Hydrological Processes Hydrol. Process. 12, 1939±1949 (1998)
Temporal variability of solute transport under vadose zone conditions 1
B. Lennartz1* and S. K. Kamra2 Institute for Water Management and Landscape Ecology, Olshausenstr. 40, 24118 Kiel, Germany 2 Central Soil Salinity Research Institute, Karnal Ð 132002, India
Abstract: The heterogeneity of the solute ¯ux ®eld in the horizontal plane at the ®eld scale has been documented in several ®eld studies. On the other hand, little information is available on the persistence of certain solute transport scenarios over consecutive in®ltration cycles. This study was initiated to analyse the recurrence of solute leaching behaviour as estimated in two soil column tests emphasizing the preferential ¯ow phenomenon. Twenty-four small-sized soil samples were subjected to two consecutive unsaturated steady-state ¯ow leaching experiments with bromide as tracer. Observed breakthrough curves (BTCs) were analysed by the method of moments and by the advection±dispersion equation (ADE) to classify solute behaviour. Frequency distributions of the parameters indicating the solute velocity were heavily skewed or bimodal, re¯ecting the broad variability of the leaching scenarios, including some with pronounced preferential solute breakthrough. Exclusion of the preferential ¯ow columns from our calculations revealed an average amount of 37% of immobile water. The large-scale BTCs derived from assembling the individual concentration courses of each run showed similar features, such as an early bromide breakthrough. However, two distinct apices, viz. one preferential and one matrix, were observed only in the ®rst run, whereas the concentration decrease between the peaks was missing from the second run. A change in soil structure with continuous leaching was presumed to modify the interplay of the various ¯ow domains, thereby altering the spreading of the BTCs. Correlation analysis between parameters of both tests suggests that preferential transport conditions are likely to occur at the same locations in the ®eld over several in®ltration cycles, whereas the `classical' or expected matrix ¯ow is time variant and therefore seems to be hardly predictable. # 1998 John Wiley & Sons, Ltd. KEY WORDS
solute transport; temporal variability; preferential ¯ow
INTRODUCTION The heterogeneity of ¯ow and solute transport of the vadose soil zone has been widely recognized. Field methods, such as soil coring and extraction of the soil solution by suction soil solution samplers, and laboratory analysis of soil columns have often revealed the occurrence of preferential solute transport as a dominant process driving solute mobility in soils, secondary to the expected soil matrix ¯ow regime (Roth et al., 1991; Van Weesenbeck and Kachanoski, 1991; Ward et al., 1995). Heterogeneous ¯ow ®elds with widely dierent solute velocities may be interpreted in terms of the stochastic stream tube model. Within this concept, the soil is considered to be comprised of individual, non-interacting soil columns. All columns are described by a common set of transport laws but the individual columns have dierent values for the model parameters (Dagan and Bresler, 1979; Jury and Roth, 1990). Assembly of the results across the individual * Correspondence to: B. Lennartz, Institute for Water Management and Landscape Ecology, Olshausenstr. 40, 24118 Kiel, Germany. Email address: B. Lennartz (
[email protected]). CCC 0885±6087/98/121939±11$1750 # 1998 John Wiley & Sons, Ltd.
Received 21 October 1997 Accepted 22 November 1997
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(local) measurements depicts the `large-scale' or `®eld-scale' solute transport process (Van Wesenbeeck and Kachanoski, 1991; Sassner et al., 1994). Breakthrough curves (BTCs), the response signal of a speci®c soil volume to a short tracer pulse, as monitored at a certain soil depth, of both the individual samples and the assembled columns, may be regarded as results of intrinsic soil properties and, as such, as time invariant. Time invariance of solute transport features may be assumed providing that extrinsic factors such as the rainfall rate vary within certain limits. Notwithstanding the large body of data from ®eld and laboratory investigations on solute migration in soils, only a small number of studies have explored the change of ¯ow and transport pathway systems with time. The persistence of preferential ¯ow pathways over subsequent in®ltration cycles, such as those caused by wetting front instabilities, has been reported by Glass et al. (1989). Buchter et al. (1995) have found, on examining 19 individual outlets from a large soil monolith, that the pore water velocities, dispersion coecients and dispersivities of two consecutive runs are highly correlated. From a ®eld test on the seasonal scale, Lennartz et al. (1998) have concluded that preferential solute transport is an intrinsic soil property but not necessarily the predominant mechanism governing non-reactive tracer movement. Column tests of the time variance of solute transport by using multiple samples have, to our knowledge, not been conducted to date. The present study was therefore initiated to analyse ®eld-scale solute movement by means of bromide leaching studies in small undisturbed soil columns, and the subsequent averaging of measured local BTCs. Two consecutive leaching tests were compared with respect to large-scale concentration curves and to the solute transport parameters to study the persistence of solute transport features as captured in small soil samples. Additional information on the ®eld-scale solute transport process was expected from the analysis of variance of the assembled BTCs. METHODOLOGY Twenty-four undisturbed soil samples, 5.7 cm in diameter and 10 cm long, were collected from a soil depth of 5 to 15 cm, on a regular grid with a 15 m spacing. Sampling started by carefully removing the top 5 cm of soil and subsequently inserting sharp-edged, stainless steel cylinders vertically into the soil. Soil cores were excavated and sealed at the lower and upper end with polyethylene caps for safe transport to the laboratory. Bulk soil samples were taken in the vicinity of the cylinders to determine classical soil physical and chemical parameters. Textural analysis revealed a mean sand, silt and clay content of 63.3, 26.2 and 10.3%, respectively. The soil type was classi®ed as crumbed structured loamy sand. Bulk density was 1.53 g cm73. The site was not ploughed for four years prior to sampling, allowing the soil to develop a natural structure. All 24 samples were mounted simultaneously on an apparatus similar to that described by Rambow and Lennartz (1993) in order to perform displacement experiments under water-unsaturated ¯ow conditions. This set-up facilitates the simulation of a broad range of ®eld conditions relating to rainfall characteristics and soil water tension for studies of the leaching behaviour of soil-applied chemicals. Vertical downward ¯ow was induced by applying suction at the lower end of the samples. The soil surface was subjected to atmospheric pressure; rainfall was applied via a sprinkler consisting of four hypodermic needles. Each of the two consecutive leaching tests started with the adjustment of the ¯ow regime for 2 days. A pressure of ÿ3 kPa was applied to the lower end of the ®eld-wet samples and was maintained throughout both runs. After 6 h, rainfall was initiated at a rate of 8.9 and 7.6 mm per day for tests 1 and 2, respectively. Flow conditions were adjusted according to tensiometer and water content observations on large soil monoliths taken from the same site (results not shown here, Meyer-Windel et al., 1996) to obtain unit water pro®les within the samples. Because of small variations in applied rain between individual columns and because of minor constructional dierences in, for instance, hose lengths and diameters of the irrigation system, ¯ow rate was determined individually for each sample via the column out¯ow volume. After 2 days of equilibration of steady-state ¯ux, potassium bromide was applied pulse-wise with a surface density of rA 0.04 mg cm72 in both runs. The leachate of each column was fractionated at 4 h intervals during early stages of the study and at # 1998 John Wiley & Sons, Ltd.
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8 h intervals during the remaining experimental period. The percolate was analysed for bromide by ion chromatography with a conductivity detector. Irrigation was stopped for 5 days between tests 1 and 2 and evaporation was allowed by removing the sprinkler from the columns. The leaching test failed in one column in test 2, because of technical problems; data analysis of test 2 was therefore con®ned to 23 samples. DATA TREATMENT The observed individual bromide breakthrough curves (BTCs) were analysed by the method of temporal moments and by the advection±dispersion equation (ADE) to classify solute behaviour. Time moments analysis is a statistical technique for characterizing the BTCs without bias towards a speci®c transport model (Skopp, 1985). In dimensionless form, the temporal moments, Mp , are de®ned as Z1 T p C
Z; T=C 0 dT p 0; 1; 2; . . .
1 Mp 0
where Z is the dimensionless space coordinate, T is the dimensionless time expressed as pore volumes (T vtz71), v is the pore water velocity (LT71), t is the time, z is the column length (L) and C and C0 are the solute concentrations in the liquid phase and of the in¯uent solute pulse respectively (ML73). The superscript p is the order of the moment. The zeroth moment, M0 , equals the mass of solute eluted from the column, whereas the ®rst and second moments can be used to characterize the mean and the variance. In addition to the absolute moments de®ned above, normalized, m0p , and central moments, mp , are often used. 0
mp M p =M 0 Z1 1 0 p
T ÿ m1 C
Z; T=C 0 dT mp M0 0
2 p 0; 1; 2; . . .
3
The ®rst normalized moment, m01 , yields the mean breakthrough time. The second central moment, m2 , quanti®es the variance, i.e. a measurement of the average spread of the BTC relative to the mean breakthrough time. Experimental moments m01 and m2 of the individual columns were determined by numerical integration of the integral in Equations (1)±(3) using the trapezoidal rule. The classical ADE is a mechanistic model approach that characterizes solute transport in terms of passive mass ¯ow and dispersion @c @2 c @c RD 2ÿv @t @z @z
4
where D(L2T71) denotes the dispersion coecient from which, for comparison purposes, the dispersivity, l D/v(L), and the dimensionless column Peclet number, P vz/D, may be calculated. The retardation factor, R 1 rKD/Y, where r is the bulk density of the soil (ML73), Y the volumetric soil water content (L3L73) and KD the equilibrium adsorption constant (L3M71), is dimensionless and should be unity for nonreactive solutes (KD 0). The analytical solution of the model as presented by Van Genuchten and Alves (1982) was used in conjunction with a non-linear, least-square, curve-®tting programme assuming initial and boundary conditions as described by Parker and Van Genuchten (1984) to estimate the two model parameters v and D. The ratio of measured and ®tted pore water velocity, called the solute mobility index here, MI v/v®t , quanti®es the amount of soil water participating in transporting solutes. Theoretically, MI should be close to 1 but, experimentally, it has been manifoldly shown that only part of the gravimetrical water content participates in transporting solutes, resulting in MI values of less than 1 (e.g. Schulin et al., 1987; Seyfried and Rao, 1987; Lennartz and Meyer-Windel, 1995). Extreme cases of up to a range of # 1998 John Wiley & Sons, Ltd.
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MI 0.1 have been classi®ed as preferential ¯ow situations, although no valid concept exists to separate `normal' ¯ux regimes with mobile and immobile water regions from those having more than 80±90% stagnant soil water (Lennartz et al., 1998). The ®tting procedure failed in one case of test 1, because of the double peak shape of the measured concentration course. The coecient of determination was less than 0.6, so that the parameter values obtained were not considered in the succeeding analysis. RESULTS AND DISCUSSION Individual BTCs
A respective average pore water velocity (coecient of variation, CV) of 2.71 cm d71 (18%) and 2.38 cm d71 (14%) resulted from the induced rainfall regime for tests 1 and 2. The corresponding volumetric water content was 0.33 (8%) and 0.32 (8%), and the mean bromide recovery rate was 88 and 86% with a CV of 9.2 and 8.6%, for tests 1 and 2, respectively. The small dierences in ¯ow regimes and bromide recovery justi®ed comparison of the two leaching experiments. Individual breakthrough curves resulting from the steady-state ¯ux conditions of the two tests re¯ected a large and irregular variability in solute transport properties, including some having typical features of preferential ¯ow, such as early breakthrough and extensive asymmetry (Figure 1). As a consequence, frequency distributions of the transport parameters indicating the solute velocity (MI and m01 were either bimodal or heavily skewed (Figure 2). From the transport parameters of each evaluation method, it was evident that the number of samples showing pronounced preferential transport behaviour decreased from test 1 to test 2. All frequency distributions were tested for normality by using the Kolmogorov±Smirnov normality test (Table I). The normality (null) hypothesis was not rejected at the level of signi®cance of p 0.2. None of the parameter values obtained from the ADE analysis were normally distributed; logarithmic transformation led to normal distributions for the dispersion coecients only (Table I). Conversely, the moment method yielded parameter values for tests 1 and 2 that were normally distributed, with exception of the m01 values of test 1. Table I. Descriptive statistics of the computed model parameter values MI and D (ADE) and of the ®rst normalized, m01 , and second central moment, m2 , of BTCs from tests 1 and 2, n 23, and the Kolmogorov±Smirnov criterion D MI1 D1 MI2 D2 log(MI1) log(D1) log(MI2) log(D2) m10 1 m21 log(m10 1) log(m21) m10 2 m22 log(m10 2 ) log(m22)
Mean
Median
Min.
Max.
SD
CV(%)
0.53 2.38 0.51 6.84 ÿ0.37 0.28 ÿ0.34 0.66 0.55 0.05 ÿ0.29 ÿ1.33 0.59 0.09 ÿ0.25 ÿ1.07
0.62 1.51 0.60 3.02 ÿ0.21 0.18 ÿ0.23 0.48 0.62 0.05 ÿ0.21 ÿ1.32 0.62 0.08 ÿ0.21 ÿ1.09
0.08 0.85 0.10 1.50 ÿ1.12 ÿ0.07 ÿ1.02 0.18 0.17 0.02 ÿ0.78 ÿ1.65 0.19 0.04 ÿ0.71 ÿ1.38
0.77 7.49 0.71 22.94 ÿ0.12 0.87 ÿ0.15 1.36 0.74 0.12 ÿ0.13 ÿ0.93 0.74 0.13 ÿ0.13 ÿ0.90
0.24 1.90 0.19 6.73 0.36 0.28 0.23 0.39 0.18 0.02 0.20 0.15 0.14 0.02 0.14 0.11
45 80 37 98 ÿ96 99 ÿ70 59 32 38 ÿ69 ÿ11 25 25 ÿ56 ÿ11
D 0.3* 0.28* 0.28* 0.25{ 0.39{ 0.21x 0.32* 0.2x 0.27{ 0.15x 0.31* 0.12x 0.19x 0.14x 0.27* 0.11x
* p 5 0.05. { p 5 0.1. x Null hypothesis is not rejected at the 0.2 level of signi®cance ( p). { p 5 0.01. # 1998 John Wiley & Sons, Ltd.
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Figure 1. Individual bromide breakthrough curves of tests 1 and 2. Bromide concentrations were normalized with the surface density of the applied bromide
The descriptive statistics of all the parameter values are summarized in Table I. Only small dierences were observed between the average solute velocity of tests 1 and 2, irrespective of the method of determination. The median of the MI and m01 distributions was similar in both tests. On the contrary, the spreading of the individual BTCs as characterized by the dispersion coecients and m2 values, was more pronounced in test 2. Consequently, the mean dispersivity, l, increased from 0.88 to 2.87 cm, and the average Peclet number, P, decreased from 11.4 to 3.5 from test 1 to test 2. Slight changes in the pore system caused by internal erosion processes during continuous leaching might have increased the dispersivity and thereby the shape of the BTCs. The observed average solute breakthrough of both tests at MI, m01 054 re¯ects the presence of # 1998 John Wiley & Sons, Ltd.
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Figure 2. Frequency distributions of the model parameter values MI and D and of the ®rst normalized moment m01 and the second central moment m2 of tests 1 and 2 # 1998 John Wiley & Sons, Ltd.
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stagnant water regions. Assuming a pure advective±dispersive ¯ow regime with a 100% participation of the soil water, the bromide breakthrough peak should occur at 1 pore volume; this would result in MI and m01 values of close to unity. The exclusion of ®ve preferential BTCs from the calculations yielded a mean breakthrough at (MI, m01 0.64 and 0.62 pore volumes for runs 1 and 2, respectively. Neglecting other processes, such as anion exclusion, an average amount of 37% of stagnant soil water may be calculated for the two experiments. This value, although large, con®rms previous studies on unsaturated substrates (Gaudet et al., 1977; De Smedt and Wierenga, 1984; Bond and Wierenga, 1990; Booltink and Bouma, 1991; Caron et al., 1996). Large-scale BTCs The individual BTCs of both tests were assembled by computing arithmetic average concentrations to represent the large-scale or ®eld-scale solute transport process. The computed bromide courses are depicted in Figure 3. Each BTC is dominated by an early ®rst occurrence of the solute. However, only the bromide course of test 1 exhibits two distinct apices. The concentration decrease between the preferential and the matrix peak is not visible in test 2. In addition, the desorption branch of the test 2 BTC has a greater tailing compared with the BTC of test 1. Two dierent ¯ow situations may have caused the change from solute breakthrough behaviour with two apices to that with one broad peak. When the soil water is separated into one preferential and one matrix ¯ow domain, with the advective±dispersive transport law governing solute movement in each phase (Gerke and Van Genuchten, 1993), then separation between the breakthrough peaks becomes less visible, if the borders between the two regions become less eective, because of an increasing solute transfer between both domains. Assuming the soil water not to be comprised of two ¯ux regions but of many, each representing a pore size class as suggested by Durner and FluÈhler (1996), and given that lateral solute exchange between domains does not take place, a two-peak BTC would result when only certain pore sizes, namely the small and the large, contribute to transport, whereas the remaining, middle-sized, pore classes are ineective. With each additional domain that is switched into the solute transport process, the dispersivity increases and the separation between a fast and slow transporting region becomes less pronounced. The coecient of variation of the mean concentrations of both large-scale BTCs (Figure 4) shows a similar development with time. Large values during early stages of the test indicate the uncertainty of the preferential breakthrough peak. During the matrix peak, the CV remains at a low level of about 50%. This value is small compared with the results of Sassner et al. (1994) who have reported a CV value of 100% during the appearance of the matrix peak of an assembled chloride BTC.
Figure 3. Large-scale bromide breakthrough curves of both tests as derived from assembling the individual bromide courses # 1998 John Wiley & Sons, Ltd.
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Figure 4. Large-scale bromide breakthrough curves together with the coecient of variation (%) of the mean concentrations
Time invariance of solute transport regimes The continuity of the transport regimes over two consecutive in®ltration cycles was tested by computing simple Pearson correlation coecients for all estimated transport parameter values and only for those obtained for the non-preferential ¯ow columns (NPFC) (Table II). A threshold of MI, m01 4 035 was chosen to separate the NPFC from the samples with preferential ¯ow features. The relationship between the mobility parameters of both leaching runs (MI, m01 is illustrated in Figure 5. The correlation analysis was con®ned to 22 and 23 observations for the ADE and moment parameters, respectively, as mentioned in the Methodology section. From the scatter plots (Figure 5), it is evident that the calculated positive correlation coecients for the MI and m01 parameters have to be interpreted carefully. Large coecients resulted from two separated groups of observation points and not from a data population equally distributed over the measurement range. The observed correlations are therefore not valid for the entire data set, although they indicate that the preferential ¯ow features remained within the same columns, suggesting that extreme transport situations are con®ned to speci®c locations in the ®eld. # 1998 John Wiley & Sons, Ltd.
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Table II. Pearson correlation coecients among parameter values of tests 1 and 2, NFPC non preferential ¯ow columns n 22
NPFC, n 18
MI1
D1
MI1
MI2 D2
0.84* ÿ0.90*
ÿ0.71* 0.81*
0.36 ÿ0.13
m10 2 m22
m10 1 0.70* ÿ0.09
m21 ÿ0.17 0.23
NPFC, n 19 m10 1 m21 ÿ0.67{ ÿ0.72 ÿ0.10 0.20
n 23
D1 0.42 0.39
* At p 0.001. { At p 0.01.
Figure 5. Parameter values indicating solute mobility of test 1 against those of test 2
Omission of the preferential ¯ow columns (PFC) from the statistical analysis yields a reverse relationship in the case of the m01 parameters and no relationship at all in the case of the MI values (Table II). A negative relationship of the solute velocity expressed as the ®rst normalized moment among the two consecutive leaching runs is hardly interpretable in a physical manner. The negative correlation coecient is presumably a random result. Correlation results between the MI and m01 parameters obtained with the NPFC indicate that the transport regime with breakthrough apices at around 0.6±0.7 pore volumes of euent is not recurrent. The ¯ow system is dynamic with respect to time, within certain limits. With every new in®ltration cycle, a new ¯ow path system with a new solute ¯ux velocity is established, and only regions with preferential ¯ux features retain their status. SUMMARY AND CONCLUSIONS Twenty-four small-sized soil samples were subjected to two consecutive leaching tests under unsaturated ¯ow conditions with bromide-traced water. The established steady-state ¯ow regime was similar in both runs, although irrigation was stopped for ®ve days between the two tests. The observed breakthrough curves (BTCs) were analysed by the method of temporal moments and by the classical advection±dispersion equation (ADE). # 1998 John Wiley & Sons, Ltd.
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The individual BTCs of both runs re¯ected a broad range of transport scenarios, including some with pronounced preferential ¯ow, con®rming that extreme transport situations are not con®ned to water saturation nor to transient ¯ow conditions. Mean breakthrough times of the non-preferential ¯ow columns (NPFC), as calculated from both evaluation methods, indicated an average of 37% immobile water for the two tests. An increase in the mean values of the parameters accounting for the spreading of the BTCs from test 1 to test 2 was assigned to a rearrangement of the soil structure, presumably caused by internal erosion processes. The large-scale solute transport process, as derived from assembling the individual BTCs, exhibited similar features, such as the early occurrence of bromide in both tests. However, only two distinct breakthrough peaks were observed during the ®rst run, whereas the second had one broad apex. In terms of model concepts, it is believed that the borders of ¯ow domains become ineective with continuous leaching, because of an increasing solute exchange between phases or because of additional pore classes participating in solutes transport. The soil structure is not rigid but changes during in®ltration and thereby modi®es the interplay and borders of ¯ow domains. Correlation analysis between transport parameters has revealed that preferential ¯ow occurs predominantly at the same locations in the ®eld over several in®ltration cycles. The expected, normal, classical or matrix solute movement, however, is time variant and, as such, should be predicted in terms of probability density functions only.
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Skopp, J. 1985. `Analysis of solute movement in structured soils', in Bouma, J. and Raats, P. A. C. (eds), Proc. ISSS Symposium on Water and Solute Movement in Heavy Clay Soils. ILRI, Wageningen, The Netherlands. pp. 220±228. Van Genuchten, M. Th. and Alves, W. J. 1982. `Analytical solutions of the one-dimensional convective±dispersive solute transport equation', Tech. Bull. No. 1661. US Dept of Agriculture, Salinity Lab, Riverside. 151 pp. Van Weesenbeck, I. J. and Kachanoski, R. G. 1991. `Spatial scale dependence of in situ solute transport', Soil Sci. Soc. Am. J., 55, 3±7. Ward, A. L., Kachanoski, R. G., von Bertoldi, A. P., and Elrick, D. E. 1995. `Field and undisturbed column measurements for predicting transport in unsaturated layered soil', Soil Sci. Soc. Am. J., 59, 52±59.
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