A field experiment with variable-suction multi-compartment samplers to measure the spatio-temporal distribution of solute leaching in an agricultural soil

Solutes spread out in time and space as they move downwards from the soil surface with infiltrating water. Solute monitoring in the field is often limited to observations of resident concentrations, while flux concentrations govern the movement of solutes in soils. A recently developed multi-compartment sampler is capable of measuring fluxes at a high spatial resolution with minimal disturbance of the local pressure head field. The objective of this paper is to use this sampler to quantify the spatial and temporal variation of solute leaching below the root zone in an agricultural field under natural rainfall in winter and spring. We placed two samplers at 31 and 25 cm depth in an agricultural field, leaving the soil above undisturbed. Each sampler contained 100 separate cells of 31 × 31 mm. Water fluxes were measured every 5 min for each cell. We monitored leaching of a chloride pulse under natural rainfall by frequently extracting the collected leachate while leaving the samplers buried in situ. This experiment was followed by a dye tracer experiment. This setting yielded information that widely surpassed the information that can be provided by separate anionic and dye tracer trials, and solute transport monitoring by coring or suction cups. The detailed information provided by the samplers showed that percolation at the sampling depth started much faster (approximately 3 h after the start of rainfall) in initially wet soil (pressure head above − 65 cm) than in drier soil (more than 14 h at pressure heads below − 80 cm). At any time, 25% of the drainage passed through 5–6% of the sampled area, reflecting the effect of heterogeneity on the flow paths. The amount of solute carried by individual cells varied over four orders of magnitude. The lateral concentration differences were limited though. This suggests a convective–dispersive regime despite the short vertical travel distance. On the other hand, the dilution index indicates a slight tendency towards stochastic–convective transport at this depth. There was no evidence in the observed drainage patterns and dye stained profiles of significant disturbance of the flow field by the samplers.     

Leaching of mecoprop and dichlorprop in calcareous soil. Effect of the exogen organic matter addition in this process.

Leaching studies of mecorprop (R,S)-2-(4-chloro-2-methylphenoxy)propanoic acid, and dichlorprop, (R,S)-2-(4-chloro-2,4-dichlorophenoxy) propanoic acid, under saturated conditions were conducted in unamended and amended soil columns. The purpose of the study was to investigate the leaching of these herbicides in three type of soils and the exogen organic matter effect on this process. The leaching patterns could be related to variation in the soil texture and diffusion processes of the herbicides into micropores within the walls of conducting pore. The leaching rate in the amended soil columns decreased with the addition of organic matter. The breakthrough curves (BTC) of these herbicides in the leachates of the amended soil columns were wider and more diffused than the BTC obtained for the corresponding unamended soil. The theoretical BTC overestimated the pore volume required for the displacement of these pesticides from the soil column. This may be due to the differences in the adsorption process between the bacth and soil columns methods.     

Leaching of mecoprop and dichlorprop in calcareous soil. Effect of the exogen organic matter addition in this process

Abstract

Leaching studies of mecorprop (R,S)‐2‐(4‐chloro‐2‐methylphenoxy)propanoic acid, and dichlorprop, (R,S)‐2‐(4‐chloro‐2,4‐dichlorophenoxy) propanoic acid, under saturated conditions were conducted in unamended and amended soil columns. The purpose of the study was to investigate the leaching of these herbicides in three type of soils and the exogen organic matter effect on this process. The leaching patterns could be related to variation in the soil texture and diffusion processes of the herbicides into micropores within the walls of conducting pore. The leaching rate in the amended soil columns decreased with the addition of organic matter. The breakthrough curves (BTC) of these herbicides in the leachates of the amended soil columns were wider and more diffused than the BTC obtained for the corresponding unamended soil. The theoretical BTC overestimated the pore volume required for the displacement of these pesticides from the soil column. This may be due to the differences in the adsorption process between the bacth and soil columns methods     

Use of lysimeters to estimate leaching of pesticides in agricultural soils

In this review of lysimeters, different aspects concerning soil-filling technique, lysimeter size and materials, and drainage-system type are discussed. The placement of lysimeters in the field is dealt with, as are other types of field measurements that can provide complementary information. Evaluations of various properties are based on the assumption that the lysimeters are to be used for estimating pesticide leaching. Guidelines for use in designing a suitable lysimeter experiment for this purpose are described, with special emphasis placed on using the results as a basis for pesticide registration. In this context, some general recommendations are identified. Concerning the lysimeter itself, stress is placed on the importance of using undisturbed soil monoliths. It is recommended that two soil types, i.e. sand and clay, be used and that the management practices carried out closely resemble normal farming practices. Further recommendations include weekly water sampling, two watering regimes, and use of the normal and double the normal application rate of pesticides.     

Uncertainty in Nonpoint Source Pollution Models and Associated Risks

The usefulness of water quality simulation models for environmental management is explored with a focus on prediction uncertainty. The specific objective is to demonstrate how the usability of a flow and transport model (here: MACRO) can be enhanced by developing and analyzing its output probability distributions based on input variability. This infiltration-based model was designed to investigate preferential flow effects on pollutant transport. A statistical sensitivity analysis is used to identify the most uncertain input parameters based on model outputs. Probability distribution functions of input variables were determined based on field-measured data obtained under alternative tillage treatments. Uncertainty of model outputs is investigated using a Latin hypercube sampling scheme (LHS) with restricted pairing for model input sampling. Probability density functions (pdfs) are constructed for water flow rate, atrazine leaching rate, total accumulated leaching, and atrazine concentration in percolation water. Results indicate that consideration of input parameter uncertainty produces a 20% higher mean flow rate along with two to three times larger atrazine leaching rate, accumulated leachate, and concentration than that obtained using mean input parameters. Uncertainty in predicted flow rate is small but that in solute transport is an order of magnitude larger than that of corresponding input parameters. Macropore flow is observed to contribute to the variability of atrazine transport results. Overall, the analysis provides a quantification of prediction uncertainty that is found to enhance a user's ability to assess risk levels associated with model predictions.     

Transport and degradation of propylene glycol in the vadose zone: model development and sensitivity analysis

Transport and degradation of de-icing chemical (containing propylene glycol, PG) in the vadose zone were studied with a lysimeter experiment and a model, in which transient water flow, kinetic degradation of PG and soil chemistry were combined. The lysimeter experiment indicated that aerobic as well as anaerobic degradation occurs in the vadose zone. Therefore, the model included both types of degradation, which was made possible by assuming advection-controlled (mobile) and diffusion-controlled (immobile) zones. In the mobile zone, oxygen can be transported by diffusion in the gas phase. The immobile zone is always water-saturated, and oxygen only diffuses slowly in the water phase. Therefore, the model is designed in a way that the redox potential can decrease when PG is degraded, and thus, anaerobic degradation can occur. In our model, manganese oxide (MnO₂, which is present in the soil) and NO \(_{3}^{-}\) (applied to enhance biodegradation) can be used as electron acceptors for anaerobic degradation. The application of NO \(_{3}^{-}\) does not result in a lower leaching of PG nor in a slower depletion of MnO₂. The thickness of the snowcover influences the leached fraction of PG, as with a high infiltration rate, transport is fast, there is less time for degradation and thus more PG will leach. The model showed that, in this soil, the effect of the water flow dominates over the effect of the degradation parameters on the leaching at a 1-m depth.     

Uncertainty in Nonpoint Source Pollution Models and Associated Risks

The usefulness of water quality simulation models for environmental management is explored with a focus on prediction uncertainty. The specific objective is to demonstrate how the usability of a flow and transport model (here: MACRO) can be enhanced by developing and analyzing its output probability distributions based on input variability. This infiltration-based model was designed to investigate preferential flow effects on pollutant transport. A statistical sensitivity analysis is used to identify the most uncertain input parameters based on model outputs. Probability distribution functions of input variables were determined based on field-measured data obtained under alternative tillage treatments. Uncertainty of model outputs is investigated using a Latin hypercube sampling scheme (LHS) with restricted pairing for model input sampling. Probability density functions (pdfs) are constructed for water flow rate, atrazine leaching rate, total accumulated leaching, and atrazine concentration in percolation water. Results indicate that consideration of input parameter uncertainty produces a 20% higher mean flow rate along with two to three times larger atrazine leaching rate, accumulated leachate, and concentration than that obtained using mean input parameters. Uncertainty in predicted flow rate is small but that in solute transport is an order of magnitude larger than that of corresponding input parameters. Macropore flow is observed to contribute to the variability of atrazine transport results. Overall, the analysis provides a quantification of prediction uncertainty that is found to enhance a user's ability to assess risk levels associated with model predictions.     

Coupled pot and lysimeter experiments assessing plant performance in microbially assisted phytoremediation

We performed an experiment at pot scale to assess the effect of plant growth-promoting bacteria (PGPB) on the development of five plant species grown on a tailing dam substrate. None of the species even germinated on inoculated unamended tailing material, prompting use of compost amendment. The effect of inoculation on the amended material was to increase soil respiration, and promote elements immobilisation at plant root surface. This was associated with a decrease in the concentrations of elements in the leaching water and an increase of plant biomass, statistically significant in the case of two species: Agrostis capillaris and Festuca rubra. The experiment was repeated at lysimeter scale with the species showing the best development at pot scale, A. capillaris, and the significant total biomass increase as a result of inoculation was confirmed. The patterns of element distribution in plants also changed (the concentrations of metals in the roots of A. capillaris and F. rubra significantly decreased in inoculated treatments, while phosphorus concentration significantly increased in roots of A. capillaris in inoculated treatment at lysimeter scale). Measured variables for plant oxidative stress did not change after inoculations. There were differences of A. capillaris plant–soil system response between experimental scales as a result of different substrate column structure and plant age at the sampling moment. Soil respiration was significantly larger at lysimeter scale than at pot scale. Leachate concentrations of As, Mn and Ni had significantly larger concentrations at lysimeter scale than at pot scale, while Zn concentrations were significantly smaller. Concentrations of several metals were significantly smaller in A. capillaris at lysimeter scale than at pot scale. From an applied perspective, a system A. capillaris—compost—PGPB selected from the rhizosphere of the tailing dam native plants can be an option for the phytostabilisation of tailing dams. Results should be confirmed by investigation at field plot scale.     

Analysis of the long-term behavior of solute transport with nonlinear equilibrium sorption using breakthrough curves and temporal moments

We analyzed the long-term behavior of breakthrough curves (BTCs) and temporal moments of a solute subjected to Freundlich equilibrium sorption (s = kc(n)). For one-dimensional transport in a homogeneous porous medium, we derived a power-law relation between travel time, tau, and solute displacement, chi, with the exponent being equal to the Freundlich n exponent. The mean solute velocity, derived from the first time moment, was found to change as tau(n-1). For n values larger than 0.66, the second time moment could be related to c chi(2/n), where c is a constant. An approach based on the use of a critical concentration was developed to estimate the presence of the asymptotic regime in the tail of the BTC. This approach was tested successfully using numerical case studies. One-dimensional numerical simulations with varying values of k, n and initial mass were run to verify the closed form analytical expressions for the large time behavior of temporal moments and the tailing part of breakthrough curves. Good agreement between the slope of the tailing part of log-log transformed BTCs and the predicted slope using asymptotic theory was found. Asymptotic theory in general underestimated the magnitude of the concentration in the tail. The quality of the estimated concentrations in the tail improved for small values of the dispersivity. Experimental BTCs of uranin and benazolin were analyzed in combination with sorption/desorption batch experiments using asymptotic theory. A good agreement between the value of n parameter derived from desorption experiment with benazolin and the value of the n parameter derived from the tail of the BTC was found.     

Characterization of preferential flow in undisturbed, structured soil columns using a vertical TDR probe

Rapid movement of agricultural chemicals through soil to groundwater via preferential flow pathways is one cause of water contamination. Previous studies have shown that time domain reflectometry (TDR) could be used to characterize solute transport in soil. However, previous studies have only scarcely addressed preferential flow. This study presents an extended application of TDR for determining preferential flow properties. A TDR method was tested in carefully controlled laboratory experiments using 20-cm long and 12-cm diameter undisturbed, structured soil columns. The method used a vertically installed TDR probe and a short pulse of tracer application to obtain residual mass (RM) breakthrough curves (BTC). The RM BTC obtained from TDR were used to estimate mobile/immobile model (MIM) parameters that were compared to the parameter estimates from effluent data. A conventional inverse curve fitting method (CXTFIT) was used to estimate parameters. The TDR-determined parameters were then used to generate calculated effluent BTC for comparison with observed effluent BTC for the same soil columns. Time moments of the calculated and observed BTC were calculated to quantitatively evaluate the calculated BTC. Overall, the RM BTC obtained from TDR were similar to the RM BTC obtained from effluent data. The TDR-determined parameters corresponded well to the parameters obtained from the effluent data, although they were not within the 95% confidence intervals. Correlation coefficients between the parameters obtained from TDR and from effluent data for the immobile water fraction (theta im/theta), mass exchange coefficient (alpha), and dispersion coefficient (Dm) were 0.95, 0.95, and 0.99, respectively. For three of the four soil cores, theta im/theta ranged from 0.42 to 0.82, indicating considerable preferential flow. The TDR-calculated effluent BTC also were similar to the observed effluent BTC having an average coefficient of determination of 0.94. Time moments obtained from calculated BTC were representative of those obtained from observed BTC. The vertical TDR probe method was simple and minimally destructive and provided representative preferential flow properties that enabled the characterization of solute transport in soil.     

Retention behavior of hydrophobic organic chemicals as a function of temperature in soil leaching column chromatography

To study the transport mechanism of hydrophobic organic chemicals (HOCs) and the energy change in soil/solvent system, a soil leaching column chromatographic (SLCC) experiment at an environmental temperature range of 20-40 degrees C was carried out, which utilized a reference soil (SP 14696) packed column and a methanol-water (1:4 by volume ratio) eluent. The transport process quickens with the increase of column temperature. The ratio of retention factors at 30 and 40 degrees C (k'30/k'40) ranged from 1.08 to 1.36. The lower enthalpy change of the solute transfer in SLCC (from eluent to soil) than in conventional reversed-phase liquid chromatography (e.g., from eluent to C18) is consistent with the hypothesis that HOCs were dominantly and physically partitioned between solvent and soil. The results were also verified by the linear solvation energy relationships analysis. The chief factor controlling the retention was found to be the solute solvophobic partition, and the second important factor was the solute hydrogen-bond basicity, while the least important factors were the solute polarizability-dipolarity and hydrogen-bond acidity. With the increase of temperature, the contributions of the solute solvophobic partition and hydrogen-bond basicity gradually decrease, and the latter decreases faster than the former.     

Water and solute movement in soil as influenced by macropore characteristics: 2. Macropore tortuosity

The paper describes the results of a laboratory study on the effects of macropore tortuosity on breakthrough curves BTCs and solute distribution in a Forman loam (fine loamy-mixed Udic Haploborolls) soil. BTC were obtained using 2-D columns (slab) containing artificial macropores of five different tortuosity levels. The BTCs were run under a constant hydraulic head of 0.08 m over an initially air dry soil. The input solutions contained 1190 mg l⁻¹ of potassium bromide, 10 mg l⁻¹ of Rhodamine WT, and 100 mg l⁻¹ of FD&C Blue #1. A soil column without macropores served as a control. The displacement of a non-adsorbed tracer was not affected by the tortuosity level. An increase in macropore tortuosity progressively increased the breakthrough time, increased the apparent retardation coefficient (R′), decreased the depth to the center of mass of a given adsorbed tracer, and increased the anisotropy in tracer distribution profile. The relative importance of macropore tortuosity increased with an increase in the adsorption coefficient of the tracer. Compared to macropore continuity, the macropore tortuosity had greater impact on solute distribution profile than in its leaching.     

Leaching of pesticides through normal-tillage and low-tillage soil--a lysimeter study. II. Glyphosate

Glyphosate is a widely used non-selective herbicide. Leaching of glyphosate (N-(phosphonomethyl)glycine) and/or its metabolite AMPA (aminomethylphosphonic acid) was studied in four lysimeters, two of them being replicates from a low-tillage field (lysimeter 3 and 4), the other two being replicates from a normal tillage field (lysimeter 5 and 6). In both cases the soil was a sandy loam soil with 13-14% clay. The lysimeters had a surface area of 0.5 m2 and a depth of 110 cm. Lysimeter 3 and 4 were sprayed with a mixture of 14C-labelled glyphosate and unlabelled glyphosate, while lysimeter 5 and 6 were sprayed with unlabelled glyphosate. The spraying took place September 18, 1997. The total amount of glyphosate sprayed onto each lysimeter was 40 mg, corresponding to 0.8 kg active ingredient per ha. The lysimeters were installed in an outdoor system in Research Centre Flakkebjerg and were thus exposed to normal climatic conditions of the area. A mean of 260 l drainage water were collected from lysimeter 3 and 4 and a mean of 375 litres from lysimeter 5 and 6. The mean yearly concentration of leached glyphosate and/or AMPA was significantly below 0.1 microg/l from both sets of lysimeters, and thus no significant difference between the two lysimeter sets was shown. However, in both sets of lysimeters several single findings at concentrations above 0.1 microg/l was seen, which might be due to the leaching of particle-bound compounds. A significant difference between the soil residual concencentrations of AMPA was seen, the higher concentration was found in the set of lysimeter where low-tillage had been practiced and where Round Up had been used several times in the years before sampling of the lysimeter soil.     

Simulations of physical nonequilibrium solute transport models: Application to a large-scale field experiment

Equations expressing the spatial moments of solute concentration distributions simulated by various models, in terms of model parameters, have recently been presented. Using independently obtained parameter values, these equations are used to compare simulations of physical non-equilibrium models with spatial moment data collected in a large-scale natural gradient experiment on solute transport. The physical nonequilibrium models examined postulate the existence of layered zones of immobile water through which solute is transported by a diffusion mechanism. It is found that the qualitative aspects of the measured moment behavior are simulated by the physical nonequilibrium models if the independently obtained parameters are modified somewhat on the basis of reasonable corrective assumptions. It is further demonstrated that the physical nonequilibrium models, using parameter values obtained from spatial data, can qualitatively simulate temporal behavior at individual well points in this relatively homogeneous aquifer.     

Grid lysimeter study of steady state chloride transport in two Spodosol types using TDR and wick samplers.

Solute transport in soils is affected by soil layering and soil-specific morphological properties. We studied solute transport in two sandy Spodosols: a dry Spodosol developed under oxidizing conditions of relatively deep groundwater and a wet Spodosol under periodically reducing conditions above a shallow groundwater table. The wet Spodosol is characterized by a diffuse and heterogeneous humus-B-horizon (i.e., Spodic horizon), whereas the dry Spodosol has a sharp Spodic horizon. Drainage fluxes were moderately variable with a coefficient of variation (CV) of 25% in the wet Spodosol and 17% in the dry Spodosol. Solute transport in 1-m-long and 0.8-m-diameter soil columns was investigated using spatial averages of solute concentrations measured by a network of 36 Time Domain Reflectometry (TDR) probes. In the dry Spodosol, solute transport evolves from stochastic-convective to convective-dispersive at a depth of 0.25 m, coinciding with the depth of the Spodic horizon. Chloride breakthrough at the bottom of the soil columns was adequately well predicted by a convection-dispersion model. In the wet Spodosol, solute transport was heterogeneous over the entire depth of the column. Chloride breakthrough at 1 m depth was predicted best using a stochastic-convective transport model. The TDR sampling volume of 36 probes was too small to capture the heterogeneous flow and concomitant transport in the wet Spodosol.     

Surfactant-induced changes in gravity fingering of water through a light oil

Gravity-driven preferential flow (fingering) can greatly affect how one fluid displaces another in the subsurface. We have studied the internal properties of these preferential flow paths for water, with and without surfactants, infiltrating into oil saturated porous media using synchrotron X-rays, and miniature tensiometers to characterize fluid content and pressure relationships. We also used a light transmission technique to visualize overall flow pattern. Capillary pressure and water content decrease behind the front, similar to fingers in air-dry sand, with quantitative differences for five different surfactants with surface tensions ranging from 4–21 g/s². Using unstable flow theory, the finger widths, capillary pressure drops within the fingers, finger tip lengths, and finger splitting dynamics were scaled successfully with interfacial tension, fluid density, and the contact angle using the fingers in air–water systems as the reference.     

Spatial and temporal variability of water repellency in a sandy soil contaminated with tar oil and heavy metals

Water repellency can induce preferential flow and thus affect water flow and contaminant transport at hazardous waste sites. Since the spatial patterns of water repellency are mostly unknown, it is problematic to use numerical transport models to predict leachate composition. In this study, the spatial variability of soil water repellency was studied at an industrial site contaminated with tar oil, chromium, copper and arsenic. The persistence of water repellency was assessed by the water drop penetration time (WDPT), and the degree of water repellency was quantified by the ethanol percentage (EP) test. Measurements were made at the soil surface along 3.5-12.1 m long transects at different times between March and October 2002. The spatial variability of WDPT, EP, water content, and organic matter content was quantified by variogram analyses. Both the persistence and the degree of water repellency varied seasonally, with the highest water repellency during the summer months. The correlation lengths of WDPT values ranged between 16 and 406 cm, whereas EP values showed no spatial correlation. For field-moist samples, a critical soil water threshold, below which water repellency prevails, was estimated to be 2.5-4%. For oven dry samples, the WDPT values were dependent on the water content prior to drying. The wide range of correlation lengths and the temporal dynamics of spatial repellency patterns suggest that simulations of solute leaching must consider the spatial and temporal variability of soil hydrophobic properties.     

Laboratory analog and numerical study of groundwater flow and solute transport in a karst aquifer with conduit and matrix domains

New mathematical and laboratory methods have been developed for simulating groundwater flow and solute transport in karst aquifers having conduits imbedded in a porous medium, such as limestone. The Stokes equations are used to model the flow in the conduits and the Darcy equation is used for the flow in the matrix. The Beavers–Joseph interface boundary conditions are adopted to describe the flow exchange at the interface boundary between the two domains. A laboratory analog is used to simulate the conduit and matrix domains of a karst aquifer. The conduit domain is located at the bottom of the transparent plexiglas laboratory analog and glass beads occupy the remaining space to represent the matrix domain. Water flows into and out of the two domains separately and each has its own supply and outflow reservoirs. Water and solute are exchanged through an interface between the two domains. Pressure transducers located within the matrix and conduit domains of the analog provide data that is processed and stored in digital format. Dye tracing experiments are recorded using time-lapse imaging. The data and images produced are analyzed by a spatial analysis program. The experiments provide not only hydraulic head distribution but also capture solute front images and mass exchange measurements between the conduit and matrix domains. In the experiment, we measure and record pressures, and quantify flow rates and solute transport. The results present a plausible argument that laboratory analogs can characterize groundwater water flow, solute transport, and mass exchange between the conduit and matrix domains in a karst aquifer. The analog validates the predictions of a numerical model and demonstrates the need of laboratory analogs to provide verification of proposed theories and the calibration of mathematical models.     

Investigation of hydrogeologic processes in a dipping layer structure: 2. Transport and biodegradation of organics

Numerical simulation tools have been used to study the dominating processes during transport of aromatic hydrocarbons in the unsaturated soil zone. Simulations were based on field observations at an experimental site located on a glacial delta plain with pronounced layered sedimentary structures. A numerical model for transport in the unsaturated zone, SWMS-3D, has been extended to incorporate coupled multispecies transport, microbial degradation following Monod kinetics and gas diffusive transport of oxygen and hydrocarbons. The flow field parameters were derived from previous work using nonreactive tracers. Breakthrough curves (BTC) from the hydrocarbon field experiment were used to determine sorption parameters and Monod kinetic parameters using a fitting procedure. The numerical simulations revealed that the assumption of homogeneous layers resulted in deviations from the field observations. The deviations were more pronounced with incorporation of reactive transport, compared with earlier work on nonreactive transport. To be able to model reasonable BTC, sorption had to be reduced compared to laboratory experiments. The initial biomass and the maximum utilisation rate could be adjusted to capture both the initial lag phase and the overall degradation rate. Nevertheless, local oxygen limitation is predicted by the model, which was not observed in the field experiment. Incorporation of evaporation and diffusive gas transport of the hydrocarbons did not significantly change the local oxygen demand. The main cause of the observed discrepancies between model and field are attributed to channelling as a result of small-scale heterogeneities such as biopores.     

Transport modeling of copper and cadmium with linear and nonlinear retardation factors

The predictive accuracy of using the one-dimensional advection–dispersion equation to evaluate the fate and transport of solute in a soil column is usually dependent on the proper determination of chemical retardation factors. Typically, the distribution coefficient (K_d) obtained by fitting the linear sorption isotherm has been extensively used to consider general geochemical reactions on solute transport in a low-concentration range. However, the linear distribution coefficient cannot be adequately utilized to describe the solute fate at a higher concentration level. This study employed the nonlinear equilibrium-controlled sorption parameters to determine the retardation factor used in column leaching experiments. Copper and cadmium transportation in a lateritic silty-clay soil column was examined. Through the explicit finite-difference calculations with a third-order total-variation-diminishing (TVD) numerical solution scheme, all results of the theoretical copper and cadmium breakthrough curves (BTCs) simulated by using the Freundlich nonlinear retardation factors revealed good agreement with the experimental observations.