Parameter and observation importance in modelling virus transport in saturated porous media-investigations in a homogenous system

This paper evaluates the importance of seven types of parameters to virus transport: hydraulic conductivity, porosity, dispersivity, sorption rate and distribution coefficient (representing physical-chemical filtration), and in-solution and adsorbed inactivation (representing virus inactivation). The first three parameters relate to subsurface transport in general while the last four, the sorption rate, distribution coefficient, and in-solution and adsorbed inactivation rates, represent the interaction of viruses with the porous medium and their ability to persist. The importance of four types of observations to estimate the virus-transport parameters are evaluated: hydraulic heads, flow, temporal moments of conservative-transport concentrations, and virus concentrations. The evaluations are conducted using one- and two-dimensional homogeneous simulations, designed from published field experiments, and recently developed sensitivity-analysis methods. Sensitivity to the transport-simulation time-step size is used to evaluate the importance of numerical solution difficulties. Results suggest that hydraulic conductivity, porosity, and sorption are most important to virus-transport predictions. Most observation types provide substantial information about hydraulic conductivity and porosity; only virus-concentration observations provide information about sorption and inactivation. The observations are not sufficient to estimate these important parameters uniquely. Even with all observation types, there is extreme parameter correlation between porosity and hydraulic conductivity and between the sorption rate and in-solution inactivation. Parameter estimation was accomplished by fixing values of porosity and in-solution inactivation.     

Assessing sensitivity of source term estimation

Source term estimation algorithms compute unknown atmospheric transport and dispersion modeling variables from concentration observations made by sensors in the field. Insufficient spatial and temporal resolution in the meteorological data as well as inherent uncertainty in the wind field data make source term estimation and the prediction of subsequent transport and dispersion extremely difficult. This work addresses the question: how many sensors are necessary in order to successfully estimate the source term and meteorological variables required for atmospheric transport and dispersion modeling?The source term estimation system presented here uses a robust optimization technique – a genetic algorithm (GA) – to find the combination of source location, source height, source strength, surface wind direction, surface wind speed, and time of release that produces a concentration field that best matches the sensor observations. The approach is validated using the Gaussian puff as the dispersion model in identical twin numerical experiments. The limits of the system are tested by incorporating additive and multiplicative noise into the synthetic data. The minimum requirements for data quantity and quality are determined by an extensive grid sensitivity analysis. Finally, a metric is developed for quantifying the minimum number of sensors necessary to accurately estimate the source term and to obtain the relevant wind information.     

Evaluating the sensitivity of a subsurface multicomponent reactive transport model with respect to transport and reaction parameters.

The input variables for a numerical model of reactive solute transport in groundwater include both transport parameters, such as hydraulic conductivity and infiltration, and reaction parameters that describe the important chemical and biological processes in the system. These parameters are subject to uncertainty due to measurement error and due to the spatial variability of properties in the subsurface environment. This paper compares the relative effects of uncertainty in the transport and reaction parameters on the results of a solute transport model. This question is addressed by comparing the magnitudes of the local sensitivity coefficients for transport and reaction parameters. General sensitivity equations are presented for transport parameters, reaction parameters, and the initial (background) concentrations in the problem domain. Parameter sensitivity coefficients are then calculated for an example problem in which uranium(VI) hydrolysis species are transported through a two-dimensional domain with a spatially variable pattern of surface complexation sites. In this example, the reaction model includes equilibrium speciation reactions and mass transfer-limited non-electrostatic surface complexation reactions. The set of parameters to which the model is most sensitive includes the initial concentration of one of the surface sites, the formation constant (Kf) of one of the surface complexes and the hydraulic conductivity within the reactive zone. For this example problem, the sensitivity analysis demonstrates that transport and reaction parameters are equally important in terms of how their variability affects the model results.     

Sensitivity of the solution of the Elder problem to density, velocity and numerical perturbations

In this paper the Elder problem is studied with the purpose of evaluating the inherent instabilities associated with the numerical solution of this problem. Our focus is first on the question of the existence of a unique numerical solution for this problem, and second on the grid density and fluid density requirements necessary for a unique numerical solution. In particular we have investigated the instability issues associated with the numerical solution of the Elder problem from the following perspectives: (i) physical instability issues associated with density differences; (ii) sensitivity of the numerical solution to idealization irregularities; and, (iii) the importance of a precise velocity field calculation and the association of this process with the grid density levels that is necessary to solve the Elder problem accurately. In the study discussed here we have used a finite element Galerkin model we have developed for solving density-dependent flow and transport problems, which will be identified as TechFlow. In our study, the numerical results of Frolkovic and de Schepper [Frolkovic, P. and H. de Schepper, 2001. Numerical modeling of convection dominated transport coupled with density-driven flow in porous media, Adv. Water Resour., 24, 63-72.] were replicated using the grid density employed in their work. We were also successful in duplicating the same result with a less dense grid but with more computational effort based on a global velocity estimation process we have adopted. Our results indicate that the global velocity estimation approach recommended by Yeh [Yeh, G.-T., 1981. On the computation of Darcian velocity and mass balance in finite element modelling of groundwater flow, Water Resour. Res., 17(5), 1529-1534.] allows the use of less dense grids while obtaining the same accuracy that can be achieved with denser grids. We have also observed that the regularity of the elements in the discretization of the solution domain does make a difference in obtaining a unique stationary solution for this problem. The results of our study also indicate that the density differences are critical in the solution of the Elder problem and that high density differences lead to the physical instability that is inherent with this problem. Other than the physical instability associated with the level of density differences used in the Elder problem, the following two points should be considered in solving the Elder problem in a consistent manner: (i) strict attention should be paid to the vertical grid Peclet number in developing the criteria for convergent grid selection; and, (ii) with a globally continuous velocity calculation stable solutions can be obtained at lower grid densities.     

Monte Carlo analysis of field water flow comparing uni- and bimodal effective hydraulic parameters for structured soil

Soil structure critically affects the hydrological behaviour of soils. In this paper, we examined the impact of areal heterogeneity of hydraulic properties of a structured soil on soil ensemble behaviour for various soil water flow processes with different top boundary conditions (redistribution and drainage plus evaporation and infiltration). Using a numerical solution of the Richards' equation in a stochastic framework, the ensemble characteristics and flow dynamics were studied for drying and wetting processes observed during a time interval of ten days when a series of relatively intense rainfall events occurred. The effects of using unimodal and bimodal interpretative models of hydraulic properties on the ensemble hydrological behaviour of the soil were illustrated by comparing predictions to mean water contents measured over time in several sites at field scale. Although the differences between unimodal and bimodal fitting are not significant in terms of goodness of fit, the differences in process predictions are considerable with the bimodal soil simulating water content measurements much better than unimodal soil. We also investigated the relative contribution of the soil variability of each parameter on the variance of the water contents obtained as the main output of the stochastic simulations. The variability of the structural parameter, weighting the two pore space fractions in the bimodal interpretative model, has the largest contribution to water content variance. The contribution of each parameter depends only partly on the coefficient of variation, much more on the sensitivity of the model to the parameters and on the flow process being observed. We observed that the contribution of the retention parameters to uncertainty increases during drainage processes; the opposite occurs with the hydraulic conductivity parameters.     

Application of the method of temporal moments to interpret solute transport with sorption and degradation

In this note, we applied the temporal moment solutions of [Das and Kluitenberg, 1996. Soil Sci. Am. J. 60, 1724] for one-dimensional advective-dispersive solute transport with linear equilibrium sorption and first-order degradation for time pulse sources to analyse soil column experimental data. Unlike most other moment solutions, these solutions consider the interplay of degradation and sorption. This permits estimation of a first-order degradation rate constant using the zeroth moment of column breakthrough data, as well as estimation of the retardation factor or sorption distribution coefficient of a degrading solute using the first moment. The method of temporal moment (MOM) formulae was applied to analyse breakthrough data from a laboratory column study of atrazine, hexazinone and rhodamine WT transport in volcanic pumice sand, as well as experimental data from the literature. Transport and degradation parameters obtained using the MOM were compared to parameters obtained by fitting breakthrough data from an advective-dispersive transport model with equilibrium sorption and first-order degradation, using the nonlinear least-square curve-fitting program CXTFIT. The results derived from using the literature data were also compared with estimates reported in the literature using different equilibrium models. The good agreement suggests that the MOM could provide an additional useful means of parameter estimation for transport involving equilibrium sorption and first-order degradation. We found that the MOM fitted breakthrough curves with tailing better than curve fitting. However, the MOM analysis requires complete breakthrough curves and relatively frequent data collection to ensure the accuracy of the moments obtained from the breakthrough data.     

Evidence of one-dimensional scale-dependent fractional advection-dispersion

A semi-analytical inverse method and the corresponding program FADEMain for parameter estimation of the fractional advection-dispersion equation (FADE) were developed in this paper. We have analyzed Huang et al.'s [Huang, K., Toride, N., van Genuchten, M.Th., 1995. Experimental investigation of solute transport in large homogeneous and heterogeneous saturated soil columns. Trans. Porous Media 18, 283-302.] laboratory experimental data of conservative solute transport in 12.5-m long homogeneous and heterogeneous soil columns to test the non-Fickian dispersion theory of FADE. The dispersion coefficient was calculated by fitting the analytical solution of FADE to the measured data at different transport scales. We found that the dispersion coefficient increased exponentially with transport scale for the homogeneous column, whereas it increased with transport scale in a power law function for the heterogeneous column. The scale effect of the dispersion coefficient in the heterogeneous soil was much more significant comparing to that in the homogeneous soil. The increasing rate of dispersion coefficient versus transport distance was smaller for FADE than that for the advection-dispersion equation (ADE). Finite difference numerical approximations of the scale-dependent FADE were established to interpret the experimental results. The numerical solutions were found to be adequate for predicting scale-dependent transport in the homogeneous column, while the prediction for the heterogeneous column was less satisfactory.     

Investigation of hydrogeologic processes in a dipping layer structure: 2. Transport and biodegradation of organics

Numerical simulation tools have been used to study the dominating processes during transport of aromatic hydrocarbons in the unsaturated soil zone. Simulations were based on field observations at an experimental site located on a glacial delta plain with pronounced layered sedimentary structures. A numerical model for transport in the unsaturated zone, SWMS-3D, has been extended to incorporate coupled multispecies transport, microbial degradation following Monod kinetics and gas diffusive transport of oxygen and hydrocarbons. The flow field parameters were derived from previous work using nonreactive tracers. Breakthrough curves (BTC) from the hydrocarbon field experiment were used to determine sorption parameters and Monod kinetic parameters using a fitting procedure. The numerical simulations revealed that the assumption of homogeneous layers resulted in deviations from the field observations. The deviations were more pronounced with incorporation of reactive transport, compared with earlier work on nonreactive transport. To be able to model reasonable BTC, sorption had to be reduced compared to laboratory experiments. The initial biomass and the maximum utilisation rate could be adjusted to capture both the initial lag phase and the overall degradation rate. Nevertheless, local oxygen limitation is predicted by the model, which was not observed in the field experiment. Incorporation of evaporation and diffusive gas transport of the hydrocarbons did not significantly change the local oxygen demand. The main cause of the observed discrepancies between model and field are attributed to channelling as a result of small-scale heterogeneities such as biopores.     

An application of the theory of kinematics of mixing to the study of tropospheric dispersion

The most common technique used for numerical simulations of tracer mixing is that of the numerical solution of the advection–diffusion equation with the unresolved fluxes parameterized using the similarity theory. Despite correct predictions of the overall directions of transport, models based on a numerical solution of the advection–diffusion equation lack sufficient accuracy to correctly reproduce the coupling of mixing with small scale processes which are sensitive to the microstructure of the tracer distribution. The objective of this paper is to revisit the basic formalism employed in numerical models used to investigate atmospheric tracers. The main mathematical method proposed here is the theory of kinematics of mixing which could be applied effectively for simulations of atmospheric transport processes. At the beginning of the paper, we introduce simple mathematical transformations in order to demonstrate how complex topological structures are created by mixing processes. These idealistic flow systems are essential to explain transport properties of much more complex three-dimensional geophysical flows. An example of the application of the kinematics of mixing to the analysis of tracer transport on a planetary scale is presented in the following sections. The complex filamentary structures simulated in the numerical experiment are evaluated using some commonly applied statistical measures in order to compare the results with the data published in the literature. The results of the experiment are also analysed with the help of simple conceptual models of fluid filaments. The microstructure of the tracer distribution introduced in the paper is essential to increase our understanding of atmospheric transport and to develop more realistic parameterizations of small-scale mixing. The presented results could also be used to improve calculations of the coupling between microphysical processes and tracer mixing.     

Evaluation of ozone exposure indices in exposure-response modeling

In exposure-response modeling, a major concern is the numerical definition of exposure in relating crop loss to O3, yet few indices have been considered. This paper addresses research in which plant growth was regressed for soybean, wheat, cotton, corn, and sorghum against 613 numerical exposure indices using the Box-Tidwell model. When the minimum sum of squared errors criterion was used, optimum performance was not attained for any single index; however, near optimum performances were achieved by two censored cumulative indices and from a class of indices called the generalized, phenologically weighted, cumulative impact indices (GPWCIs). The top-performing GPWCIs accumulated concentrations, used sigmoid weighting schemes emphasizing O3 concentrations of 0.06 ppm (118 microg m(-3)) or higher, and had phenological weighting schemes with greatest weight occurring 20 to 40 days prior to crop maturity. These findings indicate that (1) peak concentrations are important, but lower concentrations should be included in the calculations, (2) increased plant sensitivity occurs between flowering and maturity, and (3) plants respond to cumulative exposure impact.     

Transport modeling of copper and cadmium with linear and nonlinear retardation factors

The predictive accuracy of using the one-dimensional advection–dispersion equation to evaluate the fate and transport of solute in a soil column is usually dependent on the proper determination of chemical retardation factors. Typically, the distribution coefficient (K_d) obtained by fitting the linear sorption isotherm has been extensively used to consider general geochemical reactions on solute transport in a low-concentration range. However, the linear distribution coefficient cannot be adequately utilized to describe the solute fate at a higher concentration level. This study employed the nonlinear equilibrium-controlled sorption parameters to determine the retardation factor used in column leaching experiments. Copper and cadmium transportation in a lateritic silty-clay soil column was examined. Through the explicit finite-difference calculations with a third-order total-variation-diminishing (TVD) numerical solution scheme, all results of the theoretical copper and cadmium breakthrough curves (BTCs) simulated by using the Freundlich nonlinear retardation factors revealed good agreement with the experimental observations.     

Influence of rate-limited sorption on the cleanup of layered soils by vapor extraction

The conditions under which rate-limited sorption is important for cleanup of layered soils by vapor extraction are investigated. The investigation includes two steps: (a) the cleanup time is estimated for a number of scenario cases by means of a numerical model and (b) the numerical results are approximated using analytical solutions derived for simplified models. In this way, equations are derived, which give insight into the influence of different parameters characterizing the properties of the soil, the geometry of the formation, the mass transfer mechanisms in it, and the distribution of the contaminant mass in the different phases (gas phase, water phase and solid phase). The numerical model used is based on the advection-dispersion differential equations for Darcian isothermal airflow, local equilibrium contaminant mass transfer between gas phase and soil water and first-order kinetics for mass transfer between soil water and solid phase. The numerical results are approximated combining an analytical solution to estimate cleanup time in layered formations for local equilibrium sorption, which has been presented in a previous work (J. Contam. Hydrol., 36 (1999) 105). with an analytical solution based on the well-mixed reservoir model under consideration of rate-limited sorption. The analytical approximation of the cleanup time is in reasonable agreement with the numerical results and allows its estimation with small computational effort.     

An interpretation of potential scale dependence of the effective matrix diffusion coefficient

Matrix diffusion is an important process for solute transport in fractured rock, and the matrix diffusion coefficient is a key parameter for describing this process. Previous studies have indicated that the effective matrix diffusion coefficient values, obtained from a large number of field tracer tests, are enhanced in comparison with local values and may increase with test scale. In this study, we have performed numerical experiments to investigate potential mechanisms behind possible scale-dependent behavior. The focus of the experiments is on solute transport in flow paths having geometries consistent with percolation theories and characterized by multiple local flow loops formed mainly by small-scale fractures. The water velocity distribution through a flow path was determined using discrete fracture network flow simulations, and solute transport was calculated using a previously derived impulse-response function and a particle-tracking scheme. Values for effective (or up-scaled) transport parameters were obtained by matching breakthrough curves from numerical experiments with an analytical solution for solute transport along a single fracture. Results indicate that a combination of local flow loops and the associated matrix diffusion process, together with scaling properties in flow path geometry, seems to be an important mechanism causing the observed scale dependence of the effective matrix diffusion coefficient (at a range of scales).     

Identification and reliability of microbial aerobic respiration and denitrification kinetics using a single-well push-pull field test

Methods to derive reaction rates of microbial processes are important since these processes are determining many chemical reactions influencing groundwater quality. Thereby, it is not only important to derive the parameters, but also to have a firm idea about the reliability with which these are determined. Analysis of residuals, sensitivity analyses and analysis of joint confidence intervals provide an interesting tool for this purpose. The method is illustrated in this paper using a push-pull test designed to derive aerobic respiration and denitrification. Therefore, a test solution containing dissolved oxygen and nitrate as reactive tracer and bromide as non-reactive tracer was injected in organic matter rich sediment. Afterwards, this test solution was extracted and water quality was monitored. ReacTrans, a finite-difference, axial-symmetric groundwater flow and solute transport model was developed to simulate the test and derive hydraulic, solute transport and chemical parameters. Aerobic respiration and denitrification were simulated with Michaelis-Menten kinetics. Maximum reaction rates (10.4 and 2.4 mmol/ld for aerobic respiration and denitrification respectively) and Michaelis constants (0.14 and 0.1 mmol/l for aerobic respiration and denitrification respectively) were determined. The reliability with which these parameters are derived is indicated by analysis of residuals, sensitivities and joint confidence intervals. This shows that the Michaelis-Menten parameters can be derived reliable with a push-pull test, whereas the test is insensitive to effective porosity and hydraulic conductivity. Because of the small scale of the test, longitudinal dispersivity was very small and therefore unidentifiable.     

Sensitivity of the DERMA long-range Gaussian dispersion model to meteorological input and diffusion parameters

The Danish Emergency Response Model of the Atmosphere (DERMA) is described and applied to the first ETEX experiment. By using analysed low-resolution numerical weather-prediction data from the global model of the European Centre for Medium-range Weather Forecast (ECMWF) as well as higher-resolution data from two versions of the High Resolution Limited Area Model (HIRLAM), which are operational at the Danish Meteorological Institute (DMI), the sensitivity of DERMA to the resolution of meteorological data is analysed by comparing DERMA results with concentration measurements. Furthermore, the sensitivity to boundary-layer height and diffusion parameters is studied. These parameters include the critical bulk Richardson number, which is used to estimate the atmospheric boundary-layer height, the horizontal eddy diffusivity and the Lagrangian turbulence time scale. The parameters, which provide the best performance of DERMA, are 0.25 for the critical bulk Richardson number, 6×10³ m² s^-1 for the horizontal eddy diffusivity, and 3 h for the Lagrangian time scale. DERMA is much more sensitive to boundary-layer parameters when using high-resolution DMI-HIRLAM data than when using data of lower resolution from the ECMWF. Finally, the bulk Richardson number method of boundary-layer height calculation applied to DMI-HIRLAM data is verified directly against routine radiosondes released under the tracer gas plume. The boundary-layer height estimates based on analysed NWP model data agree well with observations, and the agreement deteriorates as a function of forecast length.     

Assessment of interfacial mass transfer in water-unsaturated soils during vapor extraction

This paper presents results of a numerical investigation of soil vapor extraction (SVE) systems at the laboratory scale. The SVE technique is used to remove volatile chlorinated hydrocarbons (VCHC) from the water-unsaturated soil zone. The developed numerical model solves equations of flow, transport and interfacial mass transfer regarding an isothermal n-component and three-phase system. The mathematical model is based on a simple pore network and phase distribution model and designed to be scaled by a characteristic length. All mathematical expressions are structured into VCHC specific and VCHC non-specific parameters. Furthermore, indicators are introduced that help to separate thermodynamic equilibrium from thermodynamic non-equilibrium domains and to determine the controlling physical parameters. For numerical solution, the system of partial differential equations is discretized by a finite volume method and an implicit Euler time stepping scheme. Computational effort is reduced notably through techniques that enable spatial and temporal adaptivity, through a standard multigrid method as well as through a problem-oriented sparse-matrix storage concept. Computations are carried out in two dimensions regarding the laboratory experiment of Fischer et al. [Water Resour. Res. 32 (12) 1996 3413]. By varying the characteristic length scale of the pore network and phase distribution model, it is shown that the experimental gas phase concentrations cannot be explained only by the volatility and diffusivity of the VCHC. The computational results suggest a sorption process whose significance grows with the aqueous activity of the less or non-polar organic compounds.     

Operator-splitting errors in coupled reactive transport codes for transient variably saturated flow and contaminant transport in layered soil profiles

One possible way of integrating subsurface flow and transport processes with (bio)geochemical reactions is to couple by means of an operator-splitting approach two completely separate codes, one for variably-saturated flow and solute transport and one for equilibrium and kinetic biogeochemical reactions. This paper evaluates the accuracy of the operator-splitting approach for multicomponent systems for typical soil environmental problems involving transient atmospheric boundary conditions (precipitation, evapotranspiration) and layered soil profiles. The recently developed HP1 code was used to solve the coupled transport and chemical equations. For steady-state flow conditions, the accuracy was found to be mainly a function of the adopted spatial discretization and to a lesser extent of the temporal discretization. For transient flow situations, the accuracy depended in a complex manner on grid discretization, time stepping and the main flow conditions (infiltration versus evaporation). Whereas a finer grid size reduced the numerical errors during steady-state flow or the main infiltration periods, the errors sometimes slightly increased (generally less than 50%) when a finer grid size was used during periods with a high evapotranspiration demand (leading to high pressure head gradients near the soil surface). This indicates that operator-splitting errors are most significant during periods with high evaporative boundary conditions. The operator-splitting errors could be decreased by constraining the time step using the performance index (the product of the grid Peclet and Courant numbers) during infiltration, or the maximum time step during evapotranspiration. Several test problems were used to provide guidance for optimal spatial and temporal discretization.     

Semi-analytical solution of two-dimensional sharp interface LNAPL transport models

In this paper, we present semi-analytical solutions for two-dimensional equations governing transport of Light Non-Aqueous Phase Liquids (LNAPL) in unconfined aquifers. The proposed model is based on sharp interface displacement and steady groundwater flow assumptions, where both the water–LNAPL interface and the LNAPL–air interface are represented as sharp interfaces. In the case of steady groundwater flow, these equations can be reduced to a two-dimensional nonlinear solute transport equation, with the LNAPL thickness in the free product lens being the primary unknown variable. The linearized form of this solute transport equation falls into the category of two-dimensional transport equation with time-dependent dispersion coefficients. This equation can be solved analytically for an infinite domain region. In this paper, the general form of the analytical solution for the transport equation, as well as the solutions for some specific cases are presented. To demonstrate the utility of the proposed solution, numerical results obtained for two example problems are discussed and presented comparatively with a finite-element solution and other more restrictive solutions available in the literature. Although the solutions discussed in this paper have some simplifying assumptions, such as sharp-interfaces between fluid phases, steady groundwater flow and homogeneous aquifer properties, the semi-analytical solutions presented in this study may be used effectively as bench mark solutions in evaluating LNAPL migration in the subsurface. These solutions are simple and cost effective to implement and may be used in the calibration of other more complex numerical solutions that can be found in the literature.     

Multi-process herbicide transport in structured soil columns: experiments and model analysis

Model predictions of pesticide transport in structured soils are complicated by multiple processes acting concurrently. In this study, the hydraulic, physical, and chemical nonequilibrium (HNE, PNE, and CNE, respectively) processes governing herbicide transport under variably saturated flow conditions were studied. Bromide (Br-), isoproturon (IPU, 3-(4-isoprpylphenyl)-1,1-dimethylurea) and terbuthylazine (TER, N2-tert-butyl-6-chloro-N4-ethyl-1,3,5-triazine-2,4-diamine) were applied to two soil columns. An aggregated Ap soil column and a macroporous, aggregated Ah soil column were irrigated at a rate of 1 cm h(-1) for 3 h. Two more irrigations at the same rate and duration followed in weekly intervals. Nonlinear (Freundlich) equilibrium and two-site kinetic sorption parameters were determined for IPU and TER using batch experiments. The observed water flow and Br- transport were inversely simulated using mobile-immobile (MIM), dual-permeability (DPM), and combined triple-porosity (DP-MIM) numerical models implemented in HYDRUS-1D, with improving correspondence between empirical data and model results. Using the estimated HNE and PNE parameters together with batch-test derived equilibrium sorption parameters, the preferential breakthrough of the weakly adsorbed IPU in the Ah soil could be reasonably well predicted with the DPM approach, whereas leaching of the strongly adsorbed TER was predicted less well. The transport of IPU and TER through the aggregated Ap soil could be described consistently only when HNE, PNE, and CNE were simultaneously accounted for using the DPM. Inverse parameter estimation suggested that two-site kinetic sorption in inter-aggregate flow paths was reduced as compared to within aggregates, and that large values for the first-order degradation rate were an artifact caused by irreversible sorption. Overall, our results should be helpful to enhance the understanding and modeling of multi-process pesticide transport through structured soils during variably saturated water flow.     

Application of continuous time random walk theory to nonequilibrium transport in soil

Continuous time random walk (CTRW) formulations have been demonstrated to provide a general and effective approach that quantifies the behavior of solute transport in heterogeneous media in field, laboratory, and numerical experiments. In this paper we first apply the CTRW approach to describe the sorbing solute transport in soils under chemical (or) and physical nonequilibrium conditions by curve-fitting. Results show that the theoretical solutions are in a good agreement with the experimental measurements. In case that CTRW parameters cannot be determined directly or easily, an alternative method is then proposed for estimating such parameters independently of the breakthrough curve data to be simulated. We conduct numerical experiments with artificial data sets generated by the HYDRUS-1D model for a wide range of pore water velocities (υ) and retardation factors (R) to investigate the relationship between CTRW parameters for a sorbing solute and these two quantities (υ, R) that can be directly measured in independent experiments. A series of best-fitting regression equations are then developed from the artificial data sets, which can be easily used as an estimation or prediction model to assess the transport of sorbing solutes under steady flow conditions through soil. Several literature data sets of pesticides are used to validate these relationships. The results show reasonable performance in most cases, thus indicating that our method could provide an alternative way to effectively predict sorbing solute transport in soils. While the regression relationships presented are obtained under certain flow and sorption conditions, the methodology of our study is general and may be extended to predict solute transport in soils under different flow and sorption conditions.