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where c is the propagation velocity of an electromagnetic wave in free space (2.997 x 108 m s-1), t is the travel time (s), lp is the real length of the soil probe (m), la is the apparent length (m) as measured by a cable tester, and vp is the relative velocity setting of the instrument. The relationship between 8 and e is approximately linear and is influenced by soil type, pb, clay content, and OM (Jacobsen and Schj0nning, 1993).

By measuring the resistive load impedance across the probe (ZL), ECa can be calculated with Equation (2.14) from Giese and Tiemann (1975):

where e0 is the permittivity of free space (8.854 x 10-12 F m-1), Z0 is the probe impedance (A), and ZL = Zu [2V0/Vf - 1]-1, where Zu is the characteristic impedance of the cable tester, V0 is the voltage of the pulse generator or zero-reference voltage, and V f is the final reflected voltage at a very long time. To reference ECa to 25°C, Equation (2.15) is used:

where Kc is the TDR probe cell constant (Kc [m-1] = e0cZ0/l), which is determined empirically.

The advantages of TDR for measuring ECa include (1) a relatively noninvasive nature, (2) an ability to measure both 8 and ECa, (3) an ability to detect small changes in ECa under representative soil conditions, (4) the capability of obtaining continuous unattended measurements, and (5) a lack of a calibration requirement for 8 measurements in many cases (Wraith, 2002). However, because TDR is a stationary instrument with which measurements are taken from point-to-point, thereby preventing it from mapping at the spatial resolution of ER and EM approaches, it is currently impractical for developing detailed geo-referenced ECa maps for large areas.

Although TDR has been demonstrated to compare closely with other accepted methods of ECa measurement (Heimovaara et al., 1995; Mallants et al., 1996; Reece, 1998; Spaans and Baker, 1993), it is still not sufficiently simple, robust, and fast enough for the general needs of field-scale soil salinity assessment (Rhoades et al., 1999a, 1999b). Currently, the use of TDR for field-scale spatial characterization of 8 and ECa distributions is largely limited. Even though TDR has been adapted to fit on mobile platforms such as ATVs, tractors, and spray rigs (Inoue et al., 2001; Long et al., 2002; Western et al., 1998), vehicle-based TDR monitoring is in its infancy, and only ER and EMI have been widely adapted for detailed spatial surveys consisting of intensive geo-referenced measurements of ECa at field extents and larger (Rhoades et al., 1999a, 1999b).

2.2.3 From Observed Associations to EC,-Directed Soil Sampling

Much of the early observational work with ECa correlated ECa to soil properties measured from soil samples taken on a grid, which required considerable time and effort. This early work noted the spatial correlation between ECa and soil properties and subsequently between ECa and crop yield. However, some of these observational studies were not solidly based on an understanding of the principles and theories encompassing ECa measurements, which led to presentations and even publications with misinterpretations. To ground researchers in the basic theories and principles of ECa, guidelines for ECa surveys and their interpretation were developed by Corwin and Lesch (2003).

After the research associating ECa to soil properties and to crop yield, the direction of research gradually shifted to mapping within-field variation of ECa as a means of directing soil sampling to characterize the spatial distribution and variability of properties that statistically correlate with ECa. The early observational studies compiled in Table 2.1 served as a precursor to the mapping of edaphic (e.g., salinity, clay content, organic matter, etc.) and anthropogenic (e.g., leaching fraction, compaction, etc.) properties using ECa-directed soil sampling.

Soil sampling directed by geospatial ECa measurements is the current trend and direction for characterizing spatial variability. The use of ECa-directed sampling has significantly reduced intensive grid sampling from tens of samples or even a hundred or more samples to eight to twelve sample locations for the characterization of spatial variability in a given field. The earliest work in the soil science literature for the application of geospatial ECa measurements to direct soil sampling for the purpose of characterizing the spatial variability of a soil property (i.e., salinity) was by Lesch et al. (1992).

2.3 CURRENT STATE-oF-THE-SCIENCE of eca applications in agriculture—the present

The current status of geophysical techniques in agriculture is reflected in ongoing research of the U.S. Department of Agriculture-Agricultural Research Service (USDA-ARS) laboratories at Ames, IA; Columbia, MO (Kitchen, Lund, and Sudduth); Columbus, OH (Allred); Fort Collins, CO (Buchleiter and Farahani); and Riverside; CA (Corwin and Lesch). Researchers at these facilities have been instrumental in organizing and contributing to symposia and special issues of journals that demonstrate the current role of geophysical techniques, particularly the measurement of ECa, in agriculture: Soil Electrical Conductivity in Precision Agriculture Symposium at the 2000 American Society of Agronomy-Crop Science Society of America-Soil Science Society of America Annual Meetings, Applications of Geophysical Methods in Agriculture Symposium at the 2003 Annual American Society of Agricultural Engineers International Meeting, special symposium issue of Agronomy Journal (2003, vol. 95, number 3) on Soil Electrical Conductivity in Precision Agriculture, and special issue of Computers and Electronics in Agriculture (Corwin and Plant, 2005) on Applications of Apparent Soil Electrical Conductivity in Precision Agriculture. The most up-to-date review of ECa measurements in agriculture is provided by Corwin and Lesch (2005a).

2.3.1 Factors Driving Eq-Directed Soil Sampling

Three essential factors have driven the development of ECa-directed soil sampling as a tool to characterize the spatial variability of soil properties: (1) the mobilization of ECa measurement equipment, (2) the commercialization and widespread availability of a Global Positioning System (GPS), and (3) the development or adaptation of a statistical sampling approach to select sample sites from spatial ECa data. All of these came to fruition in the 1990s.

The development of mobile ECa measurement equipment coupled to a GPS (Cannon et al., 1994; Carter et al., 1993; Freeland et al., 2002; Jaynes et al., 1993; Kitchen et al., 1996; McNeill, 1992; Rhoades, 1993) has made it possible to produce ECa maps with measurements taken every few meters. Mobile ECa measurement equipment has been developed for both ER and EMI geophysical approaches. In the case of ER, by mounting the electrodes to "fix" their spacing, considerable time for a measurement is saved. Veris Technologies* developed a commercial mobile system for

* Veris Technologies, Salinas, KS. Product identification is provided solely for the benefit of the reader and does not imply the endorsement of the USDA.

FIGURE 2.3 Veris 3100 mobile electrical resistivity equipment. (From Corwin, D.L., and Lesch, S.M., Comput. Electron. Agric., 46, 11-43, 2005a. With permission.

measuring ECa using the principles of ER (Figure 2.3). In the case of EMI, the EMI conductivity meter is carried on a sled or nonmetallic cart pulled by a pickup, ATV, or four-wheel-drive spray rig (Cannon et al., 1994; Carter et al., 1993; Corwin and Lesch, 2005a; Freeland et al., 2002; Jaynes et al., 1993; Kitchen et al., 1996; Rhoades, 1992, 1993). Both mobile ER and EMI platforms permit the logging of continuous ECa measurements with associated GPS locations at time intervals of just a few seconds between readings, which results in readings every few meters. The mobile EMI platform permits simultaneous ECa measurements in both the horizontal (EMh) and vertical (EMv) dipole configurations, and the mobile ER platform (i.e., Veris 3100) permits simultaneous measurements of ECa at 0 to 30 and 0 to 90 cm depths. No commercial mobile system has been developed for EMI, but several fabricated mobile EMI rigs have been developed (e.g., see Figure 2.4).

To establish where soil sample sites are to be located based on the spatial ECa data, the third essential component of ECa-directed sampling is needed (i.e., statistical sample design). Currently, two ECa-directed soil sampling designs are used: (1) design-based sampling and (2) model-based

FIGURE 2.4 Mobile dual-dipole electromagnetic induction equipment developed at the United States Salinity Laboratory. (From Corwin, D.L., and Lesch, S.M., Comput. Electron. Agric., 46, 11-43, 2005a. With permission.)

sampling. Design-based sampling primarily consists of the use of unsupervised classification (Johnson et al., 2001), whereas model-based sampling typically relies on optimized spatial response surface sampling (SRSS) design (Corwin and Lesch, 2005b). Design-based sampling also includes simple random and stratified random sampling. Lesch and colleagues (Lesch, 2005; Lesch et al., 1995a, 1995b, 2000) developed a model-based SRSS software package (ESAP) that is specifically designed for use with ground-based soil ECa data. The ESAP software package identifies the optimal locations for soil sample sites from the ECa survey data. These sites are selected based on spatial statistics to reflect the observed spatial variability in ECa survey measurements. Generally, eight to twelve sites are selected depending on the level of variability of the ECa measurements for a site. The optimal locations of a minimal subset of ECa survey sites are identified to obtain soil samples. Protocols are currently available to maintain reliability, consistency, accuracy, and compatibility of ECa surveys and their interpretation for characterizing spatial variability of soil physical and chemical properties (Corwin and Lesch, 2005b).

There are two main advantages to the response-surface approach. First, a substantial reduction in the number of samples required for effectively estimating a calibration function can be achieved in comparison to more traditional design-based sampling schemes. Second, this approach lends itself naturally to the analysis of remotely sensed ECa data. Many types of ground-, airborne-, and satellite-based remotely sensed data are often collected specifically because one expects this data to correlate strongly with some parameter of interest (e.g., crop stress, soil type, soil salinity, etc.), but the exact parameter estimates (associated with the calibration model) may still need to be determined via some type of site-specific sampling design. The response-surface approach explicitly optimizes this site-selection process.

2.3.2 Characterization of Soil Spatial Variability with ec a

The shift in the emphasis of field-related ECa research from observed associations to directed-sam-pling design has gained momentum, resulting in the accepted use of geospatial measurements of ECa as a reliable directed-sampling tool for characterizing spatial variability at field and landscape extents (Corwin and Lesch, 2003, 2005a, 2005b). At present, no other measurement provides a greater level of spatial soil information than that of geospatial measurements of ECa when used to direct soil sampling to characterize spatial variability (Corwin and Lesch, 2005a). The characterization of spatial variability using ECa measurements is based on the hypothesis that spatial ECa information can be used to develop a directed soil sampling plan that identifies sites that adequately reflect the range and variability of soil salinity and other soil properties correlated with ECa. This hypothesis has repeatedly held true for a variety of agricultural applications (Corwin, 2005; Corwin and Lesch, 2003, 2005a, 2005c, 2005d; Corwin et al., 2003a, 2003b; Johnson et al., 2001; Lesch et al., 1992, 2005).

The ECa measurement is particularly well suited for establishing within-field spatial variability of soil properties because it is a quick and dependable measurement that integrates within its measurement the influence of several soil properties that contribute to the electrical conductance of the bulk soil. The ECa measurement serves as a means of defining spatial patterns that indicate differences in electrical conductance due to the combined conductance influences of salinity, 8, texture, and pb. Therefore, maps of the variability of ECa provide the spatial information to direct the selection of soil sample sites to characterize the spatial variability of those soil properties correlating, either for direct or indirect reasons, to ECa.

The characterization of the spatial variability of various soil properties with ECa is a consequence of the physicochemical nature of the ECa measurement. Three pathways of current flow contribute to the ECa of a soil: (1) a liquid phase pathway via dissolved solids contained in the soil water occupying the large pores, (2) a solid-liquid phase pathway primarily via exchangeable cations associated with clay minerals, and (3) a solid pathway via soil particles that are in direct and continuous contact with one another (Rhoades et al., 1989, 1999a). These three pathways of current

Pathways of Electrical Conductance

Soil Cross Section

Pathways of Electrical Conductance

Soil Cross Section

Solid

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