A FINITE ELEMENT MODEL OF CONTAMINANT MOVEMENT IN GROUNDWATER1

ABSTRACT. Transient, two-dimensional solutions are developed which describe the movement and distribution of a conservative substance in a stream-aquifer system. The solutions are obtained by solving sequentially the groundwater flow and mass transport equations. A variational approach in conjunction with the finite element method is used to solve the groundwater flow equation. Galerkin's approach coupled with the finite element method is used to solve the mass transport equation. Linear approximated triangular elements and a centered scheme of numerical integration are employed to calculate the hydraulic head distribution and the concentration of solute in the flow region. The linear approximation used to define the concentration function within each element is not appropriate for cases involving steep concentration gradients. For such cases, higher order approximations are necessary to assure the continuity of gradients across interelemental boundaries. Numerical examples that illustrate the applicability of the model are presented.     

AN ILLUSTRATION OF MODEL STRUCTURE IDENTIFICATION1

ABSTRACT: The purpose of this article is to discuss the importance of uncertainty analysis in water quality modeling, with an emphasis on the identification of the correct model specification. A wetland phosphorus retention model is used as an example to illustrate the procedure of using a filtering technique for model structure identification. Model structure identification is typically done through model parameter estimation. However, due to many sources of error in both model parameterization and observed variables and data, error-in-variable is often a problem. Therefore, it is not appropriate to use the least squares method for parameter estimation. Two alternative methods for parameter estimation are presented. The first method is the maximum likelihood estimator, which assumes independence of the observed response variable values. In anticipating the possible violation of the independence assumption, a second method, which coupled a maximum likelihood estimator and Kalman filter model, was presented. Furthermore, a Monte Carlo simulation algorithm is presented as a preliminary method for judging whether the model structure is appropriate or not.     

A RATING-CURVE METHOD FOR HYDRODYNAMIC SIMULATIONS IN CONTAMINANT TRANSPORT MODELING1

ABSTRACT: Accurate prediction of hydrodynamics is of great importance to modeling contaminant transport and water quality in a river. Flow conditions are needed in estimating potential exposure contamination levels and the recovery time for a no-action alternative in contaminated sediments remediation. Considering highly meandering characteristics of the Buffalo River, New York, a three-dimensional hydrodynamic model was selected to route upstream flows through the 8-km river section with limited existing information based on the model's fully predictive capability and process-oriented feature. The model was employed to simulate changes in water depth and flow velocity with space and time in response to variation in flow rate and/or water surface elevation at boundaries for given bottom morphometry and initial conditions. Flow conditions of the river reach where historical flow data are not available were computed. A rating-curve approach was developed to meet continuous and event contaminant modeling needs. Rating curves (depth-discharge and velocity-discharge relationships) were constructed at selected stations from the 3-D hydrodynamic simulations of individual flow events. The curves were obtained as steady solutions to an unsteady problem. The rating-curve approach serves to link flow information provided by the hydrodynamic model to a contaminant transport model. With the approach, the linking problem resulting from incompatible model dimensions and grid sizes can be solved. The curves will be used to simulate sediment movement and to predict contaminant fate and transport in the river.     

MANAGEMENT OF FLOOD CONTROL SUMPS AND POLLUTANT TRANSPORT1

ABSTRACT: Levee sump systems are used by many riverine communities for temporary storage of urban wet weather flows. The hydrologic performance and transport of stormwater pollutants in sump systems, however, have not been systematically studied. The objective of this paper is to present a case study to demonstrate development and application of a procedure for assessing the hydraulic performance of flood control sumps in an urban watershed. Two sumps of highly variable physical and hydraulic characteristics were selected for analysis. A hydrologic modeling package was used to estimate the flow hydrograph for each outfall as part of the flow balance for the sump. To validate these results, a water balance was used to estimate the total runoff using sump operational data. The hydrologic model calculations provide a satisfactory estimate of the total runoff and its time‐distribution to the sump. The model was then used to estimate pollutant loads to the sump and to the river. Although flow of stormwater through a sump system is regulated solely by flood‐control requirements, these sumps may function as sedimentation basins that provide purification of stormwater. A sample calculation of removals of several conventional pollutants in the target sumps using a mass balance approach is presented.     

ESTIMATING THE PROBABILITY OF EXCEEDING GROUNDWATER QUALITY STANDARDS1

ABSTRACT: A model for estimating the probability of exceeding groundwater quality standards at environmental receptors based on a simple contaminant transport model is described. The model is intended for locations where knowledge about site-specific hydrogeologic conditions is limited. An efficient implementation methodology using numerical Monte Carlo simulation is presented. The uncertainty in the contaminant transport system due to uncertainty in the hydraulic conductivity is directly calculated in the Monte Carlo simulations. Numerous variations of the deterministic parameters of the model provide an indication of the change in exceedance probability with change in parameter value. The results of these variations for a generic example are presented in a concise graphical form which provides insight into the topology of the exceedance probability surface. This surface can be used to assess the impact of the various parameters on exceedance probability.     

Optimal Location and Management of Waste Disposal Facilities Affecting Ground Water Quality1

ABSTRACT: Numerical simulation of ground water solute transport is combined with linear programming to optimize waste disposal. A discretized form of the equation governing solute transport is included as a set of constraints in a linear program. Two problems are described. First, the management model is used to maximize ground water waste disposal. The model constrains disposal activities so that the quality of local ground water supplies is protected. Parametric programming is shown to be important in evaluating waste disposal tradeoffs at the various facilities. Changes in the velocity field induced by waste water injection cause a nonlinearity in the solute transport equation which is dealt with by employing an iterative procedure. The second problem is aimed at identifying all sites which are suitable for waste disposal in the subsurface. The management model is manipulated so that the optimal value of the dual variables are “unit source impact indicators.” This physical interpretation is valuable in identifying feasible disposal sites. The joint simulation and optimization approach permits the management of complex ground water systems where the aquifer is used simultaneously for waste disposal and water supply.     

Detailed characterization of solute transport in a heterogeneous field soil

There is a necessity for improved physical understanding of solute transport processes in heterogeneous soil systems. In situ nondestructive techniques like time domain reflectometry (TDR) and fiber optic miniprobes (FOMPs) permit the collection of unique measurements of solute transport processes in soils for the purposes of model development and validation. This study examined the application of TDR and FOMPs to measure solute transport at various points laterally and at two depths in a heterogeneous clay-loam soil. A miscible displacement experiment was performed at a constant irrigation flux to examine the applicability of these probes to field soils. In their first application to a field soil, the FOMPs were successfully calibrated and performed well in measuring solute breakthrough curves. Two flow regimes were identified in the soil profile, the first where lateral spreading of the solute occurred in the surface horizon, followed by convergence into preferential flow pathways in the second transport zone. The measured transport response was heterogeneous with at least two identifiable vertical flow phases. It was demonstrated using transfer function modeling and data from a corresponding laboratory study that the FOMPs were measuring the slower phase, while the TDR probes captured a composite of the fast and slow phases. The combination of these two techniques may be a means to separate solute transport phases in heterogeneous media and relate laboratory column results to field studies.     

Solute movement through an allophanic soil

Allophanic soils are widespread around the world, but little research has been done on their transport properties. This study reveals the effect of two soil water potential heads and two water-flow regimes of continuous and intermittent flow on solute transport through undisturbed soil columns of Horotiu silt loam (Typic Hapludand), an allophanic soil. Two different methods--breakthrough curves (BTCs) and time domain reflectometry (TDR)--were employed to determine the extent of preferential solute transport in the topsoil. The TDR data were also used to look at the depth dependence of the transport properties. The convection-dispersion equation (CDE) with the appropriate boundary conditions adequately described the movement of both Br and Cl under the various flow conditions. Although no preferential flow was found under the imposed unsaturated flow conditions, the flow of water and transport of solute became more uniform with depth. The results show that both Br and Cl are retarded in this allophanic soil. Retardation values range from 1.5 to 1.9, and, as the TDR data showed, increase from the depth of 5.0 to 10.0 cm. Intermittent leaching results showed that there was no effect on solute concentrations in the leachate following no-flow periods. This suggests that water and solute transport in this soil were either relatively uniform or that transverse mixing during flow was already fast enough to eliminate concentration gradients between regions of different "mobility."     

TRANSIENT STORAGE ASSESSMENTS OF DYE‐TRACER INJECTIONS IN RIVERS OF THE WILLAMETTE BASIN,OREGON1

ABSTRACT: Rhodamine WT dye‐tracer injections in rivers of the Willamette Basin yield concentration‐time curves with characteristically long recession times suggestive of active transient storage processes. The scale of drainage areas contributing to the stream reaches studied in the Willamette Basin ranges from 10 to 12,000 km². A transient storage assessment of the tracer studies has been completed using the U.S. Geological Survey's One‐dimensional Transport with Inflow and Storage (OTIS) model, which incorporates storage exchange and decay functions along with the traditional dispersion and advection transport equation. The analysis estimates solute transport of the dye. It identifies first‐order decay coefficients to be on the order of 10^?5/sec for the nonconservative Rhodamine W.T. On an individual subreach basis, the first‐order decay is slower (typically by an order of magnitude) than the transient storage process, indicating that nonconservative tracers may be used to evaluate transient storage in rivers. In the transient storage analysis, a dimensionless parameter (A_s/A) expresses the spatial extent of storage zone area relative to stream cross section. In certain reaches of Willamette Basin pool‐and‐riffle, gravel‐bed rivers, this parameter was as large as 0.5. A measure of the storage exchange flux was calculated for each stream subreach in the simulation analysis. This storage exchange is shown subjectively to be higher at higher stream discharges. Hyporheic linkage between streams and subsurface flows is the probable physical mechanism contributing to a significant part of this inferred active transient storage. Hyporheic linkages are further suggested by detailed measurements of river discharge with an Acoustic Doppler Current Profiler system delineating zones in two large rivers where water alternately enters and leaves the surface channels through gravel‐and‐cobble riverbeds. Measurements show patterns of hyporheic exchange that are highly variable in time and space.     

CALCULATION OF NONLINEAR CONFIDENCE AND PREDICTION INTERVALS FOR GROUND-WATER FLOW MODELS1

ABSTRACT: A method is derived to efficiently compute nonlinear confidence and prediction intervals on any function of parameters derived as output from a mathematical model of a physical system. The method is applied to the problem of obtaining confidence and prediction intervals for manually-calibrated ground-water flow models. To obtain confidence and prediction intervals resulting from uncertainties in parameters, the calibrated model and information on extreme ranges and ordering of the model parameters within one or more independent groups are required. If random errors in the dependent variable are present in addition to uncertainties in parameters, then calculation of prediction intervals also requires information on the extreme range of error expected. A simple Monte Carlo method is used to compute the quantiles necessary to establish probability levels for the confidence and prediction intervals. Application of the method to a hypothetical example showed that includsion of random errors in the dependent variable in addition to uncertainties in parameters can considerably widen the prediction intervals.     

Effects of initial solute distribution on contaminant availability, desorption modeling, and subsurface remediation

Low permeability regions in which solute movement is governed by diffusion reduce the availability of pollutants for remediation and can function as long-term sources of groundwater contamination. The inherent difficulty in understanding mass transfer from these regions of sequestered contamination is further complicated by unknown solute distributions within the low-permeability regions (sequestering regions). When models are calibrated to reproduce temporal histories of solute release from a sequestering region (desorption), the fitted parameter values are used to infer the physical or chemical characteristics of the media; however, the calibrated parameters also reflect the case-specific initial conditions (i.e., the solute distribution within the sequestering region domain at the onset of desorption). This phenomenon is demonstrated using model simulations of solute diffusion from hypothetical solids with characteristics similar to those of the well studied Borden, Ontario aquifer system. Solute release from the solids is simulated using a batch diffusion model under different initial solute distributions within the solids. The results of these model simulations are used to calibrate parameters of a multiple first-order rate desorption model (MRM) to illustrate how the fitted MRM parameters increase or decrease depending on the initial "aging" of the solids. Further numerical simulations are conducted for a one-dimensional flow system under steady-state and variable-rate hydraulic flushing. These simulations show that although aging reduces desorptive mass flux during early stages of flushing, aged sites have greater desorptive mass flux (greater solute availability) than "freshly" contaminated media during the later stages of remediation. Overall, the results demonstrate why the physicochemical meaning of observed desorption rates cannot be accurately deduced without first understanding the initial solute distribution within the media.     

Mapping ground water vulnerability to pesticide leaching with a process-based metamodel of EuroPEARL

To support EU policy, indicators of pesticide leaching at the European level are required. For this reason, a metamodel of the spatially distributed European pesticide leaching model EuroPEARL was developed. EuroPEARL considers transient flow and solute transport and assumes Freundlich adsorption, first-order degradation and passive plant uptake of pesticides. Physical parameters are depth dependent while (bio)-chemical parameters are depth, temperature, and moisture dependent. The metamodel is based on an analytical expression that describes the mass fraction of pesticide leached. The metamodel ignores vertical parameter variations and assumes steady flow. The calibration dataset was generated with EuroPEARL and consisted of approximately 60,000 simulations done for 56 pesticides with different half-lives and partitioning coefficients. The target variable was the 80th percentile of the annual average leaching concentration at 1-m depth from a time series of 20 yr. The metamodel explains over 90% of the variation of the original model with only four independent spatial attributes. These parameters are available in European soil and climate databases, so that the calibrated metamodel could be applied to generate maps of the predicted leaching concentration in the European Union. Maps generated with the metamodel showed a good similarity with the maps obtained with EuroPEARL, which was confirmed by means of quantitative performance indicators.     

Simulating solute transport in a structured field soil: uncertainty in parameter identification and predictions

Dual-permeability models have been developed to account for the significant effects of macropore flow on contaminant transport, but their use is hampered by difficulties in estimating the additional parameters required. Therefore, our objective was to evaluate data requirements for parameter identification for predictive modeling with the dual-permeability model MACRO. Two different approaches were compared: sequential uncertainty fitting (SUFI) and generalized likelihood uncertainty estimation (GLUE). We investigated six parameters controlling macropore flow and pesticide sorption and degradation, applying MACRO to a comprehensive field data set of bromide andbentazone [3-isopropyl-1H-2,1,3-benzothiadiazin-4(3H)-one-2,2dioxide] transport in a structured soil. The GLUE analyses of parameter conditioning for different combinations of observations showed that both resident and flux concentrations were needed to obtain highly conditioned and unbiased parameters and that observations of tracer transport generally improved the conditioning of macropore flow parameters. The GLUE "behavioral" parameter sets covered wider parameter ranges than the SUFI posterior uncertainty domains. Nevertheless, estimation uncertainty ranges defined by the 5th and 95th percentiles were similar and many simulations randomly sampled from the SUFI posterior uncertainty domains had negative model efficiencies (minimum of -3.2). This is because parameter correlations are neglected in SUFI and the posterior uncertainty domains were not always determined correctly. For the same reasons, uncertainty ranges for predictions of bentazone losses through drainflow for good agricultural practice in southern Sweden were 27% larger for SUFI compared with GLUE. Although SUFI proved to be an efficient parameter estimation tool, GLUE seems better suited as a method of uncertainty estimation for predictions.     

CRITICAL EVALUATION OF CERTAIN METHODS OF UNSTEADY GROUNDWATER HYDRAULICS1

The basic theories and fundamental assumptions usually employed in the solution of unsteady groundwater flow problems are reviewed critically. The best known method of analysis for such problems is based on the Dupuit-Forchheimer approximation and leads to a nonlinear parabolic differential equation which is generally solved by linearization or numerical methods. The accuracy of the solution to this equation can be improved by use of a different approach which does not employ the Dupuit Forchheimer assumption, but rather is based on a semi-numerical solution of the Laplace equation for quasi-steady conditions. The actual unsteady process is replaced by a sequence of steady-state conditions, and it is assumed that the actual unsteady flow characteristics during a short time interval can be approximated by those associated with “average” steady state flow. The Laplace equation is solved by a semi-discretization method according to which the horizontal coordinate is divided into subintervals, while the vertical coordinate is maintained continuous. The proposed method is applied to a typical tile drainage problem, and, based on a comparison of calculated results with experimental data, the method is evaluated and practical conclusions regarding its applicability are advanced.     

OPTIMAL ALLOCATION OF ARTIFICIAL AERATION ALONG A POLLUTED STREAM USING DYNAMIC PROGRAMMING1

ABSTRACT: When a series of aerators are used to raise the level of dissolved oxygen in a polluted stream through instream artificial aeration augmentation, the system is governed by the basic dissolved oxygen mass balance equation with the existence of artificial aeration as its boundary conditions. A mathematical model is formulated for the optimization of the allocation of aeration capacity to each of the series of aerators subject to a limitation on total available aeration capacity. The objective function is the minimization of the sum of the squares of the aeration costs and the costs incurred by damaging or unnecessarily improving the system. The original constrained allocation problem is simplified by converting it to an unconstrained one via the use of Lagrange multiplier. A discretized dynamic programming algorithm is formulated for finding the optimal allocation policy. A typical optimal aeration capacity allocation policy and its corresponding dissolved oxygen sag profile for the illustrated numerical example is presented, and the relationship between the total available aeration capacity and Lagrange multiplier is also developed treating weighting factors as parameters.     

非等距饱和指数曲线参数的灰色辨识及其应用

根据非等距ＧＭ（１,１）的建模原理,建立了非等距和指数曲线参数灰色辨识的二次一元线性回归解法。初步应用表明,本法计算简便,信息利用率高,拟合精度好,不仅为饱和指娄曲线参数辨识提供了新途径,也进一步拓广了它的应用范围。     

ASSESSMENT OF HYDRAULIC PROPERTIES IN AN UNCONFINED ALLUVIAL AQUIFER NEAR GRAND ISLAND,NEBRASKA1

ABSTRACT: A method is presented to analyze time-drawdown data from one or more observation wells for the calculation of four hydraulic parameters for unconfined aquifers: vertical hydraulic conductivity, horizontal hydraulic conductivity, storage coefficient, and specific yield. The hydraulic parameter results are further analyzed for reliability and the possible ranges of the actual parameter values. After verification using a theoretical example, the method was used to analyze pumping test data from 22 observation wells in an unconfined alluvial aquifer near Grand Island, Nebraska. Results indicate that this method can be used to efficiently calculate the four hydraulic parameters in this type of aquifer. The method can also identify the impact of measurement errors on the parameter estimates, and provide ranges of the actual parameter values. The parameter values calculated using this method were compared to those determined using other theories. It is found that this method is very useful for calculating the hydraulic properties from pumping test data and for analyzing the parameter reliability.     

Model Development and Calibration of a Saltwater Intrusion Model in Southern California1

Abstract: A nine‐layered confined‐unconfined flow and transport model is developed for the Alamitos saltwater intrusion barrier in Southern California. The conceptual model is based on the geological structure of the coastal aquifer system. The key parameters in the flow and transport models are calibrated using a two‐phase procedure which matches the types of data available for calibration. Because of the abundance of point measurements of hydraulic conductivity, the heterogeneous and random hydraulic conductivity field for each of the five aquifers is estimated by the geostatiscal method of natural‐neighbor‐kriging in Phase 1. In Phase 2, the longitudinal and transverse dispersivities in the transport model are estimated by a traditional inverse procedure that minimizes the least‐squares error for concentration (LSE‐CON). The minimum LSE‐CON is achieved near 15.2 and 1.52 m for the longitudinal and transverse dispersivities, respectively. Additional simulations with increasing transport parameter complexity did not yield significant improvements in LSE‐CON. Also, tracking least‐squares error for head while parametrically varying the transport parameters revealed there is a negligible interaction between predicted head and transport parameters.     

PARAMETER IDENTIFICATION IN A TWO‐MULTIPLIER SEDIMENT YIELD MODEL1

ABSTRACT: A process based, distributed runoff erosion model (KINEROS2) was used to examine problems of parameter identification of sediment entrainment equations for small watersheds. Two multipliers were used to reflect the distributed nature of the sediment entrainment parameters: one multiplier for a raindrop induced entrainment parameter, and one multiplier for a flow induced entrainment parameter. The study was conducted in three parts. First, parameter identification was studied for simulated error free data sets where the parameter values were known. Second, the number of data points in the simulated sedigraphs was reduced to reflect the effect of temporal sampling frequency on parameter identification. Finally, event data from a small range‐land watershed were used to examine parameter identifiability when the parameter values are unknown. Results demonstrated that whereas unique multiplier values can be obtained for simulated error free data, unique parameter values could not be obtained for some event data. Unique multiplier values for raindrop induced entrainment and flow induced entrainment were found for events with greater than a two‐year return period (～25 mm) that also had at least 10 mm of rain in ten minutes. It was also found that the three‐minute sampling frequency used for the sediment sampler might be inadequate to identify parameters in some cases.