Nobuo Toride

Evaluation of multimodal hydraulic functions in characterizing a heterogeneous field soil

Abstract Soil water retention curves are often used to estimate the hydraulic conductivity function. Unfortunately, single S-shaped functions cannot adequately describe water retention curves of structured soil, especially near saturation. The approach of superposition of two or more unimodal retention functions such as the van Genuchten model was used here to describe retention data of a macroporous soil. A total of 180 cores, 0.05 m diameter and 0.051 m long, were sampled along a 31-m-long transect in three overlying soil horizons. Use of unimodal retention curves leads to an underestimation of observed water contents both near saturation and in the midpore range, while an overestimation is found in the drier range. Superposition of two unimodal retention curves significantly improved the estimation over the entire pressure range. However, the predictions were still not ideal near saturation. With three unimodal curves, a perfect fit was obtained from saturation to residual water content. Most of the multimodal parameter values were moderately heterogeneous along the transect, with the surface horizon slightly more heterogeneous than the deeper layers. The coefficient of variation (CV) for multimodal parameters was generally in the range of 20 to 70%. Use of the multimodal van Genuchten model with the conductivity estimation model of Mualem resulted in conductivities that were generally much smaller than those estimated by the classical unimodal van Genuchten-Mualem model. A preliminary evaluation of the estimated bimodal and trimodal unsaturated hydraulic conductivity model was based on a comparison with independent conductivity measurements using a combination of crust test, hot-air method, and an unsteady drainage flux experiment on large columns. The crust and hot-air data compared best with the estimated trimodal conductivity function. The unsteady drainage data did not match well with the crust and hot-air data and could not be described with any of the estimated conductivity functions.

STANMOD: Model Use, Calibration, and Validation

This article provides an overview of STANMOD, a Windows-based computer software package for evaluating solute transport in soils and groundwater using analytical solutions of the advection-dispersion equation. The software integrates seven separate codes that have been popularly used over the years for a broad range of one-dimensional and multi-dimensional solute transport applications: the CFITM, CFITIM, CXTFIT, CHAIN, and SCREEN models for one-dimensional transport, and the 3DADE and N3DADE models for multi-dimensional transport. All of the models can be run for direct (forward) problems, and several (CFITM, CFITM, CXTFIT, and 3DADE) can also be run for inverse problems. CXTFIT further includes a stochastic stream tube model assuming local-scale equilibrium or nonequilibrium transport conditions. The 3DADE and N3DADE models apply to two- and three-dimensional transport during steady unidirectional water flow assuming equilibrium and nonequilibrium transport, respectively. Nonequilibrium transport can be simulated using the assumption of either physical nonequilibrium (two-region or mobile-immobile type transport) or chemical nonequilibrium (two-site partial equilibrium, partial kinetic sorption). The STANMOD software comes with a large number of example applications illustrating the utility of the different codes for a variety of laboratory and field-scale solute transport problems.

Exact analytical solutions for contaminant transport in rivers 1. The equilibrium advection-dispersion equation

Abstract Analytical solutions of the advection-dispersion equation and related models are indispensable for predicting or analyzing contaminant transport processes in streams and rivers, as well as in other surface water bodies. Many useful analytical solutions originated in disciplines other than surface-water hydrology, are scattered across the literature, and not always well known. In this two-part series we provide a discussion of the advection-dispersion equation and related models for predicting concentration distributions as a function of time and distance, and compile in one place a large number of analytical solutions. In the current part 1 we present a series of one- and multi-dimensional solutions of the standard equilibrium advection-dispersion equation with and without terms accounting for zero-order production and first-order decay. The solutions may prove useful for simplified analyses of contaminant transport in surface water, and for mathematical verification of more comprehensive numerical transport models. Part 2 provides solutions for advective- dispersive transport with mass exchange into dead zones, diffusion in hyporheic zones, and consecutive decay chain reactions.

Discrete Time‐ and Length‐Averaged Solutions of the Advection‐Dispersion Equation

Solute concentrations obtained from displacement experiments in porous media frequently represent discrete values as a result of averaging over a finite sampling interval. For example, effluent curves are made up of time-averaged concentrations while volume-averaged concentrations are obtained from core samples. The discrete concentrations are often described by continuous solutions of macroscopic solute transport equations such as the advection-dispersion equation (ADE). The continuous solution is often shifted to describe the average concentration. This paper compares continuous and time- or length-averaged solutions of the one-dimensional ADE cast in terms of flux- averaged and resident concentrations. Expressions for the time- and length-averaged concentrations are presented for solute applications described by Dirac delta or Heaviside functions (instantaneous and continuous releases of the solute) using four different combinations of solute application and detection modes. A temporal and spatial moment analysis was conducted to compare the traditional continuous description with the discrete time- or length-averaged approach. Graphical and tabular data are presented to evaluate the accuracy of continuous solutions of the ADE for determining transport parameters. Although significant errors may occur for extreme cases with low dispersion coefficients and large sampling intervals, shifting the continuous solution by half the sampling interval generally yields results similar to those obtained with the time- or length-averaged analysis. An advantage of averaged concentrations is that they permit greater flexibility to conduct experiments, since averaged concentrations provide an exact description of the data regardless of the sampling interval.

Exact Analytical Solutions for Contaminant Transport in Rivers

Abstract Contaminant transport processes in streams, rivers, and other surface water bodies can be analyzed or predicted using the advection-dispersion equation and related transport models. In part 1 of this two-part series we presented a large number of one- and multi-dimensional analytical solutions of the standard equilibrium advection-dispersion equation (ADE) with and without terms accounting for zero-order production and first-order decay. The solutions are extended in the current part 2 to advective-dispersive transport with simultaneous first-order mass exchange between the stream or river and zones with dead water (transient storage models), and to problems involving longitudinal advectivedispersive transport with simultaneous diffusion in fluvial sediments or near-stream subsurface regions comprising a hyporheic zone. Part 2 also provides solutions for one-dimensional advective-dispersive transport of contaminants subject to consecutive decay chain reactions.

Modeling Transport in Dual-Permeability Media with Unequal Dispersivity and Velocity

AbstractPorous media such as fractured rock and aggregated soils consist of two pore domains with distinct transport properties. A numerical code was developed to simulate solute concentrations in the two domains using a partitioned solution procedure to efficiently model transport in dual-permeability media. Furthermore, an approximate analytical solution was obtained that allows for different advective and dispersive terms in both flow domains, for a first-type or a third-type inlet condition. Solutions were obtained for local concentrations in both domains as well as effluent concentration and the concentration per medium volume. The problem was solved by decoupling the transport equations using diagonalization. This involves an error for the dispersivity matrix that is related to the difference in dispersivity of both domains. The correctness of the solution was assessed by comparison with numerical results. For low Damkohler numbers the solution was accurate even for a dispersivity ratio of 10. The n...