Soil Science Society of America Journal 66:53-57 (2002)
© 2002 Soil Science Society of America
DIVISION S-1 - SOIL PHYSICS
The Feasibility of Shallow Time Domain Reflectometry Probes to Describe Solute Transport Through Undisturbed Soil Cores
Jaehoon Leea,
Robert Horton*,b and
Dan B. Jaynesc
a Dep. of Biosystems Engineering, Environmental, and Soil Sciences, Univ. of Tennessee, Knoxville, TN 37901
b Dep. of Agronomy, Iowa State Univ., Ames, IA 50011
c USDA-ARS, National Soil Tilth Lab., 2150 Pammel Dr., Ames, IA 50011
* Corresponding author (rhorton{at}iastate.edu)
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ABSTRACT
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Rapid and nondestructive methods for determining solute transport properties are useful in many soil science applications. Recently, a series of field methods and a time domain reflectometry (TDR) method that could estimate some of the mobile-immobile model (MIM) parameters, immobile water content (
im) and mass exchange coefficient (
), have been reported. The first objective of this study was to determine an additional parameter, dispersion coefficient (Dm), using the TDR method. The three MIM parameters were estimated from the TDR-measured data, and the estimated parameters were compared with the estimated parameters from the effluent data. The second objective was to determine whether the TDR-determined parameters from the surface 2-cm soil layer could be used to predict effluent breakthrough curves (BTC) at the 20-cm depth. The TDR-determined parameters were used to calculate effluent BTCs using the CXTFIT computer program. Parameters obtained by curve fitting of the three parameters simultaneously using TDR data were not similar to the parameters obtained from the effluent BTCs. The parameter estimations were improved by fixing one or two independently determined parameter(s) before curve fitting for the remaining unknown parameter(s). The calculated BTCs were similar to the observed BTCs with coefficient of determination (r2) being 0.99 and root mean square error (RMSE) being 0.036. The TDR data obtained from shallow soil layers were successfully used to describe solute transport through undisturbed soil cores.
Abbreviations: BTC, breakthrough curves • CI, confidence interval • LLT, log-linear TDR • MIM, mobile-imobile model • RMSE, root mean square error • ST, sequence of benzoate tracers • TDR, time domain reflectometry
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INTRODUCTION
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MANY STUDIES (Rao et al., 1980; Nkedi-Kizza et al., 1983; Lee et al., 2000b) have shown that the MIM can describe some forms of preferential solute transport. The MIM includes three significant model parameters, immobile water content (im), mass exchange coefficient (), and dispersion coefficient (Dm), to describe nonsorbing, conservative solute transport. However, determining the three parameters is not easy, especially in the field.
So far, methods have been developed to estimate only some of the parameters. Clothier et al. (1992) first introduced a method to estimate im of field soil using a tension infiltrometer and a conservative tracer (Br-). The Br- tracer was applied through a tension infiltrometer with steady-state infiltration. After applying sufficient infiltration of tracer, soil samples were taken and analyzed to calculate im. If all of the soil water is mobile, the concentration of the tracer should equal the input concentration. Based on the concentration difference between the input solution and the soil solution, one can calculate im. Similarly, Jaynes et al. (1995) presented a technique that could estimate both im and . They developed a log-linear equation using the MIM. The equation represented a relationship between resident tracer concentration and time of tracer application and could be used to estimate both im and . To apply the method, a sequence of benzoate tracers (ST) were applied through a tension infiltrometer. The Jaynes et al. (1995) ST method was tested in the field (Casey et al., 1997) and in the laboratory (Lee et al., 2000b). Casey et al. (1997) and Lee et al. (2000b) reported that the ST method provided MIM parameters representative of the soil.
Based on the ST method, Lee et al. (2000a) recently presented a TDR method that could simultaneously estimate im and . The method used a shallow TDR probe installed into a surface 2-cm soil layer to measure resident concentration changes as a function of time following a surface infiltration of CaCl2 solution. They analyzed the TDR measurements to estimate im and using a log-linear relationship derived from the ST method. The TDR method provided an extensive number of data points whereas the ST method provided a limited number of data points depending on availability of the sequential tracers. Lee et al. (2000a) reported that the estimates of im and from the TDR method were very similar to the estimates obtained from inverse curve fitting of the effluent breakthrough curve (BTC) data. Although one can estimate im and in the field using one of the methods described above, the dispersion coefficient, Dm, is not estimated. Dispersion of solute is a primary mechanism for solute transport in soil. Thus, it would be useful to estimate Dm along with im and .
Furthermore, the structure of a shallow soil layer may or may not be similar to that of deeper soil. Steenhuis et al. (1999) presented a conceptual model in which a layer near the surface became saturated and distributed the water and solutes to the preferential flow paths. In the conceptual model, movement of water and solute in the layer (so-called distribution layer) was different than that below the distribution layer. It is important to examine whether solute transport properties obtained from the shallow soil layer (0–2 cm) using the TDR method can be used to characterize solute transport deeper in the soil.
The first objective of this study was to determine Dm, in addition to im and , using the shallow TDR method. The MIM parameters obtained from TDR were compared with the parameters estimated from the observed effluent BTCs for the same soil cores. The second objective was to test whether the three parameters obtained from the shallow (0–2 cm) soil layer could be used to predict effluent BTCs at a deeper depth, 20 cm. The TDR determined parameters were used in a simulation study to predict effluent BTCs for comparison with the observed effluent BTCs. The second objective is an approach to evaluate not only parameters individually but to evaluate the usefulness of the set of parameters to predict solute behavior.
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MATERIALS AND METHODS
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Parameter Determination
Data from Lee et al. (2000a) were used in this study. Briefly, Lee et al. (2000a) used three 20-cm long by 12-cm diam. undisturbed saturated soil cores. The soil was Nicollet silt loam (fine-loamy, mixed, superactive, mesic Aquic Hapludolls). A two-rod, 2-mm diam. and 80-mm long TDR probe was installed diagonally from the surface to a depth of 2 cm. Soil disturbance was minimized by installing the TDR probe diagonally instead of horizontally. Lee et al. (2000a) assumed that the TDR probe measured the average bulk soil electrical conductivity of the top 2-cm layer of soil. In this paper, the dispersion coefficient, Dm, in addition to im and , was estimated using the data from the TDR method (Lee et al., 2000a). Inverse curve fitting with the CXTFIT (Toride et al., 1999) program of the resident concentration BTCs from the TDR method was done. The depth for the curve fitting in CXTFIT was set at 1 cm, which was the average depth of the sampling volume (0–2 cm) of the TDR probe. The collected effluent samples of CaCl2 were also analyzed to determine the three parameters using CXTFIT. The TDR determined parameters were compared with the parameters estimated from curve fitting the effluent data.
Predicting Effluent Breakthrough Curves
A computer simulation study was conducted to study the feasibility of using the estimated MIM parameters obtained from TDR to predict solute transport through the soil columns. TDR data from the surface 2-cm soil layer were used to determine MIM parameters which were used to predict effluent BTCs for the 20-cm soil columns. The simulation study focuses on use of the combined parameters to predict solute transport in contrast to the direct comparison of parameters which focuses on individual comparison of the parameters. By comparing the TDR-derived predicted BTCs with the observed BTCs, we have some insight into the practical usefulness of the parameters obtained from the TDR technique.
The MIM analytical solutions from CXTFIT were used to calculate effluent BTCs. The predicted BTCs were generated using MIM parameters estimated from the TDR method. These calculated BTCs were compared with the observed effluent BTC. Two quantitative measures, coefficient of determination (r2) and RMSE (Snedecor and Cochran,1967; Willmott et al., 1985), were used to evaluate the predicted BTCs.
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RESULTS AND DISCUSSION
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Figure 1
shows the relative resident concentration values, C(t)/Co, obtained from TDR for 0- to 2-cm soil layer. The resident concentrations increased relatively quickly at the beginning of the tracer application and increased relatively slowly over the remaining application period. Conceptually, because the initial mobile water (or active flow pathways) was first replaced with the input tracer solution mainly by convection, the resident concentration increased relatively quickly at the beginning of the experiment. As the mobile domain was replaced with input tracer, tracer in the mobile domain diffused over time into the immobile water domain (or relatively nonactive flow pathways). The diffusion process was relatively slow compared with the convection process.
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Fig. 1. The relative resident conentrations, C(t)/C0, obtained from the shallow (0- to 2-cm soil layer) time domain reflectometry probe for three soil columns. The x-axis is based on the 2-cm sampling layer.
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The relative resident concentrations from the soil extracts ranged from 0.76 to 0.86 after applying 40 pore volumes of input solution. Because the relative resident concentrations from the soil extracts were less than one, some of the water-filled pore spaces were not replaced with input solution, indicating the presence of an immobile water domain. Thus, incorrectly assuming complete replacement of the soil water with input solution after 40 pore volumes of application would result in a 14 to 24% error in maximum relative resident concentration.
Comparison of the Parameter Values from the TDR Method and from the Effluent Data
The estimated MIM parameters from the effluent data and from the TDR method for the three soil columns are shown in Table 1. The estimates marked "3-fit" are obtained from curve fitting of TDR-measured resident concentrations. The 95% confidence intervals (CI) from CXTFIT are reported as well. The estimated immobile water fractions (im/) obtained from the TDR method were lower than the im/ from the effluent data. The means of im/ from the TDR method and from the effluent data were 0.15 and 0.34, respectively. The estimated values from the TDR method were lower than the estimates from the effluent data. The means of (h-1) from the TDR method and from the effluent data were 0.001 and 0.03, respectively. The means of Dm (cm2 h-1) from the TDR method and from the effluent data were 223 and 114, respectively. For all three soil columns, the parameter estimates from the TDR method were not similar to the parameter estimates from the effluent data.
Note that the C(t)/Co values from the TDR method were from the surface 2-cm soil layer where the analytical solution in CXTFIT was sensitive to the surface boundary condition. Hence, small experimental errors leading to slight changes in the measurements in the surface 2-cm soil layer could cause relatively large deviations of fitted parameters. In this case, it would be desirable to estimate one or two of the parameter(s) and fix the parameter(s) before using inverse curve fitting to determine the remaining unknown parameter(s). By fixing im or , the inverse curve fitting could be used to solve for only one or two parameter(s) rather than for all three parameters. Thus, for each soil core, im was estimated using Clothier et al. (1992) method. Immobile water content was determined based on the resident concentrations of the soil samples taken after infiltrating CaCl2 solution (Clothier et al., 1992). The im was then fixed during the inverse curve fitting of the TDR data to determine and Dm. Similarly, im and were estimated using the Lee et al. (2000a) log-linear TDR method (LLT method) so that the two parameters could be fixed for the inverse curve fitting of the TDR data. Note that both the Clothier et al. (1992) and Lee et al. (2000a) methods did not require any additional experiments or sampling. Both methods used the data obtained from the shallow TDR method. Table 1 shows the Clothier and LLT determined im or values along with other estimated parameters. In the "Clothier im-fixed" column, the im/ estimates from the Clothier et al. (1992) method were not within the 95% CI of the im/ estimates from the effluent data. The estimated and Dm by fixing the separately determined im/ were also not similar to the estimates from the effluent data. In the "Lee , im-fixed" column, the im/ and estimates from the LLT method were similar to the estimates from the observed effluent data although the CIs did not encompass each other. The Dm estimates obtained after fixing both im/ and were similar to the estimates obtained from observed effluent data. Overall, the parameter estimates obtained by "Lee , im-fixed" seemed the most representative of effluent-determined parameters.
Comparison of the Predicted and Observed Breakthrough Curves
To test whether the information from the shallow soil could be used to predict chemical transport in the whole soil column, the set of TDR determined parameters from the surface 2-cm soil layer (Table 1) were used to predict effluent BTCs at the 20-cm depth. The predicted BTCs were generated using the analytical solution of MIM from the CXTFIT. The results of predicting BTCs are shown in Fig. 2
along with measured BTCs. The BTC marked "3-fit" used , im, and Dm values obtained from fitting three parameters simultaneously. The BTC marked ", imfixed" used the MIM parameters in the "Lee , im-fixed" column in Table 1. The predicted BTCs using parameters in the "Clothier im-fixed" column in Table 1 were very similar to the predicted BTCs marked "3-fit". For clarity, "Clothier im-fixed" BTCs are not shown in Fig. 2. For all three soil cores, the calculated BTCs were similar to the observed effluent BTCs. Table 2 shows the values of r2 and RMSE to evaluate the accuracy of the inverse curve fitting and the predictions in describing the observed effluent BTCs. Coefficient of determination was computed for the nonlinear relationship based on Snedecor and Cochran (1967). The r2 values for the effluent fitted and predicted BTCs ranged from 0.98 to 0.99 indicating the accuracy of the inverse curve fitting and predictions. RMSE for both the effluent fitted BTCs and the calculated BTCs are shown in Table 2. The average RMSEs for the effluent fitted BTCs were lower than those for the calculated BTCs. The average RMSEs for the effluent fitted and calculated BTCs were 0.009 and 0.036, respectively. The ratios of the predicted BTCs to the observed BTCs for RMSE were also calculated (Table 2). The average RMSE ratio of "3-fit", "Clothier im-fixed", and "Lee , im-fixed" predicted BTCs to observed BTCs were 4.6, 4.1, and 3.2, respectively. The results implied that the parameter estimates obtained from fixing one or two parameters made better predictions of effluent BTCs than did the 3-fit estimates. The predictions were the best when "Lee , im-fixed" parameters were used.
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Fig. 2. The predicted effluent breakthrough curves (BTCs) are plotted along the observed BTCs for the three soil columns. The predicted BTCs are generated using the estimated parameters shown in Table 1. Analytical solutions of the mobile–immobile model from CXTFIT are used to calculate the effluent BTCs.
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Table 2. Coefficient of determination, r2, and root mean square error (RMSE) for the effluent fitted and the calculated breakthrough curves (BTC).
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Lee et al. (2000b) observed both resident concentrations and effluent data for a set of soil columns. They tested the MIM by evaluating the model's success in predicting resident tracer concentrations from parameters fitted to effluent BTCs and vice versa. They reported that predicting effluent data using resident concentrations seemed to work better than predicting resident concentrations using effluent data. We again note that the predicted effluent BTCs were obtained from the surface 2-cm soil layer and resident concentrations, whereas the measured effluent BTCs represented 20-cm long soil columns. In spite of these differences, the calculated effluent BTCs from the TDR method were very similar to observed effluent BTCs. These are promising results indicating the capability of the shallow TDR method to provide solute transport parameters that can be used to extrapolate chemical movement in deeper soil.
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CONCLUSIONS
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A simple TDR method designed to estimate im and was further evaluated for determining dispersion coefficient, Dm, in addition to im and . For the inverse curve fitting of the three MIM parameters, fixing one or two parameters improved estimation of dispersion coefficient. A simulation study showed that the parameters obtained from the shallow (0–2 cm) soil layer were successful in predicting effluent BTCs at the 20-cm depth. The TDR method was relatively simple. The TDR method required only a surface soil sample with minimum disturbance of soil, after applying a step input of salt solution. This shallow TDR method is a promising method and should be further examined in situ to delineate solute transport.
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NOTES
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Journal Paper no. 18677 of the Iowa Agric. and Home Econ. Exp. Stn., Ames, IA; Work supported by CSREES USDA, NRICGP Soils and Soils Biology Program award No. 2001-35107-09938 and by Hatch Act and State of Iowa Funds.
Received for publication August 21, 2000.
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REFERENCES
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- Casey, F.X.M., S.D. Logsdon, R. Horton, and D.B. Jaynes. 1997. Immobile water content and mass exchange coefficient of a field soil. Soil Sci. Soc. Am. J. 61:1030–1036.[Abstract/Free Full Text]
- Clothier, B.E., M.B. Kirkham, and J.E. McLean. 1992. In situ measurements of the effective transport volume for solute moving through soil. Soil Sci. Soc. Am. J. 56:733–736.[Abstract/Free Full Text]
- Jaynes, D.B., S.D. Logsdon, and R. Horton. 1995. Field method for measuring mobile/immobile water content and solute transfer rate coefficient. Soil Sci. Soc. Am. J. 59:352–356.[Abstract/Free Full Text]
- Lee, J., R. Horton, and D.B. Jaynes. 2000a. A time domain reflectometry method to measure immobile water content and mass exchange coefficient. Soil Sci. Soc. Am. J. 64:1911–1917.[Abstract/Free Full Text]
- Lee, J., D.B. Jaynes, and R. Horton. 2000b. Evaluation of a simple method for estimating solute transport parameters: Laboratory studies. Soil Sci. Soc. Am. J. 64:492–498.[Abstract/Free Full Text]
- Nkedi-Kizza, P., J.W. Biggar, M.Th. van Genuchten, P.J. Wierenga, H.M. Selim, J.M. Davidson, and D.R. Nielsen. 1983. Modeling tritium and chloride 36 transport through an aggregated Oxisol. Water Resour. Res. 19:691–700.
- Rao, P.S.C., D.E. Rolston, R.E. Jessup, and J.M. Davidson. 1980. Solute transport in aggregated porous media: Theoretical and experimental evaluation. Soil Sci. Soc. Am. J. 44:1139–1146.[Abstract/Free Full Text]
- Snedecor, G.W., and W.G. Cochran. 1967. Statistical methods. The Iowa State University Press, Ames, IA.
- Steenhuis, T.S., J.Y. Parlange, C.J.G. Darnault, Y.J. Kim, O. McHugh, K.S. Kung, and M.S. Akhtar. 1999. A generalized theory for preferential flow. p. 180. In 1999 Annual meeting abstracts. ASA, Madison, WI.
- Toride, N., F.J. Leij, and M.Th. van Genuchten. 1999. The CXTFIT code for estimating transport parameters from laboratory or field tracer experiments. Ver. 2.1. Res. Rep. No. 137. U.S. Salinity Laboratory, ARS–USDA, Riverside, CA.
- Willmott, C.J., S.G. Ackleson, R.E. Davis, J.J. Feddema, K.M. Klink, D.R. Legates, and C.M. Rowe. 1985. Statistics for the evaluation and comparison of models. J. Geophys. Res. 90:8995–9005.
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ABSTRACT
INTRODUCTION
