Abstract A new and relatively simple equation for the soil‐water content‐pressure head curve, θ( h ), is described in this paper. The particular form of enables one to derive closed‐form analytical expressions relative hydraulic conductivity, K r , when substituted predictive conductivity models N.T. Burdine or Y. Mualem. resulting ( ) contain three independent parameters which may be obtained by fitting proposed retention model experimental data. Results with based on Mualem theory are...

Abstract An analytical solution is presented for the movement of chemicals through a sorbing porous medium with lateral or intra‐aggregate diffusion. The liquid phase in divided into mobile and immobile regions. Diffusional transfer between two regions assumed to be proportional concentration difference liquids. Sorption processes both dynamic stagnant are instantaneous adsorption isotherm linear. model derived here describes extensive tailing observed during flow an unsaturated, aggregated...

A one-dimensional dual-porosity model has been developed for the purpose of studying variably saturated water flow and solute transport in structured soils or fractured rocks. The involves two overlaying continua at macroscopic level: a macropore fracture pore system less permeable matrix system. Water both systems is assumed to be mobile. Variably as well described with Richards' equation, convection-dispersion equation. Transfer solutes between regions simulated by means first-order rate...

Mathematical models have become indispensable tools for studying vadose zone flow and transport processes. We reviewed the history of development, main processes involved, selected applications HYDRUS related software packages developed collaboratively by several groups in United States, Czech Republic, Israel, Belgium, Netherlands. Our focus was on modeling jointly U.S. Salinity Laboratory USDA, Agricultural Research Service, University California, Riverside. This collaboration during past...

Core Ideas Review of selected capabilities HYDRUS implemented since 2008 New standard and nonstandard specialized add‐on modules significantly expanded the software applications models published in VZJ elsewhere recent years The HYDRUS‐1D (2D/3D) computer packages are widely used finite‐element for simulating one‐ two‐ or three‐dimensional movement water, heat, multiple solutes variably saturated media, respectively. In 2008, Šimůnek et al. (2008b) described entire history development...

Inversely obtained hydrologic parameters are always uncertain (nonunique) because of errors associated with the measurements and invoked conceptual model, among other factors. Quantification this uncertainty in multidimensional parameter space is often difficult complexities structure objective function. In study we describe uncertainties using uniform distributions fit these iteratively within larger absolute intervals such that two criteria met: (i) bracketing most measured data (>90%)...

A conceptual model for colloid transport is developed that accounts attachment straining, and exclusion. Colloid detachment modeled using first-order rate expressions, whereas straining described an irreversible term depth dependent. Exclusion by adjusting parameters colloid-accessible pore space. Fitting to data provided a reasonable description of effluent concentration curves, but the spatial distribution retained colloids at column inlet was severely underestimated systems exhibited...

Abstract The solution of many field‐scale flow and transport problems requires estimates unsaturated soil hydraulic properties. objective this study was to calibrate neural network models for prediction water retention parameters saturated conductivity, K s , from basic Twelve were developed predict using a data set 1209 samples containing sand, silt, clay contents, bulk density, porosity, gravel content, horizon as well data. A subset 620 used develop 19 . Prediction generally improved if...

Inversely obtained hydrologic parameters are always uncertain (nonunique) because of errors associated with the measurements and invoked conceptual model, among other factors. Quantification this uncertainty in multidimensional parameter space is often difficult complexities structure objective function. In study we describe uncertainties using uniform distributions fit these iteratively within larger absolute intervals such that two criteria met: (i) bracketing most measured data (>90%) 95%...

Abstract Analytical solutions are presented for two convection‐dispersion type transport models useful studying simultaneous pesticide sorption and degradation. One solution is the familiar two‐site model in which adsorption‐desorption proceeds kinetically on one fraction of sites, at equilibrium remaining sites. Another holds two‐region (or mobile‐immobile liquid phase) appropriate aggregated or fractured media. The account degradation both sorbed phases. dimensionless analytical shown to...

Accurate process‐based modeling of nonequilibrium water flow and solute transport remains a major challenge in vadose zone hydrology. Our objective here was to describe wide range approaches available within the latest version HYDRUS‐1D software package. The formulations from classical models simulating uniform transport, relatively traditional mobile‐immobile physical two‐site chemical models, more complex dual‐permeability that consider both nonequilibrium. are divided into three groups:...

This paper gives a review of our current conceptual understanding the basic processes water flow and chemical transport in untsaturated (vadose) zone various deterministic mathematical models that are being used to describe these processes. During past few decades, tremendous effort has been directed toward unravelling complexities interactive physical, chemical, microbiological mechanisms affecting unsaturated transport, with contributions made by soil scientists, geochemists, hydrologists,...

Accurate estimates of the unsaturated hydraulic properties are needed for any quantitative description multiphase flow in porous media. This paper presents a consistent set parametric models isothermal, hysteretic fluid phase content (retention) and conductivity functions typical two‐phase systems like water air, or hydrocarbons. The equations obtained by combining expressions retention curves with statistical pore size distribution model Mualem (1976) which predicts from more easily...

Abstract This paper presents a discussion of the physical and mathematical significance various boundary conditions applicable to one‐dimensional solute transport through relatively short laboratory soil columns. Based on mass balance considerations, it is shown that first‐type or concentration‐type condition at inlet incorrectly predicts volume‐averaged resident concentration inside both semi‐infinite finite systems. A third‐type flux‐type preserves in systems, but underpredicts effluent...

A new method is presented to account for phase changes in a fully implicit numerical model coupled heat transport and variably saturated water flow involving conditions both above below zero temperature. The based on mixed formulation similar the approach commonly used Richards equation. enabled numerically stable, energy‐ mass‐conservative solutions. was evaluated by comparing predictions with data from laboratory column freezing experiments. These experiments involved 20‐cm long soil...

Abstract The unsaturated hydraulic properties of soils are important but difficult to measure. Rather than measuring the directly, we followed a different approach by fitting analytical expressions for soil water retention and conductivity functions experimental data wide range in Netherlands. Analysis shows flexibility also gives insight into how model parameters affect calculated functions. Regression analyses used relate estimated more easily measured properties, such as bulk density...

Transformations between volume‐averaged pore fluid concentrations and flux‐averaged are presented which show that both modes of concentration obey convective‐dispersive transport equations identical mathematical form for nonreactive solutes. The pertinent boundary conditions the two modes, however, do not transform identically. Solutions convection‐dispersion equation a semi‐infinite system during steady flow subject to first‐type inlet condition is shown yield flux concentrations, while...

Breakthrough curves (BTCs) of the cation 45 Ca 2+ , an anion 36 Cl − and 3 H 2 O were measured during miscible displacement through water‐saturated soil columns packed with aggregates Oxisol. Two conceptual models used to simulate observed asymmetry tailing in BTCs caused by apparent nonequilibrium situation porous medium. In both exchange process on one type site was assumed be instantaneous while rate isotopic another either a diffusion‐controlled (model 1) or first‐order reversible...