M.Th. van Genuchten

Review and comparison of models for describing non-equilibrium and preferential flow and transport in the vadose zone

Abstract In this paper, we review various approaches for modeling preferential and non-equilibrium flow and transport in the vadose zone. Existing approaches differ in terms of their underlying assumptions and complexity. They range from relatively simplistic models to more complex physically based dual-porosity, dual-permeability, and multi-region type models. A relatively simple dual-porosity flow model results when the Richards equation is combined with composite (double-hump type) equations for the hydraulic properties to account for both soil textural (matrix) and soil structural (fractures, macropores, peds) effects on flow. The simplest non-equilibrium flow model, a single-porosity model which distinguishes between actual and equilibrium water contents, is based on a formulation by Ross and Smettem [Soil Sci. Soc. Am. J. 64 (2000) 1926] that requires only one additional parameter to account for non-equilibrium. A more complex dual-porosity, mobile–immobile water flow model results when the Richards or kinematic wave equations are used for flow in the fractures, and immobile water is assumed to exist in the matrix. We also discuss various dual-permeability models, including the formulation of Gerke and van Genuchten [Water Resour. Res. 29 (1993a) 305] and the kinematic wave approach as used in the MACRO model of Jarvis [Technical Description and Sample Simulations, Department of Soil Science, Swedish University of Agricultural Science, Uppsala, Sweden (1994) 51]. Both of these models invoke terms accounting for the exchange of water and solutes between the matrix and the fractures. Advantages and disadvantages of the different models are discussed, and the need for inter-code comparison is stressed, especially against field data that are sufficiently comprehensive to allow calibration/validation of the more complex models and to distinguish between alternative modeling concepts. Several examples and comparisons of equilibrium and various non-equilibrium flow and transport models are also provided.

Estimating Uncertain Flow and Transport Parameters Using a Sequential Uncertainty Fitting Procedure

Inversely obtained hydrologic parameters are always uncertain (nonunique) because of errors associated with the measurements and the invoked conceptual model, among other factors. Quantification of this uncertainty in multidimensional parameter space is often difficult because of complexities in the structure of the objective function. In this study we describe parameter uncertainties using uniform distributions and fit these distributions iteratively within larger absolute intervals such that two criteria are met: (i) bracketing most of the measured data (>90%) within the 95% prediction uncertainty (95PPU) and (ii) obtaining a small ratio (<1) of the average difference between the upper and lower 95PPU and the standard deviation of the measured data. We define a model as calibrated if, upon reaching these two criteria, a significant R 2 exists between the observed and simulated results. A program, SUFI-2, was developed and tested for the calibration of two bottom ash landfills. SUFI-2 performs a combined optimization and uncertainty analysis using a global search procedure and can deal with a large number of parameters through Latin hypercube sampling. We explain the above concepts using an example in which two municipal solid waste incinerator bottom ash monofills were successfully calibrated and tested for flow, and one monofill also for transport. Because of high levels of heavy metals in the leachate, monitoring and modeling of such landfills is critical from environmental points of view.

Parameter estimation for unsaturated flow and transport models. A review

Kool, J.B., Parker, J.C. and Van Genuchten, M.Th., 1987. Parameter estimation for unsaturated flow and transport models -- A review. J. Hydrol., 91: 255-293. 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.

Effect of the shape of the soil hydraulic functions near saturation on variably-saturated flow predictions

Abstract Relatively small changes in the shape of the soil water retention curve near saturation can significantly affect the results of numerical simulations of variably saturated flow, including the performance of the numerical scheme itself in terms of stability and rate of convergence. In this paper, we use a modified form of the van Genuchten–Mualem (VGM) soil hydraulic functions to account for a very small, but non-zero minimum capillary height, hs, in the soil water retention curve. The modified VGM model is contrasted with the original formulation by comparing simulation results for infiltration in homogeneous soils assuming both constant pressure and constant flux boundary conditions. The two models gave significantly different results for infiltration in fine-textured soils, even for hs-values as small as −1 cm. Incorporating a small minimum capillary height in the hydraulic properties leads to less non-linearity in the hydraulic conductivity function near saturation and, because of this, to more stable numerical solutions of the flow equation. This study indicates an urgent need for experimental studies that assess the precise shape of the hydraulic conductivity curve near saturation, especially for relatively fine-textured soils. For one example we found considerable improvement in the predicted conductivity function when a value of −2 cm for hs was used in the modified VGM model.

Models for simulating salt movement in aggregated field soils

Abstract This paper reviews several “two-region” type models for simulating salt movement in aggregated soils. A common feature of these models is the assumption that solutes are transported by convection and dispersion through well-defined pores or cracks, while diffusion-type equations are used to describe solute transfer inside the soil micropores. Analytical solutions are currently available for several aggregate shapes (spherical, cylindrical and line-sheet type aggregates). A recently developed transformation extends the two-region modeling approach to more general conditions involving aggregates of arbitrary geometry. The method is based on the replacement of a given aggregated soil by a reference soil made up of uniformly-sized spherical aggregates with the same average diffusion properties as the original soil. The method can also be used to quantify the mass transfer coefficient in a first-order rate model for solute exchange between mobile and immobile liquid zones. An advantage of the first-order approach is that it can be included easily in relatively simple management-oriented models using parameters that can be given a physical interpretation. This paper also presents several previously unpublished expressions that lump the effects of intra-aggregate diffusion into an effective dispersion coefficient for use in the classical two-parameter equilibrium transport equation.

Convective-dispersive transport of solutes involved in sequential first-order decay reactions

Abstract Problems of solute transport involving sequential first-order decay reactions frequently occur in soil systems. Examples are the migration of radionuclides, in which the chain members form a first-order decay reaction, and the simultaneous movement of various interacting nitrogen species. This study presents analytical solutions that describe the simultaneous convective-dispersive transport of up to four species involved in such a consecutive chain reaction. Evaluation of the analytical solutions is not straightforward but requires, among other things, the calculation of complex complementary error functions. A FORTRAN IV computer program (CHAIN) that can be used to evaluate the analytical solutions is described. Application of this program to problems of solute transport is illustrated with two examples, one dealing with radionuclide transport and one with nitrification.

THE TIME-DOMAIN REFLECTOMETRY METHOD FOR MEASURING SOIL WATER CONTENT AND SALINITY

Dalton, F.N. and van Genuchten, M.Th., 1986. The time-domain reflectometry method for measuring soil water content and salinity. Geoderma, 38: 237--250. This paper discusses the physical principles and use of time-domain reflectometry as a new tool for studying water and solute transport in unsaturated soils. In-situ measurements of water content and bulk soil electrical conductivity are shown to give results that are comparable with those obtained by conventional non-destructive techniques. An equation is presented that relates the bulk soil electrical conductivity to the soil solution electrical conductivity. Also derived are constraints that water content and electrical conductivity place on the use of time domain reflectometry sensors.

A new convergence criterion for the modified Picard iteration method to solve the variably saturated flow equation

Solutions of the Richards equation for water flow in variably saturated porous media are increasingly being used in water resources evaluation and environmental management. Besides the accuracy of solution, also of concern is the required computational effort, especially when highly nonlinear soil hydraulic properties and dry initial conditions are involved. In this paper we evaluate the performance of different convergence criteria when the modified Picard iteration method is used for solving the mixed-form Richards equation. Results are compared in terms of computer processing (CPU) time and number of iterations. A new nonlinear convergence criterion derived using a Taylor series expansion of the water content was implemented in the mixed-form numerical algorithm. The computational efficiency of the new criterion was evaluated against two widely used convergence criteria for different soil types, boundary conditions, initial conditions, and layered soils. Whereas all three criteria produced nearly identical results in terms of calculated water content, pressure head, and water flux distributions, all with negligible mass balance errors, the required CPU times were significantly different. In general, the new nonlinear convergence criterion was found to be computationally much more efficient than the other two criteria. The new criterion was also more robust (i.e. the solution remained convergent) for highly nonlinear flow problems for which the other two convergence criteria failed. Results of this study indicate that the new convergence criterion, when implemented in the modified Picard solution of the mixed-form Richards equation, produces a very efficient and accurate method for simulating variably saturated water flow in soils.

Evaluating non-equilibrium solute transport in small soil columns

Displacement studies on leaching of bromide and two pesticides (atrazine and isoproturon) were conducted under unsaturated steady state flow conditions in 24 small undisturbed soil columns (5.7 cm in diameter and 10 cm long) each collected from two sites differing in soil structure and organic carbon content in North Germany. There were large and irregular variabilities in the characteristics of both soils, as well as in the shapes of breakthrough curves (BTCs) of different columns, including some with early breakthrough and increased tailing, qualitatively indicating the presence of preferential flow. It was estimated that one preferential flow column (PFC) at site A, and four at site B, contributed, respectively to 11% and 58% of the accumulated leached fraction and to more than 80% of the maximum observed standard deviation (SD) in the field-scale concentration and mass flux of pesticides at two sites. The bromide BTCs of two sites were analyzed with the equilibrium convection-dispersion equation (CDE) and a non-equilibrium two-region/mobile-immobile model. Transport parameters of these models for individual BTCs were determined using a curve fitting program, CXTFIT, and by the time moment method. For the CDE based equilibrium model, the mean values of retardation factor, R, considered separately for all columns, PFCs or non-preferential flow columns (NPFCs) were comparable for the two methods; significant differences were observed in the values of dispersion coefficients of two sites using the two estimation methods. It was inferred from the estimated parameters of non-equilibrium model that 5-12% of water at site A, and 12% at site B, was immobile during displacement in NPFCs. The corresponding values for PFCs of two sites were much larger, ranging from 25% to 51% by CXTFIT and from 24% to 72% by the moment method, suggesting the role of certain mechanisms other than immobile water in higher degrees of non-equilibrium in these columns. Peclet numbers in PFCs of both sites were consistently smaller than five, indicating the inadequacy of the non-equilibrium model to incorporate the effect of all forms of non-equilibrium in PFCs. Overall, the BTCs of individual NPFCs, PFCs and of field average concentration at the two sites were better reproduced with parameters obtained from CXTFIT than by the moment method. The moment method failed to capture the peak concentrations in PFCs, but tended to describe the desorption and tail branches of BTCs better than the curve fitting approach.

Estimation of the van Genuchten soil water retention properties from soil textural data.

Abstract The van Genuchten (vG) function is often used to describe the soil water retention curve (SWRC) of unsaturated soils and fractured rock. The objective of this study was to develop a method to determine the vG model parameter m from the fractal dimension. We compared two approaches previously proposed by van Genuchten and Lenhard et al . for estimating m from the pore size distribution index of the Brooks and Corey (BC) model. In both approaches we used a relationship between the pore size distribution index of the BC model and the fractal dimension of the SWRC. A dataset containing 75 samples from the UNSODA unsaturated soil hydraulic database was used to evaluate the two approaches. The statistical parameters showed that the approach by Lenhard et al . provided better estimates of the parameter m . Another dataset containing 72 samples from the literature was used to validate Lenhards approach in which the SWRC fractal dimension was estimated from the clay content. The estimated SWRC of the second dataset was compared with those obtained with the Rosetta model using sand, silt, and clay contents. Root mean square error values of the proposed fractal approach and Rosetta were 0.081 and 0.136, respectively, indicating that the proposed fractal approach performed better than the Rosetta model.