Dani Or

A Review of Advances in Dielectric and Electrical Conductivity Measurement in Soils Using Time Domain Reflectometry

constant) of a material emerged as an elegant method of estimating water content in porous materials. For the Substantial advances in the measurement of water content and first time the same physical property (permittivity) could bulk soil electrical conductivity (EC) using time domain reflectometry be measured for a range of scales and used to estimate (TDR) have been made in the last two decades. The key to TDR’s success is its ability to accurately measure the permittivity of a material water content. Electromagnetic methods, whether TDR and the fact that there is a good relationship between the permittivity (localized measurement), ground penetrating radar of a material and its water content. A further advantage is the ability (two-dimensional profile), or active microwave remote to estimate water content and measure bulk soil EC simultaneously sensing (land surface), all estimate water content based using TDR. The aim of this review is to summarize and examine on the permittivity of the target medium. A further advances that have been made in terms of measuring permittivity and advance was the development of analysis methods using bulk EC. The review examines issues such as the effective frequency TDR. Time domain reflectometry was adapted to estiof the TDR measurement and waveform analysis in dispersive dielecmate both soil water content (Hoekstra and Delaney, trics. The growing importance of both waveform simulation and in1974; Topp et al., 1980) and soil bulk EC simultaneously verse analysis of waveforms is highlighted. Such methods hold great (Dalton et al., 1984). In spite of decades of research, potential for obtaining far more information from TDR waveform analysis. Probe design is considered in some detail and practical guidwe are only beginning to efficiently utilize electrical ance is given for probe construction. The importance of TDR measuretechnology that ranges from satellite and airborne radar ment sampling volume is considered and the relative energy storage to ground penetrating radar and localized sensors such density is modeled for a range of probe designs. Tables are provided as TDR and impedance probes. that compare some of the different aspects of commercial TDR equipThe underlying success of these techniques can be ment, and the units are discussed in terms of their performance and considered in two parts, the first of which is the equiptheir advantages and disadvantages. It is hoped that the review will ment’s ability to accurately measure the bulk dielectric provide an informative guide to the more technical aspects of permitpermittivity and EC of a material. The second is the close tivity and EC measurement using TDR for the novice and expert alike. relationship between the measured permittivity and the volumetric water content, or the ionic concentration and the bulk EC of the material. This review concentrates W is required in some way by all living things; on the first stage, the accurate measurement of bulk perit is a fundamental constituent of life on our mittivity and EC, and we confine ourselves to the use planet. Our survival as well as that of other organisms of TDR but acknowledge that other devices such as depends on a supply of water both to our own bodies impedance probes (Dean et al., 1987; Hilhorst et al., and to the flora and fauna on which we live. One of the 1993; Gaskin and Miller, 1996; Paltineanu and Starr, best ways to regulate water consumption is to know 1997) may also be used for this purpose. Time domain the quantity available and to manage the resource with reflectometry has become a large topic in soil physics, prudence and stewardship (Hillel, 1991). To achieve this primarily because of its adaptability and the continued aim, techniques are preferred that can be used to meadevelopment of novel applications. The focus of this sure a physical quantity closely related to the amount review is on the measurement of bulk permittivity and of water contained in a porous material, be it rock, soil, EC, and thus some topics are dealt with only briefly or or an artificial medium. omitted. One of the strengths of the TDR measurement The revolution in electronics in the latter half of the method is that many probes can be monitored almost last century made the measurement of the electrical simultaneously using a multiplexer (Baker and Allproperties of materials more accessible than ever before. maras, 1990; Heimovaara and Bouten, 1990; Herkelrath Measurement of the dielectric permittivity (dielectric et al., 1991). This review discusses the measurement of bulk EC; however, we don’t go any further to examine D.A. Robinson, U.S. Salinity Laboratory, USDA-ARS, 450 W. Big the interpretation of this in terms of soil solution conSprings Road, Riverside, CA 92507; S.B. Jones, Dep. Plants, Soils ductivity. The literature on this aspect of TDR applicaand Biometeorology, Utah State University, Logan, UT 84322-4820; tion is large, and the reader is referred to a recent publiJ.M. Wraith, Land Resources & Environmental Sciences Dep., Moncation for further reference (Dane and Topp, 2002). A tana State University, Bozeman, MT 59717-3120; D. Or, Dep. of Civil and Environmental Engineering, University of Connecticut, 261 further topic omitted from this review is the use of Glenbrook Road, Unit 2037, Storrs, CT 06269; S.P. Friedman, Institute coated TDR probes. Coated probes have been proposed of Soil, Water and Environmental Sciences, The Volcani Center as a way to extend the working range of TDR in saline (ARO), Bet Dagan 50250, Israel. Received 21 Nov. 2002. Special soils (Kelly et al., 1995; Nichol et al., 2002). However, Section—Advances in Measurement and Monitoring Methods. *Corresponding author (darobinson001@yahoo.co.uk). the studies of Ferre et al. (1996) and Knight et al. (1997) Published in Vadose Zone Journal 2:444–475 (2003).  Soil Science Society of America Abbreviations: EC, electrical conductivity; TDR, time domain reflectometry. 677 S. Segoe Rd., Madison, WI 53711 USA 444 Published November, 2003

Adsorption and capillary condensation in porous media: Liquid retention and interfacial configurations in angular pores

Conventional models of liquid distribution, flow, and solute transport in partially saturated porous media are limited by the representation of media pore space as a bundle of cylindrical capillaries (BCC). Moreover, the capillary model ignores the dominant contribution of adsorptive surface forces and liquid films at low potentials. We propose two new complementary elements for improving our understanding of liquid configuration in porous media: (1) an approach for considering the individual contributions of adsorptive and capillary forces to the matric potential and (2) a more realistic model for pore space geometry. Modern interface science formalism is applied to determine the thickness of adsorbed liquid films as a function of thermodynamic conditions and specific surface area of the medium. The augmented Young-Laplace (AYL) equation provided the necessary framework for combining adsorptive and capillary processes. A new pore space geometry composed of an angular pore cross section (for capillary processes) connected to slit-shaped spaces with internal surface area (for adsorption processes) offers a more realistic representation of natural porous media with explicit consideration of surface area (absent in the standard BCC model). Liquid-vapor configuration, saturation, and liquid-vapor interfacial area were calculated for different potentials and pore (unit cell) dimensions. Pore dimensions may be easily related to measurable soil properties such as specific surface area and porosity. Rigorous calculations based on the AYL equation were simplified and led to the development of algebraic expressions relating saturation and interfacial area of liquid in the proposed pore space geometry to chemical potential. These simple expressions are amenable to upscaling procedures similar to those presently used with the BCC model.

Liquid Retention and Interfacial Area in Variably Saturated Porous Media: Upscaling from Single Pore to Sample Scale Model

A new model for liquid configuration in angular pore space considering both capillary and adsorptive contributions was proposed as an alternative to the conventional bundle of capillaries representation. In this study we develop a statistical framework for upscaling pore-scale processes to represent a sample-scale response of variably saturated porous medium. The representation of pore size distribution by the gamma distribution enables derivation of closed-form expressions for sample-scale liquid retention and liquid-vapor interfacial area. The statistical framework calculates the expected values of liquid configuration as a function of pore geometry and chemical potential considerations. Media properties are used to estimate upscaling parameters by matching model predictions with measured retention data subject to specific surface area constraint. Additionally, a method for estimating liquid-solid adsorption behavior for the medium is proposed. Model predictions compare favorably with measured retention data, yielding a similar close fit as obtained with the van Genuchten parametric model. Liquid-vapor interfacial area as a function of chemical potential is readily calculated using the estimated retention parameters. Model calculations of liquid-vapor interfacial area for sand show reasonable agreement with measurements obtained with surface-active tracers. The contribution of liquid films dominates the total liquid-vapor interfacial area and often surpasses the capillary contribution (curved menisci) by several orders of magnitude. This illustrates potential limitations in using cylindrical pore network modeling of interfacial area for multiphase flow predictions. The detailed picture of liquid vapor interfaces provides a sound basis for unsaturated hydraulic conductivity calculations in the sample cross section (i.e., neglecting network effects) and offers insights into microbial habitats and related exchange processes in partially saturated porous media.

Temperature effects on soil bulk dielectric permittivity measured by time domain reflectometry: A physical model

Near-surface measurements of soil water content (θ) using time domain reflectometry (TDR) may exhibit anomalous behavior in the presence of diurnal temperature (T) fluctuations. Experimental results obtained in a companion paper led to the hypothesis that the observed bulk dielectric permittivity (ϵb) is determined by an interplay between two competing phenomena: (1) the reduction in the dielectric permittivity of bulk water with increased T; and (2) the increase in TDR-measured ϵb with increased T due to release of bound water. In this study we develop a physically based model for the temperature dependency of TDR-measured soil bulk dielectric permittivity and propose practical correction factors. The model considers the modified properties of water near solid surfaces to define a layer of rotationally hindered water (within the TDR frequency bandwidth) having a temperature dependent thickness. Changes in measured ϵb(T) are thus attributed to variations in the thickness of the rotationally hindered layer which has a lower dielectric permittivity than free water and hence is less “visible” to travel-time-based TDR waveform analyses. The model is sensitive to the soil specific surface area and the water content, both of which determine the ratio of bound to bulk soil water. Comparisons with experimental data covering a wide range of soils, water contents, and temperatures showed good agreement. Further studies are needed to evaluate some of the models critical parameters such as the cutoff frequency below which water is considered bound. A temperature correction approximation is based on analytical expressions for TDR-measured bulk dielectric permitivity and requires estimates of soil specific surface area and bulk density, which may be estimated from soil texture. The thermodielectric sensitivity of TDR-measured bulk dielectric permittivity and water content may serve as a basis for estimating soil specific surface area.

Temperature effects on soil bulk dielectric permittivity measured by time domain reflectometry: Experimental evidence and hypothesis development

Reports on temperature (T) effects on time domain reflectometry (TDR) measurements of soil water content (θ) are contradictory and often exhibit conflicting trends. We imposed step T changes on sealed columns of four soils having variable θ, while monitoring bulk apparent dielectric constant (or permittivity ϵb) and bulk electrical conductivity (σb) using TDR. Measured ϵb increased substantially with increasing temperature for one silt loam soil, for all θ. For another silt loam soil and for an Oxisol, measured ϵb increased with increasing T at relatively low θ but decreased with increasingT at higher θ. For a sandy loam soil, measured ϵb decreased with increasing T for all θ. The experimental results led to the hypothesis that TDR-measured ϵb is determined by an interplay between two competing phenomena: (1) the reduction in the dielectric constant of bulk water with increased T; and (2) the increase in TDR-measured ϵb with increased T due to release of bound water. TDRmeasured ϵb is thus dependent on solid surface area and wetness. Our results have implications for routine use of TDR in fine-textured and organic soils and potentially for microwave remote sensing of soil water status.

Hydraulic conductivity of variably saturated porous media: Film and corner flow in angular pore space

Many models for hydraulic conductivity of partially saturated porous media rely on oversimplified representation of the pore space as a bundle of cylindrical capillaries and disregard flow in liquid films. Recent progress in modeling liquid behavior in angular pores of partially saturated porous media offers an alternative framework. We assume that equilibrium liquid-vapor interfaces provide well-defined and stable boundaries for slow laminar film and corner flow regimes in pore space comprised of angular pores connected to slit-shaped spaces. Knowledge of liquid configuration in the assumed geometry facilitates calculation of average liquid velocities in films and corners and enables derivation of pore-scale hydraulic conductivity as a function of matric potential. The pore-scale model is statistically upscaled to represent hydraulic conductivity for a sample of porous medium. Model parameters for the analytical sample-scale expressions are estimated from measured liquid retention data and other measurable medium properties. Model calculations illustrate the important role of film flow, whose contribution dominates capillary flow (in full pores and corners) at relatively high matric potentials (approximately −100 to −300 J kg−1, or −1 to 3 bars). The crossover region between film and capillary flow is marked by a significant change in the slope of the hydraulic conductivity function as often observed in measurements. Model predictions are compared with the widely applied van Genuchten–Mualem model and yield reasonable agreement with measured retention and hydraulic conductivity data over a wide range of soil textural classes.

Root zone solute dynamics under drip irrigation: A review

Infiltration and subsequent distribution of water and solutes under cropped conditions is strongly dependent on the irrigation method, soil type, crop root distribution, and uptake patterns and rates of water and solutes. This review discusses aspects of soil water and solute dynamics as affected by the irrigation and fertigation methods, in the presence of active plant uptake of water and solutes. Fertigation with poor quality water can lead to accumulation of salts in the root zone to toxic levels, potentially causing deterioration of soil hydraulic and physical properties. The high frequency of application under drip irrigation enables maintenance of salts at tolerable levels within the rooting zone. Plant roots play a major role in soil water and solute dynamics by modifying the water and solute uptake patterns in the rooting zone. Modeling of root uptake of water and solutes is commonly based on incorporating spatial root distribution and root length or density. Other models attempt to construct root architecture. Corn uptake rate and pattern of nitrate nitrogen was determined from field studies of nitrate dynamics under drip irrigation using TDR monitoring. The determined nitrate nitrogen uptake rates are within literature values for corn.

Drying front and water content dynamics during evaporation from sand delineated by neutron radiography

Evaporative drying of porous media is jointly controlled by external ( atmospheric) conditions and by media internal transport properties. Effects of different atmospheric potential evaporative demand on observed drying rates were studied in a series of laboratory experiments using sand-filled Hele-Shaw cells. We examined two potential evaporation rates of about 8 and 40 mm per day. The evolution and geometry of the drying front (marking the interface between saturated and partially dry regions) and water content distribution above the drying front were measured every 5 min at 0.1 mm spatial resolution using neutron radiography. Water loss rates decreased with time for both rates, but the decrease was more pronounced for high evaporative demand. External evaporative demand had no effect on drying front geometry or spatial water content distribution for depths below 2 mm. Cycles of roughening and smoothing of drying fronts due to interfacial pinning and unpinning were observed. The water content above the front showed irregular patterns due to formation of isolated liquid clusters with the general profile showing a decrease in mean water content with deepening drying front. Measured water content profiles support the hypothesis that liquid flow supply surface evaporation during stage 1 and water content distribution were not affected by external drying rates. Additionally, observed saturation profiles indicate that the corresponding hydraulic conductivity supports fluxes larger than the highest drying rate measured for sand, suggesting that decreasing drying rate was limited by vapor exchange between progressively drying surface and the viscous boundary layer above.

Flow in unsaturated fractured porous media: Hydraulic conductivity of rough surfaces

The general trend in models for flow in unsaturated fractured porous media is to regard desaturated fractures as nonparticipating elements that impede flow. Mounting experimental and theoretical evidence shows that fractures retain and conduct liquid in the form of film and partially filled corner flow to a relatively low degree of saturation. A simple geometrical model for rough fracture surfaces is developed offering a tractable geometry for calculations of surface liquid storage due to adsorbed films and capillary menisci. Assuming that under slow laminar flow the equilibrium liquid configurations on the fracture surface are not modified significantly, the average hydraulic conductivities for film and corner flows were derived and used as building blocks for a representative fracture roughness element and an assemblage of statistically distributed surface roughness elements. Calculations for a single representative element yielded excellent agreement with surface storage and unsaturated hydraulic conductivity measurements of Tokunaga and Wan [1997]. A statistical representation of surface roughness using a gamma distribution of pit depths resulted in closed-form expressions for unsaturated hydraulic conductivity averaged across the fracture length (transverse to flow) or weighted by the liquid cross section occupying the fracture surface. An important attribute of the surface roughness model is the direct link between fracture surface and matrix processes unified by the matric potential. The proposed model represents a first step toward development of a comprehensive approach for liquid retention and hydraulic conductivity of unsaturated fractured porous media based on details of liquid configuration for different matric potentials.

Root distribution and water uptake patterns of corn under surface and subsurface drip irrigation

Information on root distribution and uptake patterns is useful to better understand crop responses to irrigation and fertigation, especially with the limited wetted soil volumes which develop under drip irrigation. Plant water uptake patterns play an important role in the success of drip irrigation system design and management. Here the root systems of corn were characterized by their length density (RLD) and root water uptake (RWU). Comparisons were made between the spatial patterns of corn RWU and RLD under surface and subsurface drip irrigation in a silt loam soil, considering a drip line on a crop row and between crop rows. Water uptake distribution was measured with an array of TDR probes at high spatial and temporal resolution. Root length density was measured by sampling soil cores on a grid centered on crop row. Roots were separated and an estimation of root geometrical attributes was made using two different image analysis programs. Comparisons of these programs yielded nearly identical estimates of RLD. The spatial patterns of RWU and RLD distributions, respectively normalized to the total uptake and root length, were generally similar only for drip line on a crop row, but with some local variations between the two measures. Both RLD and RWU were adequately fitted with parametric models based on semi-lognormal and normal Gaussian bivariate density functions (Coelho and Or, 1996; Soil Sci. Soc. Am. J. 60, 1039–1049).