e r V 2þ1 t 2 1 þ e rw e r V ð7þ

4 136 M. Bittelli et al. / Geoderma 143 (2008) Eq. (11) shows that the relative dielectric permittivity does not correspond to the real part only, but it is an apparent dielectric permittivity, characterized by a real and an imaginary part. Substituting Eq. (6) into 11 leads to: 2L ct ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 v " rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi# u e r V 2þ1 t 2 1 þ e rw e r V ð12þ Substituting the definition of relative dielectric permittivity from Eq. (9) (here renamed apparent dielectric permittivity), into Eq. (12) and rearranging, allows to obtain a definition of the apparent dielectric permittivity as: e a ¼ ev r 2 2s 4 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ e 2 rw þ 1 ev r 3 5 ð13þ The total losses are described by the imaginary part as: e r W ¼ e rel W þ r dc ð14þ e 0 x As suggested by Hasted (1973) and Topp et al. (2000), the total losses (ε r ) can be accounted as an effective conductivity (σ e ) defined as: r e ¼ e 0 xe r W ð15þ The effective conductivity encompasses both electrical conductivity and relaxations losses, and it is assumed to be equal to the TDR-measured electrical conductivity of the material (Topp et al., 2000). The imaginary part is then written as: e r W ¼ r e ð16þ e 0 x Substituting Eq. (16) into Eq. (13) and solving for ε r yields: r2 e ev r ¼ e a 4e a e 2 ð17þ 0 x2 The TDR-measurements provide both ε a and σ e (S m 1 ) but ω is unknown since the TDR does not operate at a specific frequency, but measures the propagation velocity of a step voltage pulse with a bandwidth of around 20 khz to 1.5 GHz (Heimovaara, 1994). However, as pointed out by Topp et al. (2000), it is possible to estimate a maximum frequency by calculating the pulse rise time (t r ) of the reflected signal from its first reflection from the end of the probe. Fig. 2 shows a schematic depicting the methodology to measure the rise time. To obtain the maximum frequency the following equation was used (Johnson and Graham, 1993): F max ¼ 0:5 ð18þ t r where F max is the frequency below which most energy in the digital pulses concentrates. The max frequency for a digital signal is related to the rise and fall time. If the rise time are short the F max Fig. 2. TDR waveform depicting the methodology to compute the travel time (t t ) and the rise time (t r ). The rise time is used to compute the maximum frequency (F max ) by employing the equation presented in the figure. is high and if the rise time are long the F max is low. To obtain the rise time the procedure described in Fig. 2 was employed. The rise time is computed by measuring the time difference between: (a) the second inflection point used to calculate the travel time (t t ) and (b) the intercept between the tangent used to calculate the second inflection and the tangent to the asymptotic low frequency end of the waveform. For a rise time of s, the resulting maximum frequency was Hz (150 MHz), which was used to calculate ω=2πf max, for a waveform corresponding to an average soil water content of 0.3 m 3 m 3. Topp et al. (2000) obtained values of maximum frequency ranging from 1.2 to Hz, therefore our results are quantitatively in agreement with their results. Overall, Eq. (17) allows for separation of the real and the imaginary part of the apparent dielectric permittivity, by using only the values of dielectric permittivity and electrical conductivity, without the necessity of performing a waveform analysis for each acquired trace to obtain the rise time. After obtaining the real part ε r, it is then possible to compute the SWC by using available algorithms (Topp et al., 1980; Roth et al., 1990), where ε r is used as input data, instead of ε a Apparent dielectric permittivity analysis by means of dielectric mixing models We assume that the bulk dielectric permittivity ε b of a porous medium can be written as a three-phase mixing model (Birchak et al., 1974; Roth et al., 1990): e a b ¼ h le a l þ h g e a g þ h se a s ð19þ where ε l, ε g, and ε s are the dielectric permittivities of liquid water, gas, and solid phases, respectively, α is a parameter related to the geometrical arrangement of the solid particles (usually assumed to be equal to 0.5), and θ l, θ g, and θ s are the volume fractions of the respective phases. Here, the bulk dielectric permittivity corresponds to the measured apparent dielectric permittivity. When the soil is saturated, Eq. (19) simplifies to: e a b ¼ h le a l þ h s e a s ð20þ

5 M. Bittelli et al. / Geoderma 143 (2008) By using typical values of ε l =80, ε s =14 (for clay minerals, as suggested by Olhoeft (1981)) and α =0.5, it is possible to calculate theoretical apparent dielectric permittivities at different levels of soil saturation (θ s ). For instance, for a θ s =0.5 the measured bulk dielectric permittivity should be ε b =39.5, while for θ s =0.6, ε b =47.1. The values of ε s and α may change from soil to soil depending on mineralogical composition and on the geometrical arrangement of the solid particles, thereby affecting the theoretical ε b. However, this model has been successfully used to estimate soil volumetric fractions in previous works and it provides a reliable approach to assess the reliability of measured dielectric permittivity values (Roth et al., 1990; Bittelli et al., 2004). 3. Materials and methods The TDR experimental station was installed in the Centonara watershed, located on the Northern Apennines relief, east of Bologna, Italy (lat N, long E). The climate is Mediterranean with an average annual cumulative rainfall of 750 mm and mean annual temperature of 16 C. The top graph in Fig. 4 shows daily precipitation and average temperature. The lithology is heterogeneous, characterized by a transition from marine pliocenic clays to pleistocenic sands. Soils developed on these materials are classified as Inceptisols and Vertisols. The experimental station and the sensors were installed on a steep (slope 25%) Vertisol with high clay content, classified as Aquic Chromic Haploxerert smectitic, calcareous, mesic (USDA classification). Determination of soil lithology and soil physical properties was performed through several auger and core drilling campaigns, as well as soil pits excavation. Mineralogy was determined with X-ray diffraction with Cu Ka radiation (Philips XRG 3100, Philips Analytical Inc., Mahwah, NJ). The clay fraction is characterized mostly by smectite and vermiculite. This information was used to select the values of the solid phase relative dielectric permittivity to be used in Eq. (20), based on published values for different clay minerals (Olhoeft, 1981). Table 1 shows the soil properties at the site. Oven-dry gravimetric SWC and soil bulk density were periodically measured to compare oven-dry gravimetric measurements with TDR-based measurements and test the performance of the TDR-system. The gravimetric measurements were used as independent measurements since no information collected from the gravimetric measurements was used for the TDR-based measurements. Knowledge of bulk density was needed to convert the oven-dry gravimetric measurement to the volume-based TDR measurement: maximum soil saturation as a mean of testing the TDR-based measurements. Soil porosity is derived from bulk density by: U ¼ 1 q b ð22þ q s where ρ b (kg m 3 ) is the soil bulk density and ρ s (kg m 3 )isthe soil particle density, assumed to be equal to 2650 kg m 3.Itis worth noting that the Ozzano clay soil displays pronounced seasonal shrinking swelling phenomena, causing cracks during the summer period and variation in soil bulk density. For this reason bulk density was measured each time an oven-dry gravimetric test was performed, to account for its seasonal variations. A TDR-system was installed at the site (TDR100, Campbell Scientific Inc., Logan, UT) equipped with a datalogger for automatic data collection (CR23X, Campbell Sci.,Campbell Scientific Inc., Logan, UT) and 30 cm-long probes (Model CS610, Campbell Sci. Inc.). The system was multiplexed through a single SDMX50 multiplexer (Campbell Scientific Inc., Logan, UT). Probes (three replicates) were inserted horizontally at 0.2, 0.4 and 0.8 m depth. By using 30 cm probe length, the collected waveforms were flat and did not allow waveform analysis. Analysis performed with the algorithm provided with the PCTDR software (Campbell Scientific Inc.) showed that the algorithm could not converge to identify the second inflection. Further analysis of the waveforms carried out with the dualtangent approach (Heimovaara, 1994; Wraith and Or, 1999) also showed that the algorithm could not correctly identify the second inflection point. Robinson et al. (2003) also reported that more attenuation occurs with long probes, and therefore shorter probes should be used in highly conductive soils. The option of coating the probes as a way to extend the working range of TDR in conductive soils was not chosen because of the studies of Ferré et al. (1996) and Knight et al. (1997) indicating a reduced sampling volume and questionable accuracy. By halving the probe length and therefore reducing the energy dissipation along a shorter transmission line, the second inflection point was then detectable and the TDR-systems could be successfully used to measure the travel time since the algorithm could identify the second inflection even in the wettest soil conditions. Moreover, to avoid the reported multiplexer-induced interference for electrical conductivity measurements (Castiglione et al., 2006), we used three-rod probes (Model CS610, Campbell Sci. Inc.), since two-rod probes are more sensitive to multiplexer-induced common ground interference, and we installed the probes at a minimum distance of 0.2 m between probes, since the multiplexer-induced interference rapidly decreased with increasing inter-probe distance. q w h ¼ q b w ð21þ 4. Results and discussion where ρ w is the density of water (1000 kg m 3 ), θ is the volumetric SWC (m 3 m 3 ), ρ b is the soil bulk density (kg m 3 ) and w is the gravimetric SWC (kg kg 1 ). Moreover, periodic measurements of bulk density were performed to derive the total soil porosity and therefore derive 4.1. Relative dielectric permittivity and effective electrical conductivity Fig. 3 (a) shows TDR-measured apparent (ε a ) and real (ε r ) dielectric permittivity (obtained from Eq. (17)), and (b) TDR-

6 138 M. Bittelli et al. / Geoderma 143 (2008) Fig. 3. (a) Daily values of TDR-measured apparent dielectric permittivity (ε a ) and real relative dielectric permittivity (ε r ) (obtained from Eq. (17)). (b) TDR-measured effective electrical conductivity (ω). measured effective electrical conductivity as function of time. As shown in Eq. (17), the apparent permittivity was reduced by subtracting the imaginary component that depends on the effective electrical conductivity measurements and frequency, therefore the difference between ε a and ε r in Fig. 3 (a) is the imaginary part of the relative dielectric permittivity. For the 0.2 m depth, at and close to soil saturation, ε a displayed values around 60, with higher values up to 62. Using Eq. (20) to compute the corresponding theoretical θ s, it appeared that θ s should be equal to 0.83 (m 3 m 3 ) to determine a real permittivity of 62, which is 70% higher than the oven-dry gravimetric measurements of θ s =0.56 (m 3 m 3 ). For the measured soil saturation of 0.56 (m 3 m 3 ), ε a should be approximately equal to 42, instead of 65. Indeed, the corrected ε r displayed values between 45 and 42 at and close to saturation, showing that the correction brought down the dielectric permittivity to realistic values. A confirmation for the θ s values was also provided by the bulk density measurements (Table 1). By using Eq. (22) and the bulk density measurements, soil porosity ranged from 0.52 to 0.57 (m 3 m 3 ), depending on depth. Effective electrical conductivity (σ e ) ranged from 0.2 to 0.7 Sm 1. As reported by other authors (Wyseure et al., 1997; Mojid et al., 2003) the imaginary component induced SWC overestimation at values of electrical conductivity higher than Table 1 Soil physical properties of Ozzano clay, for four different soil layers Depth Sand, % weight Silt, % weight Clay, % weight Bulk density, kg m θ s,m 3 m

7 M. Bittelli et al. / Geoderma 143 (2008) S m 1, while at values lower than 0.25 the overestimation stays reasonable and can be disregarded. Our results are therefore in agreement with previous studies. Effective electrical conductivity increased with increasing water content, somehow following a similar trend of the dielectric permittivity, confirming previous studies showing the dependence of electrical conductivity to water content changes (Hartsock et al., 2000). This behavior is due to the contribution of the fluid conductivity to the electrical conductivity, as described in Archie's law (Archie, 1942): r ¼ cr f U m ð23þ where σ is the electrical conductivity due to conductivity of the pore fluid and the surface conduction, σ f is fluid conductivity, Φ is the porosity and c and m are empirical parameters. Usually c varies between 0 and 1, while m varies between 1.4 and 2, depending on the tortuosity of the flow path. When the tortuosity of the flow path increases (due to decreased soil water content), the electrical conductivity decreases because of the hindered conduction of electrical charges. The 0.8 m depth displayed higher values of σ e in respect to the more superficial depths. The increase is due to the accumulation of carbonates and other salts in the B profile of these Vertisols, as also detected by a pedological description of the site performed before the beginning of the experiments Soil water content Fig. 4. Daily precipitation, average temperature and TDR-measured SWC after the correction for three different depths. Solid triangles are independent ovendry measurements. Fig. 4 shows soil water content for three different depths after the correction (the top graph depicts daily precipitation and average temperature). These data were obtained by using ε r from Eq. (17) as input for the Topp et al. (1980) algorithm. As shown in Table 1 the saturated water contents ranged from 0.52 to 0.57 m 3 m 3. The uncorrected SWC data (Fig. 1) reached saturated values up to 0.68 m 3 m 3, which were overestimated, as also demonstrated by the oven-dry gravimetric measurements. On the other hand, the corrected SWC data (Fig. 4) reached values of saturation of 0.57 m 3 m 3, and were in good agreement with the oven-dry measurements. To analyze these differences in more details each oven-dry gravimetric soil water content measurement was compared to the corresponding corrected and not-corrected TDR measurements. Fig. 5 shows oven-dry gravimetric measurements and corrected and notcorrected TDR measurements for each depth, ordered by increasing soil water content. The error bars for the oven-dry measurements are the standard deviations. To evaluate the differences between the corrected and not-corrected TDR measurements with respect to the oven-dry measurements, the relative error was computed, which is the absolute value of the difference between TDR and oven-dry measurement expressed as a percentage of the oven-dry value. The relative error was computed for the two cases of corrected and not-corrected TDR measurements. Table 2 shows the measured oven-dry, TDR corrected (TDRc), TDR not-corrected (TDRnc) soil water content and the relative error for the two comparisons. For each soil sample except one (sample number 2 of the 0.8 depth) the relative error for the corrected TDR was considerably smaller than for the not-corrected one. For the corrected values, the relative error was less than 20%, (except for samples 1 and 3 of the 0.2 m depth ), with an average of 11% for the 0.2 m depth, 9.6% for the 0.4 m depth and 11% for the 0.8 m depth. Overall, this analysis showed that the corrected TDR measurement provided a significant improvement in the measurement of SWC in respect to the original data without correction.

8 140 M. Bittelli et al. / Geoderma 143 (2008) Table 2 Soil water content measured with oven-dry, TDR not corrected (TDRnc) and TDR corrected (TDRc), and the relative error of the calculated values, for three soil depths Sample Oven-dry TDRnc TDRc Relative error (TDRnc) Relative error (TDRc) (m 3 m 3 ) (m 3 m 3 ) (m 3 m 3 ) (%) (%) 0.2 m m Real part, imaginary part and dielectric losses As described in Eq. (15), the TDR-measured effective electrical conductivity account not only for the electrical conductivity losses but also for the relaxation losses due to various polarization phenomena. Fig. 6 shows the real and the imaginary part (obtained from Eq. (17)) of the dielectric permittivity as function of water content, for the 0.2 m depth. The dots represent the measured ε r and ε r, plotted at the corresponding oven-dry soil water content measurements, while the solid line is the theoretical value for the real part. The theoretical values were obtained by using Eq. (17) for incremental apparent permittivity values and measured electrical conductivity values from this experiment. After obtaining the ε r, it was converted into SWC by using the Topp et al. (1980) equation. The typical relationships between SWC and ε r of the theoretical curve are given by the nonlinear relationship between dielectric permittivity and SWC as also shown by Topp et al. (2000). The scattering of the data 0.8 m Regarding the SWC time series (Fig. 4), the decreased soil water content during the summers represent the climatic, pedological and vegetational conditions at the site. The area is covered by a dense natural vegetation (various species of shrubs and herbaceous plants), typical of the natural settings of the Apennine Mountains, resulting in high plant water uptake, with roots that can reach down to 1.5 meter depth. Therefore the decrease in soil water content from the beginning of May to the end of summer is due mostly to plant transpiration and soil evaporation. The soil profile is recharged by precipitation in the fall season with SWC displaying small variations, particularly in the deepest layers ( 0.4 and 0.8 m) during the fall and the winter season. When evapotranspiration is reduced because of the diminished plant transpiration and by the reduced temperature and radiation, the water budget is mostly determined by the soil physical properties. This soil is characterized by low saturated hydraulic conductivity (from 0.2 to 0.6 cm h 1 ), therefore it keeps a SWC value close to field capacity for long periods (see the small variations in SWC during the period September May 2004, 2005 and 2006 for the 0.4 and 0.8 depths). Overall, SWC decreased from 2004 to 2007, very likely due to reduced precipitation. Indeed, the cumulative annual precipitation was 994 mm in 2004, 888 mm in 2005 and 503 mm in 2006 (in 2007 there have been 350 mm up to August 5, 2007). Fig. 5. Soil water content of different samples from three different depths obtained from: (1) oven-dry measurements, (2) TDR-based measurement without correction and (3) TDR-based measurement after the correction. The error bars are the standard deviation for the oven-dry replicates.

9 M. Bittelli et al. / Geoderma 143 (2008) obtain reliable dielectric permittivity measurements for reliable SWC analysis Dielectric mixing model Fig. 6. Real and imaginary part of the TDR-measured apparent dielectric permittivity as function of water content obtained from Eq. (17). around the theoretical values may be due to the differences between the oven-dry methods and the TDR methods (for an independent test the values of the real and the imaginary part were plotted as function of oven-dry SWC measurements) and to differences in the waveform rise time for different SWC values. The imaginary part displayed maximum losses at intermediate and high SWC (between 0.4 and 0.5 m 3 m 3 ) and decreasing at lower SWC. Apart from the discussed electrical conductivity effects, the changes in dielectric losses in clay materials as function of SWC are due to the combination of various polarization mechanisms. From low to high frequencies the dominant polarization mechanisms are: low frequency DC conductivity, Maxwell Wagner and double layer polarizations (spatial polarization), bound water polarization and bulk water polarization (Santamarina et al., 2001; Ishida and Makino, 1999). These polarization effects induce multiple relaxations occurring at different frequencies. In the dominant frequency of 150 MHz (used in this study) the two most important polarization mechanisms are bound and bulk water polarization. The contribution of bulk water polarization (with values of 78.3 at 25 C) dominates the value of the overall dielectric permittivity, increasing with increasing soil water contents. Since bulk water undergoes relaxation at much higher frequencies ( 16 GHz), the contribution of bulk water polarization can be regarded simply as function of soil water content. The relaxation mechanisms due to orientational polarization of bound water are different than the one for bulk water and are determined by a variety of processes that depends on viscosity (McBride and Baveye, 1995), ph (Ishida and Makino, 1999) and temperature (Or and Wraith, 1999; Wraith and Or, 1999). However, since the present analysis is limited to a single frequency it is difficult to distinguish between the different relaxation phenomena. Alternative methods operating in the frequency domain and analyzing several frequency ranges would be necessary for this kind of analysis. In this research, the results show that the effective electrical conductivity is a good estimator of the dielectric losses, and that by removing its effect on the TDR measurement, it is possible to Comparison of ε r with theoretical values obtained from Eq. (20), showed that ε r, after the proposed correction, is in good agreement with theoretical dielectric permittivity values. For θ s =0.5 (m 3 m 3 ), the bulk dielectric permittivity (ε b ) should be equal to Fig. 6 shows that for θ s =0.5 (m 3 m 3 ) the computed ε r =42.5, with difference of only 5.7% in respect to the theoretical mixing model. The differences between ε r and ε b may be due to different values of the solid phase permittivity ε s, different values of the geometrical parameter α, or the well known temperature dependence of the liquid phase permittivity ε l. However, this method provided a useful, quantitative methodology to test the validity of the proposed correction. 5. Conclusions A method is proposed to correct overestimated TDR-based soil water content measurements in conductive soils. The method separates the contribution of the real and the imaginary parts on the measured apparent dielectric permittivity, through knowledge of soil effective electrical conductivity. After obtaining the real part of the apparent dielectric permittivity and therefore subtracting the dielectric losses, the real component can be used to apply traditional calibration curves to obtain corrected soil water content measurements. Since the correction depends on the measured soil electrical conductivity, the difference between bcorrected and bnotcorrected apparent dielectric permittivity is not constant, but it changes with the SWC itself, because the concentration of the soil solution (and therefore its electrical conductivity) changes with SWC. Moreover, the dielectric losses due to relaxations (such as the bound water polarization) are also a function of SWC. For this reason, alternative calibration curves are not effective in addressing this problem, because they do not take into account the effect of electrical conductivity and dielectric losses. The analysis shows that it is possible to use a single frequency, computed by the rise time, to separate the real and the imaginary component. While this is an advantage, it may also be a limitation of the proposed methodology, because the computed rise time may change with water content itself, therefore affecting the computation of the real and the imaginary part. This limitation could be overcome when using time domain or frequency domain methods operating at a single frequency, with fixed rise time. Another option (and a topic for further studies), would be to implement a computer code for waveform analysis, similar to the ones currently used for automatic computation of travel time, such as the WinTDR (Or et al., 1998), to automatically compute the rise time for each collected waveform. The rise time would allow to derive a maximum frequency for each collected waveform and allow application of Eq. (17) with different angular frequencies for each data point, instead of using a single angular frequency for the whole data set.

10 142 M. Bittelli et al. / Geoderma 143 (2008) Overall, these results indicated that the errors induced by use of TDR-systems in conductive soils may be very significant, thus requiring a dielectric approach to address the problem. A method to separate the real and the imaginary component was derived and used to correct for the SWC overestimation. Acknowledgments This study was funded by the European Commission (EC) Research Project (LIFE03 ENV/IT/000366): SLID (Shallow Landslides Investigation Device), a tool to assess land susceptibility to shallow landslides. We thank the editor and three anonymous reviewers for their valuable comments. Appendix A. List of symbols ε Permittivity of the material ε 0 Permittivity of free space ( Fm 1 ) ε r Relative permittivity ε r Complex relative permittivity ε r Real part of the relative permittivity ε r Imaginary part of the relative permittivity ε rel Imaginary part due to dielectric relaxation ε a Apparent relative permittivity ε b Bulk relative permittivity ε l Liquid phase relative permittivity ε g Gas phase relative permittivity ε s p Solid phase relative permittivity j ¼ ffiffiffiffiffiffi 1 Imaginary number μ 0 Magnetic permeability of free space μ Magnetic permeability of the material μ r Relative magnetic permeability Φ Soil porosity σ Electrical conductivity due to conductivity of the pore fluid and surface conduction σ dc Zero frequency electrical conductivity (S m 1 ) σ e Effective electrical conductivity (S m 1 ) ω Angular frequency (2π f ) References Archie, G.E., The electrical resistivity log as an aid in determining some reservoir characteristics. Trans. Am. Inst. Min. Metall. 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