Vadose Zone Flow Research Articles

Numerical analysis of flow and transport in a combined heterogeneous vadose zone–groundwater system

Numerical simulations of water flow and solute transport were used to investigate the effect of the recharge (rain/irrigation) at the soil surface on solute spreading and breakthrough in a realistic, three-dimensional, heterogeneous, vadose zone–groundwater flow system. Results of the analyses suggest that smaller recharge at the soil surface increases the relative variability in the response of the unsaturated flow system, decreases the groundwater recharge from the unsaturated zone, and, concurrently, decreases the degree of nonuniformity of the groundwater flow. Consequently, smaller recharge at the soil surface enhances the longitudinal and, especially the transverse spreading of the solute plume and increases the spreading of the expected solute BTC at the lower boundary of the unsaturated zone. Furthermore, smaller recharge at the soil surface decreases the extent of the vertical penetration of the solute plume into the groundwater, slows the peak arrival of the expected BTC, and considerably increases the spreading of the expected solute BTC at a given vertical control plane in the saturated region. It was shown that for the combined flow system considered here in which the solute plume is displaced to a sufficiently large vertical distance from the inlet zone at the soil surface, the variable that controls the transport is the cumulative recharge at the soil surface, and not the recharge rate.

Analysis of Atrazine and Four Degradation Products in the Pore Water of the Vadose Zone, Central Indiana

A new method is described for the analysis of atrazine and four of its degradation products (desethylatrazine, deisopropylatrazine, didealkylatrazine, and hydroxyatrazine) in water. This method uses solid-phase extraction on a graphitized carbon black cartridge, derivatization of the eluate with N-methyl-N-(tert-butyldimethylsilyl)trifluoroacetamide (MTBSTFA), and analysis by gas chromatography/mass spectrometry (GC/MS). This method was used to analyze lysimeter samples collected from a field in central Indiana in 1994 and 1995. Atrazine and its degradation products were transported rapidly through the vadose zone. Maximum values of atrazine ranged from 2.61 to 8.44 μg/L and occurred from 15 to 57 days after application. Maximum concentrations of the degradation products occurred from 11 to 140 days after atrazine application. The degradation products were more persistent than atrazine in pore water. Desethylatrazine was the dominant degradation product detected in the first year, and didealkylatrazine was the dominant degradation product detected in the second year. Concentrations of atrazine and the degradation products sorbed onto soil were estimated; maximum concentrations ranged from 7.3 to 24 μg/kg for atrazine and were less than 5 μg/kg for all degradation products. Degradation of atrazine and transport of all five compounds were simulated by the vadose zone flow model LEACHM. LEACHM was run as a Darcian-flow model and as a non-Darcian-flow model.

Stochastic analysis of transport in unsaturated heterogeneous soils uder transient flow regimes

Approximate analytic solutions are developed to predict the transport of inert solutes in variably saturated, randomly heterogeneous porous media subject to a random boundary flux condition. The mean and variance of solute mass flux past a series of vadose zone control planes are determined using a Lagrangian approach. The method requires the specification of an advective travel time probability density function (pdf) between the soil surface and the control planes and an impulse response function which quantifies the specific flow and transport processes that affect the solute along an individual streamline in the soil. In this study an advective‐dispersive impulse response function for inert solute is assumed, and an advective travel time pdf is derived from the statistics of the boundary flux and soil properties using a one‐dimensional transient vadose zone flow model [Foussereau et al., this issue]. Monte Carlo simulations are conducted using random boundary flux sequences and spatially correlated random hydraulic conductivity fields in a multidimensional variably saturated flow and transport code to test the analytic model assumptions. The analytic model accurately predicts the ensemble mean solute flux breakthrough curves for a variety of soil‐climate combinations. The general behavior of the coefficient of variation of solute flux is also accurately reproduced; however, the minimum coefficient of variation at the mean center of mass was slightly underpredicted in most cases. Results show that for shallow soils in humid climates, boundary flux variability dominates soil variability in determining the uncertainty of solute transport predictions in the vadose zone.

Prediction of solute spreading during vertical infiltration in unsaturated, bounded heterogeneous porous media

In this study we investigate the effect of a water table boundary on solute spreading during infiltration in the vadose zone of heterogeneous soils. It has been found recently that the presence of the water table significantly affects unsaturated flow in a heterogeneous vadose zone and causes the flow to be spatially nonstationary. Because a vadose zone is by definition bounded by the water table at the bottom and the contaminants present in the vadose zone migrate into the groundwater through the water table, it is of great interest to study the behaviors of a solute plume near the water table and the effects of flow nonstationarity caused by the water table on solute spreading. To do so, we develop a Lagrangian stochastic approach for predicting field‐scale solute spreading in a spatially nonstationary velocity field. Through first‐order approximations the statistical moments of particle displacement are related to the moments of the Eulerian velocity field. Closed form expressions are obtained for the special case of unidirectional but nonuniform mean flow such as vertical infiltration. We illustrate our theoretical developments with some one‐dimensional examples of solute transport during steady state infiltration in bounded vadose zones. It is found that the inclusion of the water table significantly impacts the behaviors of the mean particle displacement and the displacement covariance, which quantify expected solute displacement and spreading about the expected value, respectively. At late times the particle displacement covariance is generally much smaller when the effect of the water table is included than when it is neglected. In particular, for the case of one‐dimensional infiltration in a bounded vadose zone the particle displacement covariance decreases with time at late times. This finding is in contrast to the result that the particle displacement covariance increases linearly at late times as found by previous stochastic studies of solute transport in unbounded vadose zones. Hence macrodispersion may be greatly overestimated in previous stochastic studies that disregarded the presence of the water table. The validity of the theoretical approach developed in this paper is investigated and confirmed by Monte Carlo simulations.

Resistivity and percolation study of preferential flow in vadose zone at Bokhorst, Germany

Traditional nondestructive resistivity techniques have been applied in combination with tracer displacement and conventional soil moisture recording methods [i.e., buried tensiometer and time domain reflectometry (TDR)] for studying flow processes at an arable site in Bokhorst, Germany. Three water infiltration experiments were carried out using tap water spiked with a nonreactive tracer at different concentrations. The study aimed at exploring the capabilities of these combined techniques for tracing the preferential movement of water in the uppermost 1.5 m of the highly heterogeneous vadose zone. The results illustrate that the applied tensiometer and TDR techniques can detect the relatively fast flow process at their position points and thus only tentatively trace the preferential flow. The additional application of the resistivity method can trace the preferential flow paths continuously along the plane of measurements. The results of the individual applied methods complement and confirm each other.

Vadose Zone Flow and Transport in Cracked Heavy Textured Soil

Investigated were physical processes governing vadose zone water flow and solute transport in a heavy-textured crack-prone soil of the semiarid Canadian Prairies. Soil moisture, soil temperature, and relevant meteorological observations were recorded over a period of about two years. Environmental chloride and tritium concentrations in the soil water were determined. Analysis of the data indicates that during snow melt, water and solutes are flushed down rapidly via cracks and fissures in the root zone. The soil at these depths is still frozen during snow melt. In late spring after the entire soil profile thaws, water and solutes move downward by a diffusion dominant advective-diffusive flow mechanism. The chloride and tritium profiles obtained within the vadose zone support this argument. This conceptual model of the flow and transport processes is supported by calculations of advective and diffusive soil water flux from chloride profiles. Simulation of the tritium profile using a simple analytical model also gives very good agreement with measured data.

TRACER STUDIES OF SUBSURFACE FLOW PATTERNS IN A SANDY LOAM PROFILE

A study designed to provide a better understanding of the mechanisms of agrichemical transport togroundwater was conducted on a 0.81-ha agricultural corn field near Plains, Georgia. The objectives were to: (1)characterize vadose zone flow paths of water and agrichemicals under normal climatic and management conditions andevaluate their spatial and temporal variability; and (2) relate spatial and temporal transport patterns to geophysicalproperties of the soil and climatic conditions. Agrichemical transport was assessed over a five-year period from 1989 to1994 through analysis of collected soil and groundwater samples. A bromide (Br ) tracer was applied at 78 kg ha1 in1989 and at 105 kg ha1 in 1991. Chloride (Cl) and nitrogen were applied with fertilizer each year except 1994. Soilcharacterization tests indicated a dramatic decrease in the saturated hydraulic conductivity associated with a largeincrease in clay content in a zone from 1 to 4 m below the soil surface. As a result of this soil feature, Br concentrationsin the vadose zone below 4 m were normally less than 2 mg kg1 throughout the study. Aquifer chemical concentrationsindicated nitrate nitrogen (NO3 N) and Cl applied to the soil surface in the spring were transported to the groundwaterat 9 m by that same fall. Bromide concentrations in ground water peaked at 0.65 mg L1 while NO3 N concentrationspeaked at 6.9 mg L1 and Cl at 4.0 mg L1. Agrichemical transport and variability were controlled by climatic patternsand soil hydraulic characteristics. Transport to groundwater increased when precipitation and irrigation volumes in thefirst 30 days after spring fertilization and planting exceeded twice the normal precipitation. If large spring thunderstormsoccur soon after chemical application, the likelihood of groundwater contamination by agrichemicals is substantiallyincreased. These data provide the means to relate transport of agrichemicals in and through the vadose zone togeophysical characteristics and irrigation and precipitation inputs.

A comparison of modeling approaches for steady-state unconfined flow

The Dupuit-Forchheimer, the fully saturated flow, and the variably saturated flow models, are compared for problems involving steady-state, unconfined flow through porous media. The variably saturated flow model is the most comprehensive of the three and requires more parameters. The performances of the three models are compared for different soil properties, problem dimensions, and flow geometries. There are certain types of problems where the simpler models may yield satisfactory results. For soils with large pores and/or broad pore-size-density functions, the variably saturated flow model solutions to steady-state problems approach those of the fully flow model, owing to the manner in which the soil-water retention curve and relative permeability function, respectively, affect the variably saturated flow model solutions. For problems of significant size, the fully saturated flow model may be sufficient, as the effects of the vadose zone are relatively diminished. For problems with radial symmetry (e.g. steady flow to a well), the fully saturated flow model performs well because the variably saturated flow model is relatively insensitive to the parameters describing the soil properties, as the amount of vadose zone flow, compared with the total flow, is relatively insignificant in such problems.

Probabilistic modeling of moisture flow in layered vadose zone: applications to waste site performance assessment

The problem of moisture flow through layers of statistically homogeneous soils in the vadose zone is studied by a probabilistic approach. A random number generator is used to characterize the spatial variability of hydraulic properties in such a way consistent with the probability distribution function observed in field measurements. The water travel time is calculated from the solution of the pressure head-based Richards' equation obtained by means of the Galerkin finite element method in conjunction with the backward Euler method for time advancement. Applications are directed toward burial sites at the Nevada Test Site (NTS) and at the Idaho National Engineering Laboratory (INEL). Uncertainties in the travel time due to the uncertain soil properties are quantified by an appropriate statistical parameter deduced from the travel times of the realizations simulated.

On the Velocity Covariance and Transport Modeling in Heterogeneous Anisotropic Porous Formations: 2. Unsaturated Flow

Velocity covariances, and the resultant macrodispersion coefficient tensor, derived by Russo (this issue) for saturated flow conditions, are applied for unsaturated flow conditions, employing the assumption that for a given mean capillary pressure head, water saturation is a deterministic constant and log conductivity is a multivariate normal, stationary random space function. The applicability of the approach for modeling flow and transport in the vadose zone was evaluated by the use of the stochastic theory of Yeh et al. (1985a, b) for steady, unsaturated flow. Results of the analyses suggest that the approach may be applicable to vadose zone flow and transport, as long as the scale of heterogeneity in the direction of the mean flow is smaller than approximately one tenth of the characteristic length of unsaturated flow. For porous formation of given statistics, the magnitude of macrodispersion in unsaturated flow is larger than that in saturated flow, and increases as water saturation decreases. For a given water saturation, transport in unsaturated flow may approach asymptotic Fickian behavior more slowly than in saturated flow, when the two formation properties log Ks and α are positively cross‐correlated and when the correlation scale of α is relatively large as compared with the correlation scale of log Ks.

Direct-Formulation Finite Element (DFFE) Method for Groundwater Flow Modeling: Two-Dimensional Case

Real-world groundwater modeling deals with heterogeneous and anisotropic aquifer systems. Numerical models, particularly the finite difference and finite element methods, are extensively used for modeling such a complex aquifer system. The finite difference method is an age-old straightforward approach, whereas the finite element method is more idealistic, relatively new, and has emerged as a popular approach. The unique advantages with the finite element method are (i) an irregular-shaped domain can be discretized into elements with a matching boundary, (ii) a node can be connected with the neighboring nodes in any direction. Thus, the finite element analysis allows water/solute to flow more freely toward the surrounding nodes along nodal links. On the other hand, the mathematical formulation of the finite element technique follows a set of rules step by step. Conventionally, this idealistic approach uses shape functions and integration techniques to develop element matrices, which, in turn, are assembled to form the global matrix. This conventional global matrix was found to be inconsistent with the basic partial differential equation representing the mass balance in a nodal domain as a control volume. As a result, the matrix solution, particularly for nonlinear problems (e.g., vadose zone flow, density dependent flow, and so forth) becomes unstable and computationally burdensome. To overcome the limitations of the conventional finite element method for real-world groundwater modeling, a new approach, called the direct-formulation finite element (DFFE) method, has been developed. In this approach, a two-dimensional model domain is discretized into triangular elements. Element matrices are formed directly based on flow principles and material properties of elements without using shape functions and integration process. The DFFE method is robust. The global matrix is consistent, and the solution is stable and efficient. The results obtained from this approach were found in a good agreement with that obtained from analytical and other widely used models.

A screening model for nonaqueous phase liquid transport in the vadose zone using Green‐Ampt and kinematic wave theory

In this paper, a screening model for flow of a nonaqueous phase liquid (NAPL) and associated chemical transport in the vadose zone is developed. The model is based on kinematic approximation of the governing equations for both the NAPL and a partitionable chemical constituent. The resulting governing equation is a first‐order, quasi‐linear hyperbolic equation to which the generalized method of characteristics can be applied. This approach generally neglects the contribution to the NAPL flux from capillary pressure gradients. During infiltration under ponded conditions, or when the NAPL flux exceeds the maximum effective conductivity of the soil, the effect of capillary suction is included in the model through the usage of the Green‐Ampt model. All of the resulting model equations are in the form of ordinary differential equations which are solved numerically by a variable time step Runge‐Kutta technique. Results from a simple column experiment were used to evaluate the vadose zone flow model assumptions. Independently measured parameters allow simulation without calibration of the model results. The match of the model to the data suggests that the model captures the qualitative behavior of the experimental system and is capable of an acceptable degree of quantitative agreement.

A Borehole Field Method to determine unsaturated hydraulic conductivity

Unsaturated hydraulic conductivity is often the single most important soil property in vadose zone flow and transport. However, at depths below the root zone there is no field method available to determine it. The proposed method is directed toward developing a practical field tool to determine Unsaturated hydraulic conductivity in discrete intervals over any depth. The basic idea is to inject water at a point and monitor the steady state pressure distribution surrounding the source. We have developed an analytical solution to use either the observed steady state pressure heads at several points due to a single injection, or steady pressure heads at a single point due to multiple injections, to determine the unsaturated hydraulic conductivity. The approach is based on a linearization of the Unsaturated flow equation which uses the piecewise exponential model of unsaturated hydraulic conductivity. Examples of hydraulic conductivity calculations for three different soils give excellent results.

The Las Cruces Trench Site: Characterization, Experimental Results, and One‐Dimensional Flow Predictions

A comprehensive field trench study was conducted in a semiarid area of southern New Mexico to provide data to test deterministic and stochastic models of vadose zone flow and transport. A 4 m by 9 m area was irrigated with water containing a tracer using a carefully controlled drip irrigation system. The area was heavily instrumented with tensiometers and neutron probe access tubes to monitor water movement and with suction tubes to monitor solute transport. Approximately 600 disturbed and 600 core samples of soil were taken to support deterministic and stochastic characterization of the soil water hydraulic parameters. The core sample‐based saturated hydraulic conductivities ranged from 1.4 to 6731 cm/d with a mean of 533 cm/d and a standard deviation of 647 cm/d, indicating significant spatial variability. However, visual observation of the wetting front on the trench wall shows no indication of preferential flow or water flow through visible root channels and cracks. The tensiometer readings and the neutron probe measurements also suggest that the wetting front moves in a fairly homogeneous fashion despite the significant spatial variability of the saturated hydraulic conductivity. In addition to the description of the experiment and the presentation of the experimental results, predictions of simple one‐dimensional uniform and layered soil deterministic models for infiltration are presented and compared to field observations. These models are presented here to provide a base case against which more sophisticated deterministic and stochastic models can be compared in the future. The results indicate that the simple models give adequate predictions of the overall movement of the wetting front through the soil during infiltration. However, the models give poor predictions of point values for water content due to the spatial variability of the soil. Comparisons between the one‐dimensional infiltration model predictions and field observations show that the use of the layered soil model rather than the uniform soil model does not consistently improve the accuracy of the predictions for this particular field application. This result illustrates that increasing the spatial resolution of the deterministic characterization of the site in the vertical direction does not always improve the model predictions. Uncertainties due to horizontal spatial variability and due to other difficulties associated with experimental characterization appear to be more significant.

Preferential flow in a sandy vadose zone: 1. Field observation

Field experiments of water movement in the lower portion of an unsaturated zone (i.e., vadose zone) are far more difficult to conduct than those in the root zone; thus our concept of the transport mechanism in the vadose zone is still primitive and mainly an extrapolation of our understanding of transport in the root zone. Recent results from field experiments conducted at the Hancock Agricultural Research Station indicated that water and solute applied uniformly to soil surfaces did not flow through the entire vadose zone. By using dye tracing and profile excavation, field experiments were conducted during the 1987 growing season to examine water flow patterns in the unsaturated zone of the Central Sand Area of Wisconsin (CSAW). The results confirmed that preferential flow paths constitute the dominant flow pattern at this location. Water flowing through the root zone was funneled into concentrated flow paths that occupied only a small portion of the soil matrix in the vadose zone yet accounted for most of the transport. The observed phenomena of preferential flow in a sandy vadose zone are discussed in this paper. The mechanism and implications of preferential flow are presented in a companion paper.

Preferential flow in a sandy vadose zone: 2. Mechanism and implications

Field experiments conducted at the Hancock Agricultural Research Station during the 1987 growing season showed that preferential flow paths were the dominant flow pattern in the Central Sand Area of Wisconsin (CSAW). The observed preferential flow was different from other preferential flow patterns mentioned in the literature (e.g., “short circuiting” flow and “fingering” flow). This paper presents a detailed discussion of the mechanism of this preferential flow and its influence on groundwater contamination, soil solution sampling, and solute transport modeling. Four factors that will determine the occurrence of a funneled flow are: (A) conductivity of the upper finer layer, K; (B) slope of the inclined layer, sin (β); (C) retention potential of the upper finer layer, 2 σ/ r; and (D) ponding potential, ρ g L.

Parameter estimation for unsaturated flow and transport models — A review

This paper reviews the current status of parameter estimation techniques and their utility for determining key parameters affecting water flow and solute transport in the unsaturated (vadose) zone. Historically, hydraulic and transport properties of the unsaturated zone have been determined by imposing rather restrictive initial and boundary conditions so that the governing flow and transport equations can be inverted by analytical or semi-analytical methods. Contrary to these direct methods, parameter estimation techniques do not impose any constraints on the model, on the stipulation of initial and boundary conditions, on the constitutive relationships, or on the treatment of inhomogeneities via deterministic or stochastic representations. While parameter estimation analyses of subsurface saturated flow are increasingly common, their application to unsaturated flow and transport processes is a relatively new endeavor. Nevertheless, a number of laboratory and field applications currently exist that show the great potential of parameter estimation techniques for improved designs and analyses of vadose zone flow and transport experiments. Several practical examples for determining unsaturated soil hydraulic functions and various transport parameters are presented, and advantages and limitations of the estimation process are discussed. Specific research areas in need of future investigation are outlined.