Dissolved plume attenuation with DNAPL source remediation, aqueous decay and volatilization--analytical solution, model calibration and prediction uncertainty

A vertically-integrated analytical model for dissolved phase transport is described that considers a time-dependent DNAPL source based on the upscaled dissolution kinetics model of Parker and Park with extensions to consider time-dependent source zone biodecay, partial source mass reduction, and remediation-enhanced source dissolution kinetics. The model also considers spatial variability in aqueous plume decay, which is treated as the sum of aqueous biodecay and volatilization due to diffusive transport and barometric pumping through the unsaturated zone. The model is implemented in Excel/VBA coupled with (1) an inverse solution that utilizes prior information on model parameters and their uncertainty to condition the solution, and (2) an error analysis module that computes parameter covariances and total prediction uncertainty due to regression error and parameter uncertainty. A hypothetical case study is presented to evaluate the feasibility of calibrating the model from limited noisy field data. The results indicate that prediction uncertainty increases significantly over time following calibration, primarily due to propagation of parameter uncertainty. However, differences between the predicted performance of source zone partial mass reduction and the known true performance were reasonably small. Furthermore, a clear difference is observed between the predicted performance for the remedial action scenario versus that for a no-action scenario, which is consistent with the true system behavior. The results suggest that the model formulation can be effectively utilized to assess monitored natural attenuation and source remediation options if careful attention is given to model calibration and prediction uncertainty issues.     

Modeling field-scale multiple tracer injection at a low-level waste disposal site in fractured rocks: effect of multiscale heterogeneity and source term uncertainty on conceptual understanding of mass transfer processes

Multiple factors may affect the scale-up of laboratory multi-tracer injection into structured porous media to the field. Under transient flow conditions and with multiscale heterogeneities in the field, previous attempts to scale-up laboratory experiments have not answered definitely the questions about the governing mechanisms and the spatial extent of the influence of small-scale mass transfer processes such as matrix diffusion. The objective of this research is to investigate the effects of multiscale heterogeneity, mechanistic and site model conceptualization, and source term density effect on elucidating and interpreting tracer movement in the field. Tracer release and monitoring information previously obtained in a field campaign of multiple, conservative tracer injection under natural hydraulic gradients at a low-level waste disposal site in eastern Tennessee, United States, is used for the research. A suite of two-pore-domain, or fracture-matrix, groundwater flow and transport models are calibrated and used to conduct model parameter and prediction uncertainty analyses. These efforts are facilitated by a novel nested Latin-hypercube sampling technique. Our results verify, at field scale, a multiple-pore-domain, multiscale mechanistic conceptual model that was used previously to interpret only laboratory observations. The results also suggest that, integrated over the entire field site, mass flux rates attributable to small-scale mass transfer are comparable to that of field-scale solute transport. The uncertainty analyses show that fracture spacing is the most important model parameter and model prediction uncertainty is relatively higher at the interface between the preferred flow path and its parent bedrock. The comparisons of site conceptual models indicate that the effect of matrix diffusion may be confined to the immediate neighborhood of the preferential flow path. Finally, because the relatively large amount of tracer needed for field studies, it is likely that source term density effect may exaggerate or obscure the effect of matrix diffusion on the movement of tracers from the preferred flow path into the bedrock.     

Uncertainty in Nonpoint Source Pollution Models and Associated Risks

The usefulness of water quality simulation models for environmental management is explored with a focus on prediction uncertainty. The specific objective is to demonstrate how the usability of a flow and transport model (here: MACRO) can be enhanced by developing and analyzing its output probability distributions based on input variability. This infiltration-based model was designed to investigate preferential flow effects on pollutant transport. A statistical sensitivity analysis is used to identify the most uncertain input parameters based on model outputs. Probability distribution functions of input variables were determined based on field-measured data obtained under alternative tillage treatments. Uncertainty of model outputs is investigated using a Latin hypercube sampling scheme (LHS) with restricted pairing for model input sampling. Probability density functions (pdfs) are constructed for water flow rate, atrazine leaching rate, total accumulated leaching, and atrazine concentration in percolation water. Results indicate that consideration of input parameter uncertainty produces a 20% higher mean flow rate along with two to three times larger atrazine leaching rate, accumulated leachate, and concentration than that obtained using mean input parameters. Uncertainty in predicted flow rate is small but that in solute transport is an order of magnitude larger than that of corresponding input parameters. Macropore flow is observed to contribute to the variability of atrazine transport results. Overall, the analysis provides a quantification of prediction uncertainty that is found to enhance a user's ability to assess risk levels associated with model predictions.     

Uncertainty in Nonpoint Source Pollution Models and Associated Risks

The usefulness of water quality simulation models for environmental management is explored with a focus on prediction uncertainty. The specific objective is to demonstrate how the usability of a flow and transport model (here: MACRO) can be enhanced by developing and analyzing its output probability distributions based on input variability. This infiltration-based model was designed to investigate preferential flow effects on pollutant transport. A statistical sensitivity analysis is used to identify the most uncertain input parameters based on model outputs. Probability distribution functions of input variables were determined based on field-measured data obtained under alternative tillage treatments. Uncertainty of model outputs is investigated using a Latin hypercube sampling scheme (LHS) with restricted pairing for model input sampling. Probability density functions (pdfs) are constructed for water flow rate, atrazine leaching rate, total accumulated leaching, and atrazine concentration in percolation water. Results indicate that consideration of input parameter uncertainty produces a 20% higher mean flow rate along with two to three times larger atrazine leaching rate, accumulated leachate, and concentration than that obtained using mean input parameters. Uncertainty in predicted flow rate is small but that in solute transport is an order of magnitude larger than that of corresponding input parameters. Macropore flow is observed to contribute to the variability of atrazine transport results. Overall, the analysis provides a quantification of prediction uncertainty that is found to enhance a user's ability to assess risk levels associated with model predictions.     

Capability and limitations of first-order and diffusion approaches to describe long-term sorption of chlortoluron in soil

This paper compares the capability of a first-order and a spherical diffusion model to describe and predict long-term sorption and desorption processes of chlortoluron in two soils. Chlortoluron sorption was investigated at different time scales utilizing one rate experiment (120 days) and two sorption/desorption experiments. Experimental periods for sorption and desorption were set to 1 day (five desorption steps) and 30 days (three desorption steps), respectively. Upon fitting, the two models satisfactorily described the whole set of data. The spherical diffusion model performed better than the first-order model. We then tested the predictive capability of the models by predicting 30-day sorption/desorption data using kinetic parameters fitted on 1-day sorption/desorption data only. While the spherical diffusion model was able to predict the 30-day data set, the first-order model failed completely. Fitting both models to subsets of the data corresponding to different experimental time scales revealed that the rate parameter as well as the Freundlich coefficient of the first-order model are strongly time-dependent--a property that is not shared by parameters of the spherical diffusion model. The apparent stability of the spherical diffusion model with regard to time dependency of its parameters indicates that sorptive uptake may be diffusion-controlled. This also explains the models greater predictive power across different time scales compared to the first-order model. Finally, we investigate the suitability of solute class specific log-linear relationships between the first-order rate parameter and the Freundlich coefficient presented by earlier researchers in the light of the time dependency observed for the parameters of the first-order model.     

Air Quality Model Evaluation and Uncertainty

The many advances made in air quality model evaluation procedures during the past ten years are discussed and some components of model uncertainty presented. Simplified statistical procedures for operational model evaluation are suggested. The fundamental model performance measures are the mean bias, the mean square error, and the correlation. The bootstrap resampling technique is used to estimate confidence limits on the performance measures, In order to determine if a model agrees satisfactorily with data or if one model is significantly different from another model. Applications to two tracer experiments are described.

It is emphasized that review and evaluation of the scientific components of models are often of greater Importance than the strictly statistical evaluation. A necessary condition for acceptance Of a model should be that it is scientifically correct. It Is shown that even in research-grade tracer experiments, data Input errors can cause errors In hourly-average model predictions of point concentrations almost as large as the predictions themselves. The turbulent or stochastic component of model uncertainty has a similar magnitude. These components of the uncertainty decrease as averaging time increases.     

Development of a fuzzy-stochastic nonlinear model to incorporate aleatoric and epistemic uncertainty

Site uncertainties significantly influence groundwater flow and contaminant transport predictions. Aleatoric and epistemic uncertainty are both identified in site characterization and represented using proper uncertainty theories. When one theory best represents one parameter whereas a different theory may be more suitable for another parameter, the hybrid propagation of aleatoric (random) and epistemic (nonrandom) uncertainties will occur. The computational challenges of joint propagation of aleatoric and epistemic uncertainty through groundwater flow and contaminant transport models are significant. A fuzzy-stochastic nonlinear model was developed in this paper to incorporate these two types of uncertain site information and reduce the computational cost. The results show that (1) the computational cost using the nonlinear model is reduced compared with that of using the sparse grid algorithm and Monte Carlo methods; (2) the uncertainty of hydraulic conductivity (K) significantly influences the water head and solute distribution at the observation wells compared to other uncertain parameters, such as the storage coefficient and the distribution coefficient (K_d); and (3) the combination of multiple uncertain parameters substantially affects the simulation results. Neglecting site uncertainties may lead to unrealistic predictions.     

Interpretation of injection-withdrawal tracer experiments conducted between two wells in a large single fracture

Tracer experiments conducted using a flow field established by injecting water into one borehole and withdrawing water from another are often used to establish connections and investigate dispersion in fractured rock. As a result of uncertainty in the uniqueness of existing models used for interpretation, this method has not been widely used to investigate more general transport processes including matrix diffusion or advective solute exchange between mobile and immobile zones of fluid. To explore the utility of the injection-withdrawal method as a general investigative tool and with the intent to resolve the transport processes in a discrete fracture, two tracer experiments were conducted using the injection-withdrawal configuration. The experiments were conducted in a fracture which has a large aperture (>500 microm) and horizontally pervades a dolostone formation. One experiment was conducted in the direction of the hydraulic gradient and the other in the direction opposite to the natural gradient. Two tracers having significantly different values of the free-water diffusion coefficient were used. To interpret the experiments, a hybrid numerical-analytical model was developed which accounts for the arcuate shape of the flow field, advection-dispersion in the fracture, diffusion into the matrix adjacent to the fracture, and the presence of natural flow in the fracture. The model was verified by comparison to a fully analytical solution and to a well-known finite-element model. Interpretation of the tracer experiments showed that when only one tracer, advection-dispersion, and matrix diffusion are considered, non-unique results were obtained. However, by using multiple tracers and by accounting for the presence of natural flow in the fracture, unique interpretations were obtained in which a single value of matrix porosity was estimated from the results of both experiments. The estimate of porosity agrees well with independent measurements of porosity obtained from core samples. This suggests that: (i) the injection-withdrawal method is a viable tool for the investigation of general transport processes provided all relevant experimental conditions are considered and multiple conservative tracers are used; and (ii) for the conditions of the experiments conducted in this study, the dominant mechanism for exchange of solute between the fracture and surrounding medium is matrix diffusion.     

Laboratory longitudinal diffusion tests: 2. Parameter estimation by inverse analysis

This study focuses on the verification of test interpretations for different state analyses of diffusion experiments. Part 1 of this study identified that steady, quasi-steady and equilibrium state analyses for the through- and in-diffusion tests with solution reservoirs are generally feasible where the tracer is not highly sorptive. In Part 2 we investigate parameter identifiability in transient-state analysis of reservoir concentration variation using a numerical approach. For increased generality, the analytical models, objective functions and Jacobian matrix necessary for inverse analysis of transient-state data are reformulated using unified dimensionless parameters. In these dimensionless forms, the number of unknown parameters is reduced and a single dimensionless parameter represents the sorption property. The dimensionless objective functions are evaluated for individual test methods and parameter identifiability is discussed in relation to the sorption property. The effects of multiple minima and measurement error on parameter identifiability are also investigated. The main findings are that inverse problems for inlet and outlet reservoir concentration analyses are generally unstable and well-posed, respectively. Where the tracer is sorptive, the inverse problem for the inlet reservoir concentration analysis may have multiple minima. When insufficient measurement data is collected, multiple solutions may result and this should be taken into consideration when inversely analyzing data including that of inlet reservoir concentration. Verification of test interpretation by cross-checking different state analyses is feasible where the tracer is not highly sorptive. In an actual experiment, test interpretation validity is demonstrated through consistency between theory and practice for different state analyses.     

Estimating spatially-variable first-order rate constants in groundwater reactive transport systems

Numerical reactive transport models are often used as tools to assess aquifers contaminated with reactive groundwater solutes as well as investigating mitigation scenarios. The ability to accurately simulate the fate and transport of solutes, however, is often impeded by a lack of information regarding the parameters that define chemical reactions. In this study, we employ a steady-state Ensemble Kalman Filter (EnKF), a data assimilation algorithm, to provide improved estimates of a spatially-variable first-order rate constant λ through assimilation of solute concentration measurement data into reactive transport simulation results. The methodology is applied in a steady-state, synthetic aquifer system in which a contaminant is leached to the saturated zone and undergoes first-order decay. Multiple sources of uncertainty are investigated, including hydraulic conductivity of the aquifer and the statistical parameters that define the spatial structure of the parameter field. For the latter scenario, an iterative method is employed to identify the statistical mean of λ of the reference system. Results from all simulations show that the filter scheme is successful in conditioning the λ ensemble to the reference λ field. Sensitivity analyses demonstrate that the estimation of the λ values is dependent on the number of concentration measurements assimilated, the locations from which the measurement data are collected, the error assigned to the measurement values, and the correlation length of the λ fields.     

Application of first-order reliability method to modelling the fate and transport of benzene in groundwater

Parameter uncertainty plays a significant role in decision making regarding groundwater contamination and remediation, especially for non-conservative chemicals. This paper presents a probabilistic screening model to accommodate parameter uncertainty in the aquifer media, and physical–chemical parameters, using the first-order reliability method (FORM). The application of the developed model is illustrated on transport of benzene in groundwater. The results matched those obtained using the Monte Carlo simulation method, with a smaller number of functional evaluations. Parametric studies were conducted to estimate the effect of various parameters on the results.     

An inverse system for incorporation of conditioning to pressure and streamline-based calibration

A streamline-based history matching technique is employed to perform fast and efficient permeability identification and to integrate tracer data into an inverse model. To incorporate tracer data into the inverse model, a given tracer breakthrough curve is interpreted as cumulative breakthrough along independent streamlines. Permeabilities are modified along each streamline to match the tracer breakthrough curve. In this way, there is no explicit computation of sensitivity coefficients, nor any matrix inversion. However, this approach is incomplete by itself. Since the modifications occur along the streamlines, the identified permeability distribution is often incompatible with the actual permeability distribution. Thus, streamlines should be positioned correctly before the streamline-based method is applied. To accomplish this, geostatistical methods such as kriging and sequential Gaussian simulation (SGS) are implemented to provide an appropriate disposition of streamlines at the beginning of the inverse process. Then, permeabilities are iteratively calibrated in a conventional grid system to satisfy pressure and permeability observation data, and simultaneously modified along streamlines to match tracer data. The two independent optimization processes assist mutually and lead to stable convergence to a minimum. By applying the proposed inverse system to synthetic reference fields, it is observed that identified fields satisfactorily reproduce the permeability distribution of the reference fields. In addition, the pressure distributions of the identified and the reference fields are fairly alike, and the identified tracer breakthrough curves are well fitted to those of the reference fields. With regard to spatial patterns of transport behaviors, the streamlines of the identified fields show similar trajectories to those of the reference fields, and the time of flight distributions of the inversed fields are also analogous to those of the reference fields. The proposed inverse system is capable of estimating the future performance of a two-dimensional aquifer from a constrained number of permeability and pressure observation data accompanied by tracer data.     

Modelling the solute transport under nonequilibrium conditions on the basis of mass transfer equations

A solute transport model that describes nonequilibrium adsorption in soil/groundwater systems by mass transfer equations for film and intraparticle diffusion is presented. The model is useful in cases where breakthrough curve spreading cannot be explained by dispersion only. To evaluate its validity, the model was applied to several data sets from column experiments. The validity was also proved by a comparison with an analytical solution for the limiting case of predominating dispersion. Furthermore, a sensitivity analysis was performed to illustrate the influence of different process and sorption parameters (pore water velocity, intraparticle mass transfer coefficient, isotherm nonlinearity) on the shape of the calculated breakthrough curves. The application of the proposed model is discussed in comparison to the widely used dispersed flow/local equilibrium model, and a relationship between both models, which is based on a lumped parameter approach, is shown.     

Simulations of physical nonequilibrium solute transport models: Application to a large-scale field experiment

Equations expressing the spatial moments of solute concentration distributions simulated by various models, in terms of model parameters, have recently been presented. Using independently obtained parameter values, these equations are used to compare simulations of physical non-equilibrium models with spatial moment data collected in a large-scale natural gradient experiment on solute transport. The physical nonequilibrium models examined postulate the existence of layered zones of immobile water through which solute is transported by a diffusion mechanism. It is found that the qualitative aspects of the measured moment behavior are simulated by the physical nonequilibrium models if the independently obtained parameters are modified somewhat on the basis of reasonable corrective assumptions. It is further demonstrated that the physical nonequilibrium models, using parameter values obtained from spatial data, can qualitatively simulate temporal behavior at individual well points in this relatively homogeneous aquifer.     

Uncertainty Analysis of Hydrologic and Water Quality Predictions for a Small Watershed Using SWAT2000

Hydrologic and water quality (H/WQ) models are being used with increasing frequency to devise alternative pollution control strategies. It has been recognized that such models may have a large degree of uncertainty associated with their predictions, and that this uncertainty can significantly impact the utility of the model. In this study, ARRAMIS (Advanced Risk & Reliability Assessment Model) software package was used to analyze the uncertainty of the SWAT2000 (Soil and Water Assessment Tool) outputs concerning nutrients and sediment losses from agricultural lands. ARRAMIS applies Monte Carlo simulation technique connected with Latin hypercube sampling (LHS) scheme. This technique is applied to the Warner Creek watershed located in the Piedmont physiographic region of Maryland, and it provides an interval estimate of a range of values with an associated probability instead of a point estimate of a particular pollutant constituent. Uncertainty of model outputs was investigated using LHS scheme with restricted pairing for the model input sampling. Probability distribution functions (pdfs) for each of the 50 model simulations were constructed from these results. Model output distributions of interest in this analysis were stream flow, sediment, organic nitrogen (organic-N), organic phosphorus (organic-P), nitrate, ammonium, and mineral phosphorus (mineral-P) transported with water. Developed probability distribution functions for the model provided information with desirable probability. Results indicate that consideration of input parameter uncertainty produces 64% less mean stream flow along with approximately 8.2% larger sediment loading than obtained using mean input parameters. On the contrary, mean of outputs regarding nutrients such as nitrate, ammonia, organic-N, and organic-P (but not mineral-P) were almost the same as the one using mean input parameters. The uncertainty in predicted stream flow and sediment loading is large, but that for nutrient loadings is the same as that of the corresponding input parameters. This study concluded that using a best possible distribution for the input parameters to reflect the impact of soils and land use diversity in a small watershed on SWAT2000 model outputs may be more accurate than using average values for each input parameter.     

A multi-component data assimilation experiment directed to sulphur dioxide and sulphate over Europe

Fine particulate matter (PM) is relevant for human health and its components are associated with climate effects. The performance of chemistry transport models for PM, its components and precursor gases is relatively poor. The use of these models to assess the state of the atmosphere can be strengthened using data assimilation. This study focuses on simultaneous assimilation of sulphate and its precursor gas sulphur dioxide into the regional chemistry transport model LOTOS–EUROS using an ensemble Kalman filter. The process of going from a single component setup for SO₂ or SO₄ to an experiment in which both components are assimilated simultaneously is illustrated. In these experiments, solely emissions, or a combination of emissions and the conversion rates between SO₂ and SO₄ were considered uncertain. In general, the use of sequential data assimilation for the estimation of the sulphur dioxide and sulphate distribution over Europe is shown to be beneficial. However, the single component experiments gave contradicting results in direction in which the emissions are adjusted by the filter showing the limitations of such applications. The estimates of the pollutant concentrations in a multi-component assimilation have found to be more realistic. We discuss the behavior of the assimilation system for this application. The model uncertainty definition is shown to be a critical parameter. The increased complexity associated with the simultaneous assimilation of strongly related species requires a very careful specification of the experiment, which will be the main challenge in the future data assimilation applications.     

A framework for error analysis of a long-range transport model with emphasis on parameter uncertainty

A comprehensive framework for model error analysis is applied to the EMEP-W model of longrange transport of sulfur in Europe. This framework includes a proposed taxonomy of model uncertainties. Parameter uncertainties were investigated by Monte Carlo simulation of two source-receptor combinations. A 20% input parameter uncertainty (expressed as a coefficient of variation = standard deviation/mean) yielded a 15–22% output error of total sulfur deposition. The relationship between output error and input uncertainty was approximately proportional. Covariance between parameters can have an important effect on computed model error, and can either exaggerate or reduce errors compared to the uncorrelated case. Of the model state variables, SO₂ air concentration and wet deposition had the highest error, and total sulfur deposition the lowest. It was also found that it is more important to specify the dispersion of the input parameter frequency distributions than their shape. The results of the model error analysis were applied to routine calculations of deposition in Europe. An error (coefficient of variation) of 20% for transfer coefficients throughout Europe yielded spatial variations in the order of a few tens to a few hundreds of km in computed deposition isolines of 2 and 5 g sulfur m⁻²a⁻¹.     

Application of HYDRUS 1D model for assessment of phenol–soil adsorption dynamics

Laboratory-scale batch, vertical, and horizontal column experiments were conducted to investigate the attenuative capacity of a fine-grained clayey soil of local origin in the surrounding of a steel plant wastewater discharge site in West Bengal, India, for removal of phenol. Linear, Langmuir, and Freundlich isotherm plots from batch experimental data revealed that Freundlich isotherm model was reasonably fitted (R ²?=?0.94). The breakthrough column experiments were also carried out with different soil bed heights (5, 10, and 15 cm) under uniform flow to study the hydraulic movements of phenol by evaluating time concentration flow behavior using bromide as a tracer. The horizontal migration test was also conducted in the laboratory using adsorptive phenol and nonreactive bromide tracer to explore the movement of solute in a horizontal distance. The hydrodynamic dispersion coefficients (D) in the vertical and horizontal directions in the soil were estimated using nonlinear least-square parameter optimization method in CXTFIT model. In addition, the equilibrium convection dispersion model in HYDRUS 1D was also examined to simulate the fate and transport of phenol in vertical and horizontal directions using Freundlich isotherm constants and estimated hydrodynamic parameters as input in the model. The model efficacy and validation were examined through statistical parameters such as the coefficient of determination (R ²), root mean square error and design of index (d).