Inversion of TDR signals—revisited

In this study, we discuss the consistence of measured and calculated TDR traces. The calculated traces are solutions of a time domain reflectometry (TDR) forward solver, an algorithm for computing the TDR trace for a given dielectric profile along a transmission line. An unambiguous and efficient forward solver is a prerequisite for a good solution of the inverse problem, i.e., to extract the spatial distribution of the dielectric properties along the transmission line from a TDR trace. To advance our understanding of TDR inversion, we proceeded in two steps: (1) design of a TDR head section with minimal disturbances on the signal and (2) searching for causes why measured and predicted TDR traces differ. Based on a first experiment with a three‐rod TDR probe of 100 cm length, we demonstrated that our TDR forward solver—like others presented in literature—approximate the measured TDR traces apparently well but not precisely enough for signal inversion. In a second experiment, using a two‐rod TDR probe of 70 cm length, we addressed the problem of non‐parallel transmission lines. We found that the influence of a non‐parallel installation is similar to an increase of the electrical conductivity in soil water but can be distinguished from this property. A third experiment reveals that lateral and longitudinal disturbances in the vicinity of a TDR probe are of minor importance. From the analysis of our experiments, we found that neither lateral disturbances nor non‐parallel rods are responsible for the deviations between calculated and measured traces. This analysis showed us that structure in the sampled medium affects the shape of the TDR traces. Since minor deviations are essential for TDR‐signal inversion, we need new concepts to handle the fuzziness between measurements and calculations.     

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

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 TDR-measured 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 oven-dry 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.     

Measurement of volumetric water content by TDR in saline soils

Time-domain reflectometry (TDR) evaluates the bulk dielectric constant, K, of the soil by measuring the travel time of an electromagnetic pulse through a sensor, and through it estimates the volumetric water content. We show that for saline soils the effects of conductivity and frequency on the travel time cannot be neglected and that, as a result, TDR systematically overestimates the water content in saline soils. Simultaneously the bulk electrical conductivity of soils can be estimated by TDR. The equivalent impedance after multiple reflections is related to the bulk electrical conductivity, σ This relation differs from sensor to sensor and requires calibration for each individual sensor. A method is proposed for correcting the volumetric water content in saline soils. First, the bulk electrical conductivity, o, is estimated from the equivalent impedance at a specific equivalent distance of cable, several times the actual length of the sensor. The zero-salinity dielectric constant, K_O, of this soil is obtained by correcting the apparent K as a function of the measured bulk electrical conductivity. The volumetric water content is estimated from K_o. The correction of K is a function of the equivalent frequency of the electromagnetic pulse. The imaginary part of the dielectric constant is primarily due to ohmic losses. The model, which calculates the velocity of propagation of the electromagnetic pulse and which takes into consideration the imaginary part, performs reasonably well. An empirical approach based on calibration gave slightly better results.     

Calibration of the time‐domain reflectometer and determination of the volumetric water content of the soil profile in an ultisol of Costa Rica

Abstract

An experiment was conducted to determine if time‐domain reflectometry (TDR) could be used to measure the water content at different depths in the O‐to‐75 cm soil layer. Probes of three wires (1/8 inch diameter and 30 cm exposed length) were installed in field plots differing in current crop‐fertilization history. Measurements of volumetric water content using bulk density and gravimetric water content were made to calibrate the TDR method. Comparison of water contents determined by TDR with those from gravimetric samples showed that there is a linear relationship (small offset but same slope) of water content with depth, indicating that there is little difference in volumetric water content from the 0 to 75 depth. However, the TDR method gives consistently lower water content values as compared with values obtained by gravimetric determination. Continuous measurements of profile soil water content with TDR in wet and dry periods during the year indicated that the mayor differences in volumetric water content correspond to the first 30 cm depth.     

土壤电导率对时域反射仪测定土壤水分的影响

试验通过往土壤中加入电介质溶液 ,以及在不同粘粒含量土壤上用时域反射仪 (TDR)测定土壤含水量 ,研究结果表明 :在较低含水量情况下 (砂土 <0 1 5cm3cm- 3,砂质壤土 <0 .1 8cm3cm- 3) ,电导率的增加不易引起TDR测定值的明显偏差 ;但在较高含水量下 ,当溶液电导率增加到 8dSm- 1 (砂质壤土 )和 1 1dSm- 1 (砂土 )时 ,TDR测得的含水量值明显高于实际值。在较高电导率 ( <1 6dSm- 1 )下 ,K0 .5a 与实际含水量仍呈较好的线性关系 ,但电导率引起的介电损失影响了K0 .5a ～θ线性关系的斜率和截距。本文给出了考虑电导率影响的K0 .5a ～θ线性关系的校正方程。土壤粘粒含量的增加也会引起TDR测定偏差 ,在低含水量时测定值偏低 ,在高含水量时测定值偏高。粘粒含量 <5 0 %时 ,测定偏差 <0 .0 2cm3cm- 3。     

利用热脉冲-时域反射技术测定土壤水热动态和物理参数 Ⅰ.原理

由于土壤特性的时空变异性 ,对土壤含水量、温度、热特性以及其它物理参数的动态监测是土壤学研究的重要课题。本文以热脉冲技术和时域反射技术的理论为基础 ,介绍了利用热脉冲技术 时域反射技术 (Thermo TDR)连续定位测定土壤含水量、电导率、温度和热特性的原理 ,并利用土壤热特性与容重和含水量的关系 ,导出了土壤容重、饱和度和通气孔度的计算公式。     

A profiling TDR probe for water content and electrical conductivity measurements of soils

Measurements of water content profiles are of great interest in hydrology and soil science. Time domain reflectometry (TDR) is a well‐established method for water content measurements; however, most TDR probe designs are suitable for measurements in only a small soil volume. In this article, a 1‐m long TDR profiling probe with five measurement sections is described. Unlike most other previous profiling probes, our probe allows for both dielectric permittivity (ε) and electrical conductivity (σ_a) measurements. The accuracy of the ε and σ_a measurements was excellent; the precision of the measurements was, however, significantly poorer than with a 0.20‐m long standard three rod TDR probe. The new probe was installed in a field and successfully measured water content profiles during the growing season of 2009. During an infiltration experiment it was shown that because of its geometry, the profiling probe over‐estimated the wetting‐front velocity. At a 0.10‐m depth, the over‐estimation was almost 30%. The over‐estimate will be less significant at greater depths.     

滴灌均匀系数对土壤水分和氮素分布的影响

为了确定滴灌均匀系数的设计与评价标准,在日光温室内研究了滴灌施肥灌溉均匀性和施氮量对土壤水氮分布特性的影响。试验中滴灌均匀系数（Cu）设置0.62、0.80和0.96 3个水平,施氮量设置150和300 kg/hm2 2个水平。土壤含水率和电导率采用沿毛管均匀布置的TDR探头（Hydra Probe）连续监测,并定期取土样测试土壤硝态氮和铵态氮含量。结果表明,在作物生育期内3种滴灌均匀系数处理的土壤含水率一直保持很高的均匀系数,滴灌均匀系数和施氮量对土壤含水率均值及其均匀系数的影响均不显著（α=0.05）。土壤电导率及硝态氮含量的均匀性在很大程度上取决于土壤初始氮素含量的均匀性,其均匀系数低于土壤含水率的均匀系数,滴灌均匀系数的影响也不显著。从获得均匀的土壤水氮分布的角度出发,现行滴灌均匀系数标准尚有降低的空间。     

Characterization of field‐scale dryland salinity with depth by quasi‐3d inversion of DUALEM‐1 data

To understand the limitations of saline soil and determine best management practices, simple methods need to be developed to determine the salinity distribution in a soil profile and map this variation across the landscape. Using a field study in southwestern Australia, we describe a method to map this distribution in three dimensions using a DUALEM‐1 instrument and the EM4Soil inversion software. We identified suitable parameters to invert the apparent electrical conductivity (EC_a – mS/m) data acquired with a DUALEM‐1, by comparing the estimates of true electrical conductivity (σ – mS/m) derived from electromagnetic conductivity images (EMCI) to values of soil electrical conductivity of a soil‐paste extract (EC_e) which exhibited large ranges at 0–0.25 (32.4 dS/m), 0.25–0.50 (18.6 dS/m) and 0.50–0.75 m (17.6 dS/m). We developed EMCI using EM4Soil and the quasi‐3d (q‐3d), cumulative function (CF) forward modelling and S2 inversion algorithm with a damping factor (λ) of 0.07. Using a cross‐validation approach, where we removed one in 15 of the calibration locations and predicted EC_e, the prediction was shown to have high accuracy (RMSE = 2.24 dS/m), small bias (ME = ?0.03 dS/m) and large Lin's concordance (0.94). The results were similar to those from linear regression models between EC_a and EC_e for each depth of interest but were slightly less accurate (2.26 dS/m). We conclude that the q‐3d inversion was more efficient and allowed for estimates of EC_e to be made at any depth. The method can be applied elsewhere to map soil salinity in three dimensions.     

Temperature effects on N mineralization: changes in soil solution composition and determination of temperature coefficients by TDR

We studied the changes in composition of the soil solution following mineralization of N at different temperatures, with a view to using TDR to calculate temperature coefficients for the mineralization of N. Mineralization from soil organic nitrogen was measured during aerobic incubation under controlled conditions at six temperatures ranging from 5.5 to 30°C, and at constant water content in a loamy sand soil. We also monitored during the incubation the concentrations of SO₄^2–, Cl^–, HCO₃^–, Ca²⁺, K⁺, Mg²⁺ and Na⁺, and the pH and the electrical conductivity in 1:2 soil:water extracts. Zero‐order N mineralization rates ranged between 0.164 at 5.5°C and 0.865 mg N kg^?1 soil day^?1 at 30°C. There was a significant decrease in soil pH during incubation, of up to 0.6 pH units at the end of the incubation at 30°C. The electrical conductivity of the soil extracts increased significantly at all temperatures (the increase between the start and the end of the incubation was 4‐fold at 30°C) and was strongly correlated with N mineralization. The ratio of bivalent to monovalent cations increased markedly during mineralization (from 2.2 to 5.9 at 30°C), and this increase influenced the evolution of the electrical conductivity of the soil solution through the differences in molar‐limiting ion conductivity between mainly Ca²⁺ and K⁺. Zero‐order mineralization rate constants, k, for NO₃^– concentrations calculated from TDR varied between 0.070 (at 5.5°C) and 0.734 mg N kg^?1 soil day^?1 (at 30°C), which were slightly smaller, but in the same range, as the measured rates. Underestimation of the measured N mineralization rates was due, at least in part, to differences in cation composition of the soil solution between calibration and mineralization experiments. A temperature‐dependence model for N mineralization from soil organic matter was fitted to both the measured and the TDR‐calculated mineralization rates, k and k_TDR, respectively. There were no significant differences between the model parameters from the two. Our results are promising for further use of TDR to monitor soil organic N mineralization. However, the influence of changing cation ratios will also have to be taken into account when trying to predict N mineralization from measured electrical conductivities.     

于田绿洲盐渍土水、盐、温度季节变化规律与相关性研究

以于田绿洲为研究区,借助ENVI 5.1、ArcMap 10.2、Origin 8.5、SPSS 20.0,同时结合野外实测数据,对盐渍土不同土层(0~20、20~40、40~60、60~80、80~100 cm)的土壤含水量、温度、电导率的变化规律及相关性进行了研究。结果表明:研究区土壤含水量、温度、电导率从6月到8月呈升高趋势,绿洲南部和北部地区的5、8号点在60~80、80~100 cm土层的土壤含水量最高,8、22号点表层(0~20 cm)土壤电导率最高,而南部和西部地区的5、22号点在40~60 cm土层的土壤电导率最高;秋季和夏季的土壤含水量、温度、电导率均高于冬季和春季。研究区西部的16、22号点各土层的含水量与电导率呈显著正相关,在60~80 cm土层的土壤含水量与电导率的相关性最强,相关系数分别为0.970**、0.987**。     

采用新电导率指标分析土壤盐分变化规律

土壤电导率(Electrical conductivity,EC)是限制植物和微生物活性的阈值,影响到土壤养分和污染物的转化、存在状态及有效性[1],反映了在一定水分条件下土壤盐分的实际状况,且包含了土壤水分含量及离子组成等丰富信息[2]。在一定浓度范围内,土壤溶液含盐量与电导率呈正相关,溶解的盐类越多,溶液电导率就越大,故可根据溶液电导率的大小,间接地测量土壤含盐量[3-5]。     

Monitoring of root‐zone water content in the laboratory by 2D geoelectrical tomography

Root water uptake is one of the essential processes within the soil–plant–atmosphere continuum. We present a method for monitoring soil‐water redistributions due to water uptake by roots. Our aim is to image and monitor diurnal soil‐water redistribution during a small‐scale (centimeter‐to‐decimeter range) indoor experiment and to correlate water content determined by applied geoelectrical time‐lapse imaging techniques with values from single‐point time domain reflectometry (TDR) measurements. This includes establishing pedophysical relationships within the root zone and deriving the water‐content distribution from the electrical‐resistivity model. Using DC geoelectrics of high resolution (970 data points for 220 cm²), we monitored significant spatial heterogeneity of soil moisture with time, whereas no irrigation was applied. Thus, we imaged the high heterogeneity of fluid movements within the soil. We found diurnal variations with high spatial variability of soil water content during the morning and afternoon hours. The water content continuously increased from dawn to noon, whereas the increase started in the near‐surface zone from 1 cm to 3 cm above the main root zone. Between 8:00 a.m. and 10:00 a.m., water content decreases along most of the sections. Water content irregularly decreases and increases during the afternoon. During night time, we observed nearly no changes in soil water content due to the absence of transpiration and subsequently soil‐water redistribution. Most of these diurnal variations in soil water content lie within the intensive root zone, as measurements showed on soil samples excavated from these areas after the experiment. Furthermore, we quantified water content derived from geoelectrical tomography of the monitored area before and after an irrigation event using a geophysical pedotransfer function of Archie, established specifically for the used lupine and the applied physico‐chemical boundary conditions of the experiment. The resulting average water content from 2D geoelectrical tomography agreed well with the values determined by the TDR measurements.     

In situ determination of electrical conductivity of potting media using time domain reflectometry

Abstract

The possibility of measuring both the volumetric water content (_{ν θ}) and bulk electrical conductivity (EC_b) of media using a single instrument makes time domain reflectometry (TDR) invaluable for greenhouse potting media _ν and EC_b determination. Laboratory experiments in three different potting media instrumented with triple‐wire TDR probes were performed to calibrate the TDR system for the determination of potting media water electrical conductivity (EC_w). The performance of the TDR for in situ determination of EC_w, using the experimentally‐determined conductivity model, was investigated using packed columns of potting media. Linear relationships between the EC_b‐EC_w data were found for all the tested media at the three water contents (0.30, 0.36, 0.45 cm³cm^‐3) for four solute concentrations ranging from 1.481 to 3.797 dS m^‐1. Linear regression coefficient of determination, r², of between 0.97 and 0.99 were achieved. Calibration accuracies ranged from 94% to 98% for EC_wpredictions. Results indicate that TDR is a useful technique for the accurate determination of potting media Ec_b. TDR allows determination of EC_w, from the measured EC_b and θ_ν, to be made quickly and simultaneously using a single and relatively inexpensive probe combined with the TDR cable tester.     

Use of an electromagnetic technique to determine sodicity in saline-sodic soils

Soil sodicity is an increasing problem in arid‐land irrigated soils that decreases soil permeability and crop production and increases soil erosion. The first step towards the control of sodic soils is the accurate diagnosis of the severity and spatial extent of the problem. Rapid identification and large‐scale mapping of sodium‐affected land will help to improve sodicity management. We evaluated the effectiveness of electromagnetic induction (EM) measurements in identifying, characterizing and mapping the spatial variability of sodicity in five saline‐sodic agricultural fields in Navarre (Spain). Each field was sampled at three 30‐cm soil depth increments at 10–30 sites for a total of 267 soil samples. The number of Geonics‐EM38 measurements in each field varied between 161 and 558, for a total of 1258 ECa (apparent electrical conductivity) readings. Multiple linear regression models established for each field predicted the average profile ECe (electrical conductivity of the saturation extract) and SAR (sodium adsorption ratio of the saturation extract) from ECa. Despite the lack of a direct causal relationship between ECa and SAR, EM measurements can be satisfactorily used for characterizing the spatial distribution of soil sodicity if ECe and SAR are significantly auto‐correlated. These results provide ancillary support for using EM measurements to indirectly characterize the spatial distribution of saline‐sodic soils. More research is needed to elucidate the usefulness of EM measurements in identifying soil sodicity in a wider range of salt and/or sodium‐affected soils.     

Modelling soil salinity across a gilgai landscape by inversion of EM38 and EM31 data

The soil in arid and semi‐arid areas is often markedly saline, which can severely limit agricultural productivity. Increasingly, geophysical methods are being implemented to map the levels and areal extent of soil salinity. One of the most effective methods is electromagnetic (EM) induction with instruments designed to measure apparent soil electrical conductivity (EC_a). This study describes the generation of electromagnetic conductivity images (EMCIs) by inverting EC_a data obtained with the EM38 and EM31 devices along two closely‐spaced transects by the EM inversion approach in the EM4Soil package. The EM38 EC_a data are shown to be a more effective predictor of soil EC_e. Calibration equations based on calculated true electrical conductivity (σ) and measured electrical conductivity of a saturated soil‐paste extract (EC_e) provide reliable estimates of EC_a. The patterns of σ in a test of the method in soil developed over thick alluvium on a clay plain in central New South Wales, Australia, compare favourably with existing pedological mapping; the mounds and depressions of gilgai were strongly differentiated from the more sandy alluvial sediments that characterize prior stream channels. The overall approach is potentially useful for generating a single calibration equation that can be used to predict EC_e at various depths in the soil. Improvements in EMCI modelling can also be sought by joint inversion of EM with other geophysical datasets.     

Detecting a leachate plume in an aeolian sand landscape using a DUALEM‐421 induction probe to measure electrical conductivity followed by inversion modelling

Solid waste poses a serious health risk when it is disposed of inadequately because water‐based solutions derived from the decomposition of solid waste products (leachate) can enter groundwater systems via plumes. To assess the public health risk and potential ecological impacts, we require knowledge on the pedological and hydrogeological settings in which waste is disposed. This is particularly the case in coarse textured highly permeable soil. To rapidly collect data, geophysical methods such as direct current (dc) resistivity techniques have been used. Moreover, non‐contact electromagnetic (EM) induction instruments have also been employed. The aim of this research was to demonstrate how the inversion using a 1‐dimensional inversion algorithm with lateral constraints of the apparent electrical conductivity (σ_a) measured in the horizontal coplanar (HCP) and perpendicular co‐planar arrays (PRP) of a DUALEM‐421 EM induction probe can be used to develop a two‐dimensional model of the true electrical conductivity (σ) within a Quaternary aeolian sand in the Tuggerah Soil Landscape southeast of Sydney in Australia. Our results from 2D models of σ accord with estimates of bulk electrical conductivity (σ_b) of a leachate plume and uncontaminated groundwater, the stratigraphy of the Tuggerah soil landscape unit and the depth of sand used to landscape the decommissioned landfill. Further research is needed to determine the origin of the plume and a quasi‐3D modelling approach is applicable.     

基于磁感式探测的分层土壤盐分精确解译模型

为了精准解译面域尺度土壤盐分特征,有必要建立分层土壤盐分信息精确解译模型。该文应用通径分析方法,研究获得了土壤全盐量、土壤含水率、体积质量、黏粒质量分数、地下水电导率、地下水埋深等作用因子对土壤表观电导率值的方差贡献率及作用强弱排序。依据各作用因子的方差贡献率大小,结合设定的累积贡献率阀值,选取出磁感式土壤表观电导率的主导作用因子,确定为磁感式土壤盐分信息解译模型的参数体系。采用多因子及互作项逐步回归法,通过引入因子间的互作效应建立优化的基于磁感式探测的分层（0～20,＞20～60,＞60～100,＞100～160 cm）土壤盐分信息解译模型。验证结果表明,模型解译误差基本在10%以内,达到了较高精度水平。     

Mapping soil salinity in 3‐dimensions using an EM38 and EM4Soil inversion modelling at the reconnaissance scale in central Morocco

Large areas of Morocco require irrigation and although good quality water is available in dams, farmers augment river water with poorer quality ground water, resulting in salt build‐up without a sufficient leaching fraction. Implementation of management plans requires baseline reconnaissance maps of salinity. We developed a method to map the distribution of salinity profiles by establishing a linear regression (LR) between calculated true electrical conductivity (σ, mS/m) and electrical conductivity of the saturated soil‐paste extract (ECe, dS/m). Estimates of σ were obtained by inverting the apparent electrical conductivity (ECa, mS/m) collected from a 500‐m grid survey using an EM38. Spherical variograms were developed to interpolate ECa data onto a 100 m grid using residual maximum likelihood. Inversion was carried out on kriged ECa data using a quasi‐3d model (EM4Soil software), selecting the cumulative function (CF) forward modelling and S2 inversion algorithm with a damping factor of 3.0. Using a ‘leave‐one‐out cross‐validation' (LOOCV), of one in 12 of the calibration sites, the use of the q‐3d model yielded a high accuracy (RMSE = 0.42 dS/m), small bias (ME = ?0.02 dS/m) and Lin's concordance (0.91). Slightly worse results were obtained using individual LR established at each depth increment overall (i.e. RMSE = 0.45 dS/m; ME = 0.00 dS/m; Lin's = 0.89) with the raw EM38 ECa. Inversion required a single LR (ECe = 0.679 + 0.041 × σ), enabling efficiencies in estimating ECe at any depth across the irrigation district. Final maps of ECe, along with information on water used for irrigation (ECw) and the characterization of properties of the two main soil types, enabled better understanding of causes of secondary soil salinity. The approach can be applied to problematic saline areas with saline water tables.     

A transfer-function method for analysing breakthrough data in the time domain of the transport process

A transfer‐function method is proposed to determine transport parameters from solute breakthrough data. The method is based on the assumptions that a linear process governs the transport of solute through soil and that the soil is homogeneous. It needs breakthrough data at two different vertical locations from a pulse input of solute to the soil. The method predicts the response by convoluting the input with the transfer function in the time domain. Solute breakthrough data were measured in unsaturated soil columns by time‐domain reflectometry (TDR). An experimental soil column was placed over a supporting column filled with sandy soil. A constant hanging water table, maintained in the lower column, created suction in the upper column and maintained unsaturated conditions. A solution of calcium chloride (CaCl₂) was spread over the soil in the upper column during steady flow of water in the column. Resident concentrations of solute in terms of electrical conductivity were measured at two depths by TDR sensors. We analysed breakthrough curves of CaCl₂ in 81 experiments to determine the transport parameters in coarse sand, sandy loam soil and clay loam soil by the transfer‐function method. The transport parameters obtained were compared with those determined by the widely used deterministic equilibrium model of the CXTFIT program. The transfer‐function method provided a better fit between the measured and estimated breakthrough curves in almost all cases and resulted in stable values of the parameters. The method is robust against small errors in measurements. It is a mathematically sound and efficient method for analysing breakthrough data.