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DIVISION S-1-SOIL PHYSICS

Comparing Field Methods that Estimate Mobile–Immobile Model Parameters

^a Dep. of Agronomy, Iowa State Univ., Ames, IA 50011 USA
^b USDA-ARS, National Soil Tilth Lab., 2150 Pammel Dr., Ames, IA 50011 USA

fxcasey{at}iastate.edu

	ABSTRACT

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results Conclusion REFERENCES

 
Recent studies have used field techniques that estimate soil hydraulic and solute transport parameters. These methods utilize a tension infiltrometer to infiltrate either a single tracer or a series of tracers in order to estimate immobile water content (_im) and mass exchange coefficient () of the mobile–immobile solute transport model. The objective of this study was to compare two single tracer methods (basic and variance) with one multiple tracer method for estimating _im and from data obtained on the same field soil location. Hydraulic conductivity (K(h₀)) was also estimated using these methods. Research was done at five interrow sites in a ridge-tilled corn (Zea mays L.) field, and the soil was mapped as a Nicollet series (fine-loamy, mixed, superactive, mesic, Aquic Hapludoll). The values of _im and estimated by the multiple tracer method compared well with previously measured values using the same technique on the same field. The _im values for the multiple tracer technique were larger than values derived from the basic single tracer technique. The basic single tracer technique did not take into consideration a mass exchange between _im and the mobile water domain (_m). The values were less variable for the multiple tracer method than for the single tracer-variance method. Values of immobile water fraction (_im/) for the multiple and basic single tracer techniques ranged from 0.30 to 0.52 and from 0.24 to 0.35, respectively. The values of for the multiple and single tracer-variance techniques ranged from 0.06 to 0.9 d^-1 and from 0.03 to 60 d^-1, respectively. The volumetric water content () changed considerably over the course of the experiment for the estimation of using the single tracer-variance method; thus, the assumptions of this technique were compromised. The measured values of K(h₀) at the five sites ranged from 0.47 to 1.66 µm s^-1. There was evidence that the basic single tracer method underestimated _im and overestimated _m, because this method considers = 0 during the tracer application.

	INTRODUCTION

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results Conclusion REFERENCES

 
MANY AGRICULTURAL PROBLEMS involve the reactivity and transport of dissolved chemicals in the soil. Chemicals such as fertilizer and pesticide are deliberately added to the soil but may result in significant contamination of the groundwater (Pye et al., 1983). These chemicals can be managed to maximize their effectiveness within the root zone and minimize their transport below the root zone. Chemicals often move preferentially through soil, resulting in a high risk of groundwater contamination. Preferential flow is exemplified by the early breakthrough and long tailing in laboratory column experiments and in field lysimeter experiments (Beven and Germann, 1982; Ressler et al., 1998). The mobile–immobile solute transport model (Coats and Smith, 1964), developed within the field of petroleum engineering, includes preferential flow. This model has been expanded and applied to soil columns (van Genuchten and Wierenga, 1976, 1977; van Genuchten et al., 1977). The mobile–immobile model was also applied to field-scale solute transport by Toride and Leij (1996), who used a stochastic stream tube model.

The mobile–immobile solute transport model separates into _m and _im. The soil solution is stagnant in _im, and advection and dispersion occur in _m. For one-dimensional transport of a noninteracting, conservative solute, the mobile–immobile model can be written as follows:

(1)

where C_m and C_im are the solute concentrations in the mobile and immobile domains, t is time, D_m is the dispersion coefficient for _m, x is distance, and q is Darcy flux. The two domains are connected by a diffusive transfer of chemical at the boundary of _im and _m:

(2)

The diffusive mass transfer is characterized by . The mobile–immobile model can account for more rapid solute transport because flow only occurs in a fraction of total . It can also account for tailing because of the solute exchange between the domains (Eq. [2]).

Values of _im and can be estimated from solute breakthrough curves in laboratory experiments. Matching the observed flux concentrations of tracers in column effluent with concentrations predicted from analytical solutions of the mobile–immobile model results in a set of best-fit solute transport parameters (Parker and van Genuchten, 1984; van Genuchten and Wagenet, 1989; Gamerdinger et al., 1990; Toride et al., 1995). Although the observed and calculated flux concentrations may match closely with this method, the estimated transport parameters may not be a unique set of values. Alternative methods for estimating parameter values are needed so that unique sets of solute transport values can be determined. There also exists a need to estimate these parameters without running extensive column breakthrough experiments. Methods that do not require effluent breakthrough curves to estimate solute transport properties are also useful in estimating these parameters in situ.

Tracer techniques have been proposed for estimating _im and in the field. These methods give an alternative approach for the estimation of _im and without the need for breakthrough curves or solute distribution profiles. These methods are a single tracer method (Clothier et al., 1992, 1995; Angulo-Jaramillo et al., 1996) and a multiple tracer method (Jaynes et al., 1995; Jaynes and Horton, 1998; Casey et al., 1997, 1998; Lee et al., 1996, 1997). The single and multiple tracer methods have been applied in the field and have received limited validation. The multiple tracer method was field tested by Casey et al. (1997) and further laboratory tested by Lee et al. (1996, 1997), the latter of whom used both the breakthrough curve method and the multiple tracer method to estimate _im and in the same aggregated soil columns. In these studies a series of tracers were applied, after which the soil columns were sectioned and analyzed for resident tracer concentrations. The multiple tracer method was used with the resident tracer concentrations to estimate _im and . Lee et al. (1996, 1997) were able to use these estimates to accurately predict solute breakthrough curves and resident concentration profiles in soil columns. The single tracer method has been field tested in several studies (Clothier et al., 1992, 1995; Angulo-Jaramillo et al., 1996) but no laboratory validation has been done.

Both the multiple and single tracer methods are simplifications of the full mobile–immobile model. There exist two separate single tracer methods: the basic single tracer method to estimate _im (Clothier et al., 1992) and the single tracer-variance method to estimate (Clothier et al., 1995). The basic single tracer method used to estimate _im assumes that and that there is no significant solute exchange between _m and _im during the course of the experiment. The single tracer-variance method for estimating does not assume = 0 but that can be measured over a long period of time. The multiple tracer method simultaneously estimates and _im with the assumption that is not negligible. Both single and multiple tracer methods assume that there is piston displacement of tracer within _m and that C_m behind the tracer front is approximated by the input tracer concentration. There are advantages with both of these methods. The basic single tracer method is simple to use when estimating _im and the analytical techniques are not complex; however, the single tracer-variance method is more involved when estimating . Both techniques are capable of simultaneously determining soil hydraulic properties. To date there has not been a critical comparison of the two methods. The objective of this study is to compare the single and multiple tracer methods for estimating and _im of a field soil.

	Materials and methods

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results Conclusion REFERENCES

 
Research took place in a ridge-tilled corn field between 30 August and 14 September 1996 at the Agronomy and Agricultural and Biosystems Engineering Research Center west of Ames, IA. The soil was mapped as a Nicollet series derived from glacial till. Five infiltration sites were located in the interrow areas of adjacent corn rows. The infiltration sites were cleared of corn debris and weeds to ensure suitable hydraulic contact between the infiltrometer disk and the soil surface. Experiments to estimate soil hydraulic properties preceded experiments to estimate the solute transport coefficients _im and .

Near each site a soil core was taken using a beveled brass ring with height 37 mm and diameter 73 mm. These soil cores were used to determine the antecedent and bulk density. A large-base diameter (230 mm, Perroux and White, 1988) tension infiltrometer was filled with a 4-mmol L^-1 solution of KCl and placed on the flat soil surface. Infiltration began at a pressure head of -30 mm and the early cumulative infiltration (I) volumes were automatically recorded every second for the first 100 s. These early I values were later used to calculate sorptivity (S). The infiltrometers were automated with transducers as described by Ankeny et al. (1988). After the first 100 s of cumulative infiltration, the automated recording interval was changed to read every 576 s for 16 h. These later I values were used to determine the steady state infiltration rates (i) according to White and Sully (1987).

To estimate S, early stages of I values were used with the following expression (Philip, 1957; White and Sully, 1987, 1988):

(3)

where t is the infiltration time. Sorptivity was estimated from the slope of the measured I vs. t^1/2, and coefficients of determination were determined for the regression.

To estimate K(h₀), the White and Sully (1987) method was used. White and Sully (1987) derived the following expression for the matrix flux potential ():

(4)

where b is a shape factor between ¹ ₂ and /4, and is the change in during the entire infiltration period. Taking a reasonable approximation for b of 0.55 (Smettem and Clothier, 1989) and substituting Eq. [4] into Wooding's (1968) solution for unconfined steady state infiltration from a disk results in the following expression:

(5)

where R is the base radius of the infiltrometer (115 mm) and h₀ is the pressure head (-30 mm).

After the 4-mmol L^-1 KCl solution had reached steady state infiltration rate, a series of four benzoic acid tracer solutions was applied to each site. The tracer solutions were mixed in the same manner as described by Jaynes et al. (1995) and Casey et al. (1997, 1998). The tracers used were o-trifluoromethylbenzoate; 2,6-difluorobenzoate; pentafluorobenzoate; and 2,3,6-trifluorobenzoate. Tracer application order was randomized to minimize any error caused by nonidentical transport, recovery, and analysis. Each tracer solution was applied using a separate infiltrometer; detailed laboratory experiments have shown that infiltration rates quickly return to steady state after brief removal of a tension infiltrometer (Clothier et al., 1992). The final tracer solution was applied for approximately 1 to 2.5 h so that the tracer front was well beyond the soil sampling depth of 15 mm. Clothier et al. (1995) determined that infiltrating 25 to 30 mm of tracer was sufficient to sample soil 10 to 15 mm deep while well avoiding the tracer front. We used the same criteria as the Clothier et al. (1995) study for tracer application and sampling depth.

Within seconds after the final tracer application the infiltrometer was removed, and the soil was sampled from the area that had been beneath the tension infiltrometer. The infiltration area was sectioned into four equal parts, and eight cylindrical samples (15 mm deep and 10.6 mm diameter) were taken from one of the quarters (Fig. 1) at the same time. The infiltration area was sectioned into four quarters so that sampling disturbance was localized to a single quarter and minimized at the other quarters. The infiltration sites were then covered with plastic and loose soil was spread over the plastic. This was done to prevent water loss by evaporation and infiltration from precipitation. During the course of the experiment there was no precipitation. Approximately 2 d after the start of the tracer application, the soil and plastic sheets were taken off the infiltration sites and eight more soil samples were taken from another quarter of the infiltration site. The soil was then covered again with the plastic and loose soil. This procedure was repeated at approximately 7 d and 15 d after the start of the tracer application. Figure 1 shows the sampling scheme. All soil samples were weighed and placed in plastic zip-lock bags and refrigerated to prevent any loss of tracer or change in .

View larger version (80K): [in this window] [in a new window]   Fig. 1 A diagram of the soil sampling scheme beneath the tension infiltrometer. The soil sampled immediately after the tracer application was used to estimate im and with the Jaynes et al. (1995) method, and to estimate im with the Clothier et al. (1992) method. All sampling dates were used to estimate with the Clothier et al. (1995) method. The sampling dates immediately after the final tracer application, 0, 2, 7, and 15 d, correspond to the numerals, 0, 2, 7, and 15 within the white circles, respectively

Analysis for the fluorobenzoate tracers was done on a Dionex Series 4500i ion chromatograph (Dionex, Sunnyvale, CA) as described by Bowman and Gibbens (1992). For the fluorobenzoates, a SAX column (Regis Chemical Co., Morton Grove, IL)¹ was used with 230 mM KH₂PO₄, adjusted to a pH of 2.65 with H₃PO₄ and 20 mL L^-1 acetonitrile as the eluting solution. The flow rate was 1 mL min^-1 and the detection wavelength was set to 205 nm.

Extracted tracer concentrations from the soil sampled immediately after the tracer application were used to estimate _im and with the modified Jaynes et al. (1995) method (Casey et al., 1997; Jaynes and Horton, 1998):

(6)

where C is the measured tracer concentration from the extract, C₀ is the tracer concentration from the input tracer solution, t is tracer application time, and is the soil sampling depth. It is assumed that when the soil is sampled. Plotting ln(1 - C/C₀ ) as a function of t should result in a straight line with the intercept of [ln(_im/) + _m/(_imq)] and the slope -/_im (Fig. 2) . Since _im is in both the intercept and slope, a least squares optimization has to be done to estimate and _im.

View larger version (20K): [in this window] [in a new window]   Fig. 2 Regressions of the ln(1 - C/C0) vs. time used by the Jaynes et al. (1995) method to estimate im and at each site. The slope gives -/im and the intercept gives ln(im/) + m/(imq)

(7)

Equation [7] is identical to Eq. [6] if is zero. Extracted tracer concentrations that were used to estimate _im from Eq. [7] were of the longest applied tracer in the series. The basic single tracer method assumed for the entire tracer experiment, so it should not have mattered which tracer we chose. However, to diminish concern that the assumption that was not being violated, we chose to use to final tracer in the series. The longer the tracer was applied the higher the probability that was true.

Clothier et al. (1995) proposed a single tracer-variance method to estimate by measuring the variance of tracer concentration over time. First, Clothier et al. (1995) analytically expressed the decrease of C_m through time:

(8)

and the simultaneous increase of C_im through time:

(9)

where C* is the equilibrium tracer concentration when as t approaches infinity. Finally, Clothier et al. (1995) developed the following expression to predict the normalized variance in tracer concentration under the infiltrometer through time:

(10)

where is the predicted normalized variance in the soil samples over time. The temporal decline in [C_m(t) - C*] and [C_im(t)] incline in [C_im(t) - C*] can be found using the analytical expressions of Eq. [8] and Eq. [9]. At the time the soil is first sampled it is assumed that the values of and the value of . Also, the values for _m and _im that were used in Eq. [8], [9], and [10] came from Eq. [7].

The variance of each of the tracer concentrations from each application site was determined at approximately 0, 2, 7, and 15 d after the tracer infiltration. The time at 0 d was the time the first tracer was applied, and the first sampling occurred at the completion of the last tracer infiltration. The following expression was used to determine the sample variance (s²) of the tracer concentrations (Steel and Torrie, 1980):

(11)

where n is the number of the soil samples (n = 8), and is the mean value of the n samples. The sample variance values from Eq. [11] were normalized by dividing through by the initial sample variance, s²₀, calculated from all of the tracers. This approach for estimating assumed that the soil samples that were taken from the infiltration site were either sampled from _m or _im (Clothier et al., 1995).

All four tracers were used in estimating the measured values. The tracers were assumed to move through the soil identically, and the tracers were applied at different times. Each tracer was used to estimate an value. Figure 3 shows the observed values (Eq. [11]) from all four tracers and corresponding model curves that were calculated from Eq. [10]. To calculate Eq. [10] it was necessary to calculate C_m(t) and C_im(t) values which were calculated using Eq. [8] and Eq. [9], respectively. The varying calculated values from Eq. [10] were obtained by using various values, which are reported in Fig. 3.

View larger version (33K): [in this window] [in a new window]   Fig. 3 The predicted and measured normalized sample variance as a function of time elapsed from the start of the tracer application for each site. Here the predicted values next to the curves are derived from Eq. [10]. Note that measured values that were >1 were excluded from Site 2 on the second sampling date and from Site 4 and 5 on the last sampling date

Values of _im/ and from this study were compared with the Casey et al. (1997) study using a one-way ANOVA at a 0.05 significance level (Steel and Torrie, 1980, p. 64, 137–167).

	Results

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results Conclusion REFERENCES

 
Soil Hydraulic Properties
The first objective of this study was to estimate the hydraulic properties of the soil at -30 mm pressure head; these values are presented in Table 1 for the five measurement sites. The coefficients of determination for the estimation of S that used the early time infiltration data ranged from 0.77 to 0.99 with a mean of 0.87. Estimations of K(h₀) from the longtime steady state infiltration data using the White and Sully (1987) method were reasonable and fell within the ranges that others have found in soils near this research area (Logsdon and Jaynes, 1996; Logsdon, 1993). Under similar tillage systems and time of the season, Logsdon and Jaynes (1996) found the mean K(h₀) values at to be 4.52 µm s^-1 with a plus or minus one standard deviation range of 1.81 to 10.70 µm s^-1. These values are slightly higher than the values reported in the present study. Also, Logsdon (1993) found K(h₀) values in similar soils to range from 0.67 to 2.2 µm s^-1, which were similar to our values (Table 1).

The median values for Sites 1, 2, 3, 4, and 5 were 0.6, 0.9, 0.3, 0.7, and 0.1 d^-1, respectively. The variances of values were low, ranging from 2.5 x 10^-5 d^-2 at Site 5 to 0.4 d^-2 at Site 2. The values from this study were not significantly different from the Casey et al. (1997) study at a 5% level.

Single Tracer Methods
The estimates of _im that used the basic single tracer method for Sites 1, 2, 3, 4, and 5 were 0.10, 0.15, 0.10, 0.14, and 0.10 m³ m^-3, respectively. The variances of _im values ranged from 1.0 x 10^-4 m⁶ m^-6 at Site 1 to 2.1 x 10^-5 m⁶ m^-6 at Site 2, which was lower than the variance values estimated by the multiple tracer method. The _im/ values estimated by the basic single tracer technique were 0.24, 0.35, 0.26, 0.33, and 0.24 for the respective Sites 1, 2, 3, 4, and 5.

Although the exact same soil samples were used, the estimates of _im and _im/ from the single tracer method were lower than the estimates from the multiple tracer method. The single tracer method assumes that the tracer enters the soil surface and moves through _m exclusively. The single tracer technique assumes that ; therefore, there is no mass exchange between _im and _m and no accumulation of tracer in _im. If , then the concentration of the tracer should not change through time, which is contrary to the negative slopes shown for the ln(1 - C/C₀) vs. t function (Fig. 2). Clothier et al. (1995) expressed concern that some of their samples did not reach final concentration due to dispersion. As a result Clothier et al. (1995) recommended that a tracer should infiltrate to depths of 25 to 30 mm for soil samples taken to the 10 to 15 mm depth. This sampling criterion was exceeded in this study. Since the Clothier et al. (1995) sampling recommendation was exceeded, it is less likely the tracer concentrations changed with time because of dispersion rather than as a consequence of . The Clothier et al. (1995) recommendation is supported by several studies showing that dispersion approaches zero close to the solute application source at the soil surface (Yates, 1992; Gimmi, 1994). Our soil samples were taken at a shallow depth so that the effect of dispersion approached zero. A likely explanation of the increase in tracer concentration through time in Fig. 2 [i.e., decrease of ln(1 - C/C₀) vs. t] was diffusion of tracer into _im.

Assuming does not appear realistic. For instance, using of 0.5 d^-1, as estimated by Clothier et al. (1995), a measurable diffusion of solute into _im occurs within a few hours (Jaynes and Horton, 1998). Ignoring this diffusion with the basic single tracer method leads to an underestimation of _im/. As a demostration, C_im was calculated using CXTFIT 2.0 (Toride et al., 1995) with values from the multiple tracer method (Eq. [6]). Figure 4 shows the relative C_im as a function of time and indicates appreciable accumulation of tracer in _im at the time of the first soil sampling. This gives further evidence for the underestimation of _im with the basic single tracer method.

View larger version (27K): [in this window] [in a new window]   Fig. 4 The calculated relative tracer concentration in the immobile domain as a function of time. Relative immobile tracer concentrations were calculated using CXTFIT 2.0 (Toride et al., 1995), and values were obtained from the multiple tracer method

The calculated values did not decrease with time as the assumptions of this method predict. Furthermore, the spread of values between the tracers at each sampling date did not diminish with time (Fig. 3). Values of even went above one for Site 2 on the second day of sampling and again at Sites 4 and 5 on the last day of sampling. The values that were >1 were excluded when we created Fig. 3.

The single tracer-variance method requires constant throughout the course of the experiment to estimate (Clothier et al., 1995). Although the infiltration areas were covered by plastic and loose soil between each of the sampling periods, values decreased either from lateral distribution, drainage, condensation on the plastic, or transpiration during the experiment (Fig. 5) . An increase in tracer concentration over time at some of the sites was measured and was consistent with the occurrence of transpiration. Corn plants may have drawn soil water from the experimental volume and concentrated the tracer. The large decrease in during the 15-d period compromised the single tracer-variance method and probably added variability in the tracer concentration with time. During the first two sampling dates the mean values changed the least: 20%; but there still was no consistent decrease in values within the first 2 d. We speculate that the variation in for the first two sampling dates was caused by the wetting properties of the soil as affected by the interface with the infiltrometer base, not by the exchange of tracer between _m and _im. Clothier et al. (1995) showed the same disagreement between the single tracer-variance model and their measured values but attributed the disagreement to advective transport. As a rule, the multiple tracer method fit the C data better than the single tracer-variance method.

View larger version (17K): [in this window] [in a new window]   Fig. 5 Soil volumetric water content as a function of time

	Conclusion

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results Conclusion REFERENCES

 
Two single tracer (basic and variance) methods and a multiple tracer method have been proposed for the estimation of the mobile–immobile model transport parameters and _im, but they have not been used on the same site. By using these methods at one site, we estimated the hydraulic parameters along with the solute transport parameters. The multiple tracer method consistently gave _im values that were larger than those given by the basic single tracer method, and we attributed this result to an invalid assumption of used in the basic single tracer method. The single tracer-variance method for estimating was less practical than the multiple tracer method because it took a long time and was less consistent with the measured data. The single tracer-variance method gave biased estimates of because of decreasing soil water during the test period.

	ACKNOWLEDGMENTS

 
This material is based upon work supported by the CSREES-USDA under agreement 94-37102-01906.

	NOTES

TOP NOTES ABSTRACT INTRODUCTION Materials and methods Results Conclusion REFERENCES

 
Journal Paper J-17829 of the Iowa Agriculture and Home Economics Exp. Stn., Ames, IA, Project no. 3287, with support by Hatch Act and state of Iowa funds.

¹ Names are necessary to report factually on available data; however, the USDA neither guarantees nor warrants the standard of the product, and the use of the name by USDA implies no approval of the product to the exclusion of others that may be suitable.

Received for publication May 8, 1998.

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