Unsaturated Hydraulic Parameters Research Articles

Modelling of water flow through typical Bavarian soils: 1. Estimation of hydraulic characteristics of the unsaturated zone

Over an eight-year period (1984–1991), seven experimental lysimeters filled with different soil materials from the State of Bavaria (quartz and tertiary sands, quartz and fluvioglacial gravels) were used to study water flow and tracer transport through the unsaturated zone under natural atmospheric conditions. The experiments were performed in the input—output mode using weekly water flow and tracer contents (environmental deuterium) in the precipitation and in the outflow in order to estimate the unsaturated hydraulic and transport parameters of the soils with limited measured data. This paper (Part 1) presents the evaluation of soil hydraulic parameters for tested soils, while the second paper (Part 2) is concerned with the estimation of transport parameters (dispersion, water content and possible zones with stagnant water). The estimation of the soil physical characteristics, i.e. the relationship between water pressure head and water content, performed by applying the van Genuchten model, showed a satisfactory accuracy against the measured data. Determination of the hydraulic conductivity as a function of water content using the van Genuchten-Mualem conductivity model did not yield good results, due to the fact that the theoretical water flow model based on such soil parameters was not able to fit the measured values of water content at the upper 20 cm and the cumulative water outflow simultaneously. To estimate the conductivity—water content characteristics, the inverse modelling technique was used for each lysimeter. The cumulative outflow curves were fitted to the observed outflow data by a trial-and-error procedure using the conductivity—water content relationship as the fitting function. It was shown that this method of estimating the soil characteristics yields parameters which are closer to the true values compared to those found in small-scale column experiments. The soil characteristics obtained in this part of the study were further used for modelling environmental deuterium transport through the soils (Part 2).

A Film Depositional Model of Permeability for Mineral Reactions in Unsaturated Media

A film depositional modeling approach is developed for modeling changes in permeability due to mineral precipitation and dissolution reactions in unsaturated porous media. Such a model is needed for describing glass dissolution and secondary mineral precipitation in a low-level waste facility. The model is based on the assumption that the mineral precipitate is deposited on the pore walls as a continuous film, which may cause a reduction in permeability. Previous work in saturated media has used continuous pore-size distributions to represent the pore space. In this study, the film depositional model is developed for a discrete pore-size distribution, which is determined using the unsaturated hydraulic properties of the porous medium. This facilitates the process of dynamically updating the unsaturated hydraulic parameters used to describe fluid flow through the media. Single mineral test simulations have been conducted to test both the Mualem and Childs and Collis-George permeability models. Results from simulation of the simultaneous dissolution of low-level glassified waste and secondary mineral precipitation show that the film depositional models yield physically reasonable predictions of permeability changes due to solid–aqueous phase reactions.

A Film Depositional Model of Permeability for Mineral Reactions in Unsaturated Media

A film depositional modeling approach is developed for modeling changes in permeability due to mineral precipitation and dissolution reactions in unsaturated porous media. Such a model is needed for describing glass dissolution and secondary mineral precipitation in a low‐level waste facility. The model is based on the assumption that the mineral precipitate is deposited on the pore walls as a continuous film, which may cause a reduction in permeability. Previous work in saturated media has used continuous pore‐size distributions to represent the pore space. In this study, the film depositional model is developed for a discrete pore‐size distribution, which is determined using the unsaturated hydraulic properties of the porous medium. This facilitates the process of dynamically updating the unsaturated hydraulic parameters used to describe fluid flow through the media. Single mineral test simulations have been conducted to test both the Mualem and Childs and Collis‐George permeability models. Results from simulation of the simultaneous dissolution of low‐level glassified waste and secondary mineral precipitation show that the film depositional models yield physically reasonable predictions of permeability changes due to solid–aqueous phase reactions.

Pedotransfer functions for solute transport parameters of Portuguese soils

SummaryThe purpose of this study is to quantify solute transport parameters of fine‐textured soils in an irrigation district in southern Portugal and to investigate their prediction from basic soil properties and unsaturated hydraulic parameters. Solute displacement experiments were carried out on 24 undisturbed soil samples by applying a 0.05 mKCl pulse during steady flow. The chloride breakthrough curves (BTCs) were asymmetric, with early breakthrough and considerable tailing characteristic of non‐equilibrium transport. The retardation factor (R), dispersion coefficient (D), partitioning coefficient (β), and mass transfer coefficient (ω) were estimated by optimizing the solution of the non‐equilibrium convection–dispersion equation (CDE) to the breakthrough data. The solution could adequately describe the observed data as proved by a median of 0.972 for the coefficient of determination (r2) and a median for the mean squared error (MSE) of 5.1 × 10−6. The median value forRof 0.587 suggests that Cl–was excluded from a substantial part of the liquid phase. The value forβwas typically less than 0.5, but the non‐equilibrium effects were mitigated by a large mass transfer coefficient (ω > 1). Pedotransfer functions (PTFs) were developed with regression and neural network analyses to predictR,D,βandωfrom basic soil properties and unsaturated hydraulic parameters. Fairly accurate predictions could be obtained for logD(r2 ≈ 0.9) andβ(r2 ≈ 0.8). Prediction forR andlogωwere relatively poor (r2 ≈ 0.5). The artificial neural networks were all somewhat more accurate than the regression equations. The networks are also more suitable for predicting transport parameters because they require only three input variables, whereas the regression equations contain many predictor variables.

Evaluation of alternative cover systems using GIS

Abstract Geographic Information Systems (GIS) can be used to determine and display the depths of native soil covers required for waste containment sites. Readily available data for the State of New Mexico are used in a GIS environment to determine the required depth of two separate cover systems. The depth of an evapotranspirative (ET) soil cover is determined using the available water capacity of the soil and the amount of dormant precipitation. The thickness of a capillary barrier cover system is determined using unsaturated hydraulic parameters, the amount of dormant precipitation, and an iterative numerical model. A difference map showing the savings using a capillary barrier instead of an ET cover is then created. The use of a capillary barrier in areas with fine-grained soils can decrease the necessary soil cover thickness by 90 cm of soil. The computed cover thickness compare well with those determined using Hydrologic Evaluation of Landfill Performance (HELP) (Schroeder et al., 1994), a model commonly used in New Mexico to determine if alternative cover systems can meet the required performance criteria.

Inverse modeling of a radial multistep outflow experiment for determining unsaturated hydraulic properties

Modeling flow and solute transport in the unsaturated zone on the basis of the Richards equation requires specifying values for unsaturated hydraulic conductivity and water potential as a function of saturation. The objectives of the paper are to evaluate the design of a transient, radial, multi-step outflow experiment, and to determine unsaturated hydraulic parameters using inverse modeling. We conducted numerical simulations, sensitivity analyses, and synthetic data inversions to assess the suitability of the proposed experiment for concurrently estimating the parameters of interest. We calibrated different conceptual models against transient flow and pressure data from a multi-step, radial desaturation experiment to obtain estimates of absolute permeability, as well as the parameters of the relative permeability and capillary pressure functions. We discuss the differences in the estimated parameter values and illustrate the impact of the underlying model on the estimates. We demonstrate that a small error in absolute permeability, if determined in an independent experiment, leads to biased estimates of unsaturated hydraulic properties. Therefore, we perform a joint inversion of pressure and flow rate data for the simultaneous determination of permeability and retention parameters, and analyze the correlations between these parameters. We conclude that the proposed combination of a radial desaturation experiment and inverse modeling is suitable for simultaneously determining the unsaturated hydraulic properties of a single soil sample, and that the inverse modeling technique provides the opportunity to analyze data from nonstandard experimental designs.

Maximum-likelihood estimation of unsaturated hydraulic parameters

Maximum-likelihood estimators properly represent measurement error, thus provide a statistically sound basis for evaluating the adequacy of a model fit and for finding the multivariate parameter confidence region. We demonstrate the advantages of using maximum-likelihood estimators rather than simple least-squares estimators for the problem of finding unsaturated hydraulic parameters. Inversion of outflow data given independent retention data can be treated by an extension to a Bayesian estimator. As an example, we apply the methodology to retention and transient unsaturated outflow observations, both obtained on the same medium sand sample. We found the van Genuchten expression to be adequate for the retention data, as the best fit was within measurement error. The Cramer–Rao confidence bound described the true parameter uncertainty approximately. The Mualem–van Genuchten expression was, however, inadequate for our outflow observations, suggesting that the parameters (α, n) may not always be equivalent in describing both retention and unsaturated conductivity.

A hybrid global optimization method for inverse estimation of hydraulic parameters: Annealing‐Simplex Method

Inverse estimation of unsaturated hydraulic parameters is often a highly nonlinear optimization problem with multiple parameters. The objective functions involved are often topographically complex and may contain many local minima. Because of these reasons, the inverse solutions are commonly very sensitive to the initial guess of the parameters when conventional optimizers are used. This paper presents an annealing‐simplex method that incorporates simulated annealing strategies into a classical downhill simplex method. An upward infiltration experiment was used as an example of inverse estimation to test the method. Numerical experiments of both minimizing an algebraic function and inversion of upward infiltration data showed that the new method successfully converged to the global minimum in all cases, irrespective of the initial hydraulic parameter estimates, while the classical downhill method often converged to unfavorable local minima. The CPU times needed for the annealing‐simplex method to estimate 5 and 7 hydraulic parameters simultaneously are about a half hour and 1 hour on a PC, respectively. Additionally, no special requirements are imposed on the objective function, and the method is independent of the details of the simulation submodel. Therefore the proposed method should be applicable to other optimization problems in water resources when it is important to have a robust global search capability.

Experimental evidence of randomness and nonuniqueness in unsaturated outflow experiments designed for hydraulic parameter estimation

Single transient outflow experiments are commonly conducted for inverse estimation of unsaturated hydraulic parameters. We assess the validity of this procedure through several repeated experiments on the same sample, a medium sand contained in a pressure cell. Outflow was induced by. one or multiple step changes in bottom boundary suction, such that there were replicates for each of several step levels in suction. We observed that experiments with small initial step changes were poorly reproducible, even though our setup allowed reproduction of almost identical initial saturation for each run. Experiments with large step changes were well reproducible, but the outflow response was virtually the same for different step levels. Neither type of observation was predicted by a theoretical sensitivity analysis of the Richards equation, given the minimal inaccuracy in our experiments. Inverse estimation yielded incompatible apparent hydraulic parameters for different flow conditions. Our results imply experimental limitations of the inversion procedure.

An iterative geostatistical inverse method for steady flow in the vadose zone

An iterative geostatistical inverse approach is developed to estimate conditional effective unsaturated hydraulic conductivity parameters, soil‐water pressure head, and degree of saturation in heterogeneous vadose zones. This approach is similar to the classical cokriging technique, and it uses a linear estimator that depends on covariances and cross covariances of unsaturated hydraulic parameters, soil‐water pressure head, and degree of saturation. The linear estimator is, however, improved successively by solving the governing flow equation and by updating the residual covariance and cross‐covariance functions in an iterative manner. As a result, the nonlinear relationship between unsaturated hydraulic conductivity parameters and head is incorporated in the estimation and the estimated fields are approximate conditional means. The ability of the iterative approach is demonstrated through some numerical examples.

A Geostatistical Inverse Method for Variably Saturated Flow in the Vadose Zone

A geostatistical inverse technique utilizing both primary and secondary information is developed to estimate conditional means of unsaturated hydraulic conductivity parameters (saturated hydraulic conductivity and pore size distribution parameters) in the vadose zone. Measurements of saturated hydraulic conductivity and pore size distribution parameters are considered as the primary information, while measurements of steady state flow processes (soil‐water pressure head and degree of saturation) are regarded as the secondary information. This inverse approach relies on the classical linear predictor (cokriging) theory and takes the advantage of the spatial cross correlation between the soil‐water pressure head and each of the following: degree of saturation, saturated hydraulic conductivity, and a pore size distribution parameter. Using an approximate perturbation solution for steady, variably saturated flow under general boundary conditions, the cross covariances between the primary and secondary information are derived. The approximate solution is formulated on the basis of a first‐order Taylor series expansion of a discretized finite element equation. The sensitivity matrix in the solution is evaluated by an adjoint state sensitivity approach for flow in heterogeneous media under variably saturated conditions. Through several numerical examples the inverse model demonstrates its ability to improve the estimates of the spatial distribution of saturated hydraulic conductivity and pore size distribution parameters using the secondary information.