Reproduced from Soil Science Society of America Journal. Published by Soil Science Society of America. All copyrights reserved. Frequency Dependence of the Complex Permittivity and Its Impact on Dielectric Sensor Calibration in Soils T. J. Kelleners,* D. A. Robinson, P. J. Shouse, J. E. Ayars, and T. H. Skaggs ABSTRACT tiveness of TDR. However, the emergence of low-cost, high-frequency oscillators has led to an increased inter- The capacitance (CAP) method and time domain reflectometry est in CAP techniques (e.g., Dean et al., 1987; Evett (TDR) are two popular electromagnetic techniques used to estimate soil water content. However, the frequency dependence of the real and Steiner, 1995; Paltineanu and Starr, 1997). Present- and imaginary part of the permittivity complicates sensor calibration. day CAP sensors are relatively inexpensive and easy to The frequency dependence can be particularly significant in fine- operate, and are becoming a popular choice for routine textured soils containing clay minerals. In this work, we applied both monitoring purposes. the CAP method and TDR to a nondispersive medium (fine sand) Both TDR and CAP techniques measure soil water and a strongly dispersive medium (bentonite). The measurements content indirectly. Both techniques actually respond to were conducted for a range of water contents. Results using a network the permittivity of the soil. The relationship between analyzer showed that the frequency dependence of the real permittiv- the permittivity of the soil and the instrument output ity of the bentonite was particularly strong below 500 MHz. Above (travel time for TDR; resonant frequency for most CAP this frequency, the real permittivity of the bentonite was mainly a techniques) can be described with electric circuit theory. function of the water content. The TDR predicted apparent permittiv- ity in the bentonite was below the CAP predicted real permittivity Examples of circuit theory applications can be found in at low water contents. This was attributed to the dispersive nature of Topp et al. (1980), Heimovaara (1994), and Lin (2003) the bentonite combined with the high frequency of operation of TDR for TDR and in Dean (1994), Robinson et al. (1998), (up to 3 GHz in dry soil). The CAP sensor (frequency of 100–150 and Kelleners et al. (2004a) for CAP techniques. The MHz) overestimated the real permittivity of the bentonite at high relationship between permittivity and soil water content, water contents. An electric circuit model proved partially successful on the other hand, can be described separately using in correcting the CAP data by taking the dielectric losses into account. physical dielectric mixing models (e.g., Birchak et al., The TDR signal became attenuated at higher water contents. It seems 1974; Dobson et al., 1985; Friedman, 1998) or empirical worthwhile to raise the effective frequency of dielectric sensors above models (e.g., Topp et al., 1980; Malicki et al., 1996). 500 MHz to benefit from the relatively stable permittivity region at The interpretation of electromagnetic measurements this frequency. is relatively straightforward if the soil is nonconductive and if all water molecules in the soil rotate freely as a function of the applied electromagnetic field. This is W ater content impacts crop growth directly, and the case in sandy soils wetted with deionized water for also influences the fate of agricultural chemicals frequencies below 17 GHz (the relaxation frequency applied to soils. Estimation of soil water content, there- of free water). The interpretation of electromagnetic fore, is important in agriculture (Dane and Topp, 2002, measurements in saline soils and in fine-textured soils p. 417–1074). In the field, basically three methods are is more complicated. Ionic conductivity and clay-water- available: gravimetric techniques, nuclear techniques (e.g., ion interactions may affect the permittivity reading. The neutron scattering), and electromagnetic techniques. Of significance of these processes is generally a function these, electromagnetic techniques have become popular of the measurement frequency. Hence, permittivity may because they facilitate a rapid, safe, nondestructive, and be both a function of water content and of frequency. easily automated estimation of soil water content. Different frequencies propagate through a medium at Among the electromagnetic techniques, TDR is different velocities if the permittivity of the medium widely used in research (e.g., Topp et al., 1980; Heimo- changes with frequency. Such a medium is called a dis- vaara, 1994; Robinson et al., 2003). The ability to mea- persive dielectric medium (Von Hippel, 1954a; Kraus, sure both water content and bulk electrical conductivity 1984). (EC) in the same soil volume contributes to the attrac- In this work we will investigate the effect of the fre- quency dependence of permittivity on the estimation of T.J. Kelleners and D.A. Robinson, Dep. of Plants, Soils, and Bio- soil water content with TDR and the CAP technique. meteorology, Utah State Univ., Logan, UT 84322; P.J. Shouse and T.H. The effect of ionic conductivity will be discussed as well. Skaggs, USDA-ARS, George E. Brown, Jr. Salinity Lab., 450 W. Big Experimental data are collected in the laboratory for a Springs Road, Riverside, CA 92507; J.E. Ayars, USDA-ARS, Water nondispersive medium (fine sand) and a strongly disper- Management Research Lab., 9611 S. Riverbend Ave., Parlier, CA 93648. This research was conducted at the George E. Brown, Jr. sive medium (bentonite). The frequency-dependence of Salinity Laboratory, USDA-ARS, Riverside, CA. The mention of the permittivity of most natural soils will be somewhere trade or manufacturer names is made for information only and does between these two extremes. The results therefore serve not imply an endorsement, recommendation, or exclusion by the USDA- as bounds for most routine measurement work. The ARS. Received 6 May 2004. *Corresponding author (tkelleners@ cc.usu.edu). specific objectives of this study are (i) to quantify the Published in Soil Sci. Soc. Am. J. 69:67–76 (2005).  Soil Science Society of America Abbreviations: CAP, capacitance; EC, electrical conductivity; SF, scaled frequency; TDR, time domain reflectometry. 677 S. Segoe Rd., Madison, WI 53711 USA 67