Published online 3 October 2006
Published in Vadose Zone J 5:1069-1070 (2006)
DOI: 10.2136/vzj2006.0043L
© 2006 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
COMMENTS
Response to "Comments on ‘Monitoring Soil Water Content Profiles with a TDR Commercial System: Comparative Field Tests and Laboratory Calibration’"
Jean-Paul Laurent
Laboratoire d'étude des Transferts en, Hydrologie et Environnement, CNRS-INPG-IRD-UJF, BP53, F-38041 Grenoble-cedex 9, France
jean-paul.laurent{at}hmg.inpg.fr
In their comment on our paper (Laurent et al., 2005), Regalado et al. (2006) suggest that an alternative logarithmic relationship between permittivity K and pseudo transit time t2 as measured with a TRIME TDR system:
 | [1] |
may be more appropriate, general, or convenient than the linear relationship between square root of permittivity and pseudo transit time:
 | [2] |
that we introduced on the basis of a laboratory experiment conducted on a natural soil.
To further test this, we reexamined our laboratory results and compared them with the new data obtained by Regalado et al. (2006) and with the earlier data set of Stacheder (1996). The results in Fig. 1 indicate that Eq. [2] gives a better representation of the TRIME-tube probe data for pseudo transit times between 100 (dry soil) to approximately 700 (close to saturation). This is confirmed by calculating the Nash criterion Ceff on K estimates as suggested by Regalado et al. (2006) for the same set of data, for which we obtained a value of 0.990 when using Eq. [2] as compared with 0.855 when using Eq. [1]. However, it is also evident, as mentioned by Regalado et al. (2006), that Eq. [2] is not appropriate for transit times >700, but this is to be expected since this is outside the calibration range.
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Fig. 1. Plot of laboratory TRIME measurements of Laurent et al. (2005) (yellow squares and red diamonds), Regalado et al. (2006) (blue squares) and Stacheder (1996) (triangles). Comparison of the different empirical models considered here: Eq. [1] (gray solid line) fitted to the data set obtained by Regalado et al. with a P2 two-rod probe operated in liquids and dry and water-saturated glass beads, Eq. [2] fitted to TRIME measurement taken with a tube probe operated inside a plastic access tube placed in a 10-L sample of natural soil dried from saturation, and Eq. [4] of Regalado et al. (dotted line) having the same mathematical form as Eq. [2] but fitted to all of the measurements by Regalado et al. (2006).
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If only empirical equations are to be considered, one could indeed apply different mathematical expressions to the various types of TRIME measurements. Equation [2] in that case would give accurate estimates of the soil permittivity from TRIME-tube probe measurements, while Eq. [1] would perform better for a broader range of pseudo transit times. However, we believe that such a pragmatic approach may hide more fundamental issues that could explain the observed discrepancies. For example, if we look more closely at our respective data for the reference materials (mainly liquids, but unfortunately not exactly the same materials since we initially had no contact) within the same 100 to 700 range of pseudo transit times, significant differences also occur between the different TRIME measurements themselves. This suggests that the different geometries of the two TRIME TDR probes considered here (we used TRIME-tube probes operating in a plastic tube, while Regalado et al. (2006) and Stacheder (1996) used P2 two-rod coated probes) could yield different averages between the coating material and the surrounding medium. This is not surprising if we consider corresponding relevant literature, such as studies by Ferré et al. (1996) and Knight et al. (1997). In our opinion it would be very useful to numerically simulate the TRIME measurement resulting from different probe types.
Another interesting aspect of such simulations would be to study the effect of an air gap between the soil and the probes. This may well have played also a role in our laboratory study (Laurent et al., 2005) and clearly should be considered when dealing with field measurements. Such an approach actually could provide a convenient framework for evaluating Eq. [1] versus Eq. [2]. For example, if the equations are used in conjunction with a permittivity–water content relationship, such as the Topp polynomial (Topp et al., 1980), would one of them prove to be more accurate than the other? Following a suggestion by Regalado (personal communication, 2006), we tried to apply this approach to the field TRIME data used by Laurent et al. (2005). Results are shown in Fig. 2.
Unfortunately, again, it was not possible to ascertain which equation provided the better estimates since both differ from the proposed new calibration Eq. [1] suggested by Regalado et al. (2006, their Eq. [5]). That equation, combined with Topp's relationship, was indeed close to the TRIME standard calibration and Stacheder measurements, but this was to be expected since the Stacheder (1996) data were used to establish this calibration and were close to the new set of data of Regalado et al. (2006) that were used to fit Eq. [1]. This disappointing result could be explained again by the roles of probe geometry and contact quality. As mentioned by Laurent et al. (2005), other factors such as temperature, soil type, or spatial variability may have interfered also.
To conclude, we note that in Laurent et al. (2005) we made a physically based attempt to facilitate the TRIME calibration, leading to a linear dependency of the square root of the permittivity on the pseudo transit time. Regalado et al. (2006) suggested that a logarithmic equation is more appropriate when applied to the entire range of pseudo transit times. Unfortunately, when coupled with the Topp polynomial, both equations failed to closely match actual field data. In our opinion this is due to the possible interference of many factors, of which probe geometry and air gaps are probably the most likely. It would be very useful to solve this problem theoretically using some numerical approach. Practically, however, the only way for now to obtain accurate absolute soil water content measurements with the TRIME system is to locally calibrate field measurements as stated and tested in Laurent et al. (2005).
We thank Regalado and his coauthors from Imko for their interest in our work.
REFERENCES
- Ferré, P.A., D.L. Rudolph, and R.G. Kachanoski. 1996. Spatial averaging of water content by time domain reflectometry: Indications for twin rod probes with and without dielectric coatings. Water Resour. Res. 32:271–279.[CrossRef]
- Knight, J.H., P.A. Ferré, D.L. Rudolph, and R.G. Kachanoski. 1997. A numerical analysis of the effects of coatings and gaps upon relative dielectric permittivity measurement with time domain reflectometry. Water Resour. Res. 33:1455–1460.[CrossRef]
- Laurent, J.-P., P. Ruelle, L. Delage, A. Zaïri, B. Ben Nouna, and T. Akjmi. 2005. Monitoring soil water content profiles with a commercial TDR system: Comparative field tests and laboratory calibration. Available at www.vadosezonejournal.org. Vadose Zone J. 4:1030–1036.[Abstract/Free Full Text]
- Regalado, M.C., A. Ritter, and R. Becker. 2006. Comments on "Monitoring soil water content profiles with a commercial TDR system: Comparative field tests and laboratory calibration." Available at www.vadosezonejournal.org. Vadose Zone J. 5:1067–1068 (this issue).[Free Full Text]
- Stacheder, M. 1996. Die Time Domain Reflectometry in der Geotechnik, Messung von Wassergehalt, elektrischer Leitfähigkeit und Stofftransport. Ph.D. diss. Schriftenreihe angewandte Geologie, Karlsruhe.
- Topp, G.C., J.L. Davis, and A.P. Annan. 1980. Electromagnetic determination of soil water content: Measurements in coaxial transmission lines. Water Resour. Res. 16:574–582.[CrossRef]
