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Soil Science Society of America Journal 63:1615-1617 (1999)
© 1999 Soil Science Society of America

DIVISION S-1-SOIL PHYSICS

Comparison of calibration and direct measurement of cable and probe properties in time domain reflectometry

J.A. Huismana and W. Boutena

a Dep. of Physical Geography and Soil Sci., Univ. of Amsterdam, Nieuwe Prinsengracht 130, 1018 VZ Amsterdam, The Netherlands

s.huisman{at}frw.uva.nl


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 Methods
 Results and Discussion
 REFERENCES
 
For the measurement of soil bulk electrical conductivity using time domain reflectometry (TDR), it is necessary to determine cable and probe properties. This can be done by direct measurement or by calibration of the TDR system in salt solutions. For a three-wire probe system, the results showed that with least-squares fitting, the electrical conductivity of salt solutions could be measured most accurately. Comparison of several calibration techniques suggested that directly measured cable properties deviate from their calibrated (optimal) values. The difference in accuracy between calibration and direct measurements of cable properties could not be explained with overfitting, as has been suggested. It was concluded that a reduction of calibration time by direct measurement of probe and cable properties is not advisable in case of three-wire probes. When necessary, a reduction of calibration time can be achieved by limiting the calibration procedure to two well chosen combinations of cable length and solution concentration.

Abbreviations: TDR, time domain reflectometry


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
Methods
 Results and Discussion
 REFERENCES
 
TIME DOMAIN REFLECTOMETRY (TDR) is used to measure soil bulk electrical conductivity ({sigma}soil). Giese and Tiemann (1975) suggested to calculate the load resistance RL ({Omega}) from the reflection coefficient at long times ({rho}{infty}). To avoid overestimation of the sample resistance, RL should be corrected for resistance of the cable per meter Rc ({Omega} m-1) and the combined extra series resistance R0 ({Omega}) caused by connectors and cable tester (Heimovaara et al., 1995):

(1)
where CL is the cable length (m) and Kp the probe constant (-).

Heimovaara et al. (1995) and Mallants et al. (1996) calibrated cable and probe properties (R0, Rc and Kp) using a least-squares fitting of TDR conductivity measurements in solutions of different concentrations to conductivity measurements made with a laboratory conductivity meter (Radiometer Copenhagen CDM83 conductivity meter with CDC314 measurement cell). Recently, Reece (1998) proposed a method to measure Rc, R0, and Kp directly. He suggested that direct measurements would eliminate the need for a time-consuming calibration in multiple solutions. His method is based on resistance measurements of a coaxial cable with and without a shorted transmission waveguide. For his two-wire probes, direct measurement of Rc, R0, and Kp resulted in reliable conductivity measurements, but the cable and probe properties obtained with least-squares fitting resulted in even more accurate conductivity measurements. He stated that the higher accuracy obtained with the least-squares fitting method indicated that the fitting procedure adjusts Rc, R0, and Kp to account for small measurement errors that are not necessarily associated with these parameters (overfitting). However, the higher accuracy may also suggest that the theory is incomplete and that the fitting procedure corrects for the deviations from the theory. Besides the comparison of calibration and direct measurements, this suggestion of overfitting from Reece (1998) is also examined in this note.


   Methods
TOP
 ABSTRACT
 INTRODUCTION
 Methods
Results and Discussion
 REFERENCES
 
There are two approaches for obtaining direct estimates of the probe constant Kp. For probes correctly emulating a coaxial cable, the probe constant can be calculated from

(2)
where, in case of the three-wire probes used in this study, Z0 can be approximated by (Heimovaara, 1993)

(3)
and {epsilon} is the permitivity of the material in the probe (-), c is the speed of light (3 x 108 m s-1), L is the length of the probe (m), Z0 is the characteristic impedance of the probe ({Omega}), {epsilon}0 is the dielectric permitivity of free space (8.854 x 10-12 F m-1), a is the outer diameter of the inner wire, and b is the inner diameter of the outer wires (m). Alternatively, Z0 can be inferred from measurements of the reflection coefficient ({rho}t) at a time t, which corresponds to the location of the waveguide in a nonconductive medium of known permitivity, {epsilon}, according to

(4)
where Zu is the characteristic impedance of the cable tester system (50 {Omega}). In a lossy or dispersive medium the reflection coefficient will be diminished by conduction, thus reducing the ratio in Eq.[4]. Generally, it is suggested to measure {rho}t in a lossless medium like demineralized water, but the choice of the position of {rho}t remains arbitrary (Heimovaara, 1992; Baker and Spaans, 1993).

To compare calibration with direct measurement (Reece, 1998), a total of 25 measurements were made in five KCl solutions with conductivities of 0, 11, 119, 232, and 439 mS m-1 for five cable lengths (ranging from 5 to 25 m of RG58 C/U coaxial cable). We used a three-wire probe (Heimovaara, 1993) and a Tektronix 1502C cable tester (Beaverton, OR). The methods to obtain Rc, R0, and Kp directly [Kp with Eq. [2] and [3] (Method 1) or Eq. [2] and [4] (Method 2)] are compared with results of least-squares fitting of Kp with directly measured cable properties (Method 3), and with least-squares fitting of both Kp and cable properties (Method 4). Measurements were randomly separated into a calibration set (12 measurements) and a validation set (13). Subsequent calibration and validation were repeated 150 times for different sets.


   Results and Discussion
TOP
 ABSTRACT
 INTRODUCTION
 Methods
 Results and Discussion
REFERENCES
 
Resistance measurements with shorted coaxial cables, as proposed in the method of Reece (1998), resulted in a cable resistance Rc of 0.050 {Omega} m-1 and an internal cable tester and connector resistance of 0.080 {Omega} (Fig. 1) . Resistance measurements with shorted probes attached to the cables resulted in an upward resistance shift, which resulted in a probe resistance of 0.373 {Omega} and a total internal resistance R0 of 0.453 {Omega}. This confirms Reece's (1998) speculation that the probes used by Heimovaara et al. (1995) had a relatively high R0.



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  		Fig. 1 Resistance as a function of cable length as measured by a cable tester on coaxial cables that terminate in a short circuit (with and without a probe). Fitted regression lines are for the shorted cables and for the shorted probe with cables

 
Validation of the methods for obtaining Rc, R0, and Kp (Table 1) showed that probe constants estimated from either Eq. [3] or [4] resulted in less reliable conductivity measurements. Apparently, both methods of obtaining Kp directly should be applied with care in the case of three-wire probes. For the probe constant calculated from probe dimensions (Eq. [3]) this was expected, because it is well established that three-wire probes do not behave as coaxial probes and tend to underestimate true probe constants (Zegelin et al., 1989). Direct estimation of Kp from TDR waveforms (Eq. [4]) did not result in reliable conductivity measurements either, because Z0 was overestimated. Again, an explanation for this overestimation can probably be found in the noncoaxial behavior of three-wire probes.


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  		Table 1 Results of calibration and validation for five procedures for obtaining probe and cable properties. Results presented are mean and standard deviations (in parentheses) of 150 randomly selected calibration and validation sets. If no calibration was performed, the methods were validated on 150 randomly selected validation sets consisting of 13 measurements each. Results of direct measurements are given in italics

 
Acceptable conductivity measurements were obtained when directly measured cable properties were combined with a probe constant fitted to measurements in multiple solutions (Method 3). This illustrates that calibration with measurements in multiple solutions improves the accuracy of conductivity measurements with TDR in the case of three-wire probes. However, Table 1 also shows that an even higher accuracy of conductivity measurements for both calibration and validation was easily achieved by optimizing all three parameters (Method 4c). This improvement in accuracy was accompanied by a greater magnitude of fitted Rc, as can be seen from the partial optimization of cable properties (Method 4a and 4b). Apparently, direct measurements of cable properties do not result in the most accurate conductivity measurements. The fact that the improvement in accuracy was seen in both the calibration and validation set indicates that overfitting is not the primary explanation for the higher accuracy of the fitting procedures, as has been suggested by Reece (1998).

A reduction of calibration time by direct measurement of Rc, R0, and Kp does not appear feasible in the case of three-wire probes. A simplification of the calibration procedure might be considered when extensive calibration in multiple solutions is a problem. One possibility is to reduce the fitting procedure to only two cable lengths and two solution concentrations. For the validation set this approach resulted in a low root mean square error of 1.152 when cables of 25.6 and 4.1 m and solutions of 120 and 439 mS m-1 were used. Other calibration sets of four measurements also resulted in accurate conductivity measurements, provided that the selected cable lengths and solution concentrations covered the range of expected values. This illustrates that only four well chosen measurements contain all the information needed to obtain Rc, R0, and Kp, as can be expected from the simple nature of the underlying equations.

In summary, although the methods presented by Reece (1998) do have the advantage of being direct measurements, care should be taken in the application of these methods to three-wire probes. For a three-wire probe system, least-squares fitting of probe and cable properties resulted in the most accurate conductivity measurements. Comparison of several calibration techniques suggested that directly measured cable and probe properties deviate from their calibrated (optimal) values. It is certainly important (and curious) to note that there are unexplained differences between direct and empirical methods. Furthermore, it was suggested that a reduction of calibration time can be achieved by limiting the calibration procedure to two well chosen cable lengths and solution concentrations.


   ACKNOWLEDGMENTS
 
This study was financially supported by The Netherlands Geosciences Foundation of The Netherlands Organization for Scientific Research (NWO-GOA). Koos Verstraten is thanked for correcting an earlier draft. The detailed comments of the reviewers also improved the text.

Received for publication November 2, 1998.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 Methods
 Results and Discussion
 REFERENCES
 




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