Evaluating the ability of a numerical weather prediction model to forecast tracer concentrations during ETEX 2

In this paper the meteorological processes responsible for transporting tracer during the second ETEX (European Tracer EXperiment) release are determined using the UK Met Office Unified Model (UM). The UM predicted distribution of tracer is also compared with observations from the ETEX campaign. The dominant meteorological process is a warm conveyor belt which transports large amounts of tracer away from the surface up to a height of 4 km over a 36 h period. Convection is also an important process, transporting tracer to heights of up to 8 km. Potential sources of error when using an operational numerical weather prediction model to forecast air quality are also investigated. These potential sources of error include model dynamics, model resolution and model physics. In the UM a semi-Lagrangian monotonic advection scheme is used with cubic polynomial interpolation. This can predict unrealistic negative values of tracer which are subsequently set to zero, and hence results in an overprediction of tracer concentrations. In order to conserve mass in the UM tracer simulations it was necessary to include a flux corrected transport method. Model resolution can also affect the accuracy of predicted tracer distributions. Low resolution simulations (50 km grid length) were unable to resolve a change in wind direction observed during ETEX 2, this led to an error in the transport direction and hence an error in tracer distribution. High resolution simulations (12 km grid length) captured the change in wind direction and hence produced a tracer distribution that compared better with the observations. The representation of convective mixing was found to have a large effect on the vertical transport of tracer. Turning off the convective mixing parameterisation in the UM significantly reduced the vertical transport of tracer. Finally, air quality forecasts were found to be sensitive to the timing of synoptic scale features. Errors in the position of the cold front relative to the tracer release location of only 1 h resulted in changes in the predicted tracer concentrations that were of the same order of magnitude as the absolute tracer concentrations.     

One-dimensional simulation of solute transfer in saturated–unsaturated porous media using the discontinuous finite elements method

A one-dimensional transport model for simulating water flow and solute transport in homogeneous–heterogeneous, saturated–unsaturated porous media is presented. The model is composed of a combination of accurate numerical algorithms for solving the nonlinear Richard's and advection–dispersion equations (ADE). The mixed form of Richard's equation is solved using a standard finite element method (FEM) with primary variable switching. The transport equation is solved using operator splitting, with the discontinuous finite element method (DFE) for discretization of the advective term. A slope limiting procedure for DFE avoids numerical instabilities but creates very limited numerical dispersion for high Peclet numbers. An implicit finite differences scheme (FD) is used for the dispersive term.The unsaturated flow and transport model (Wamos-T) is applied to a variety of rigorous problems including transient flow, heterogeneous medium and abrupt variations of velocity in magnitude and direction due to time-varying boundary conditions. It produces accurate and mass-conservative solutions for a very large range of grid Peclet numbers. The Wamos-T model is a good and robust alternative for the simulation of mass transport in unsaturated domain.     

Optimum design of the entrance of a fishpond laterally to the main stream of an open channel

In this study, the optimum design of the entrance of a fishpond laterally to the main flow of an open channel was investigated numerically and experimentally. The flow characteristic measurements were realized with the PIV (particle image velocimetry) method. The mathematical simulations were based on the development of a two dimensional -mean in depthhydrodynamic model and a quasi three dimensional sediment transport model which includes processes of advection, diffusion, and settling of conservative suspended matter. The study was completed with the comparison of the final results of the mathematical models with the findings of the physical model revealing the hydrodynamic interaction and coupling between the main flow of the channel and the lateral reservoir—fishpond and leading to the optimum technical design of the system.     

First-passage-time transfer functions for groundwater tracer tests conducted in radially convergent flow

Forced-gradient groundwater tracer tests may be conducted using a variety of hydraulic schemes, so it is useful to have simple semi-analytic models available that can examine various injection/withdrawal scenarios. Models for radially convergent tracer tests are formulated here as transfer functions, which allow complex tracer test designs to be simulated by a series of simple mathematical expressions. These mathematical expressions are given in Laplace space, so that transfer functions may be placed in series by simple multiplication. Predicted breakthrough is found by numerically inverting the composite transfer function to the time-domain, using traditional computer programs or commercial mathematical software. Transport is assumed to be dictated by a radially convergent or uniform flow field, and is based upon an exact first-passage-time solution of the backward Fokker–Planck equation. These methods are demonstrated by simulating a weak-dipole tracer test conducted in a fractured granite formation, where mixing in the injection borehole is non-ideal.     

Modeling tracer diffusion in fractured and unfractured, unsaturated, porous media

A proposed tracer diffusion test for the Exploratory Shaft Facility at Yucca Mountain, NV, is modeled. For the proposed test, a solution containing conservative tracers will be introduced into a borehole in the geologic medium of interest. The tracers will diffuse and advect from the saturated source region into the unsaturated matrix in the surrounding tuff. After some time, the borehole is to be overcored, and tracer concentrations in the fluid will be measured in the core as a function of distance from emplacement. The data will be used to evaluate diffusive behavior and to derive effective diffusion coefficients for the tracers in the specific tuff. Numerical simulations are used to study the effects of effective diffusion coefficient, porosity, saturation, and fracturing on tracer transport. Results are reported for numerical simulations of tests in the Topopah Spring Member and the Tuff of Calico Hills, which have significantly different porosities and saturations. The simulations make the following predictions: The spread of tracer during the test will be sensitive to the effective diffusion coefficient of the tracer. Tracer will diffuse farther in the Topopah Spring Member than in the Tuff of Calico Hills because of the former's lower porosity and saturation. Tracer transport by advection into the Topopah Spring Member will be greater than that into the Tuff of Calico Hills because of capillary effects. While advection will be a significant mechanism for tracer penetration into the Topopah Spring tuff, it will be less significant for tracer penetration into the Calico Hills tuff. The proximity of a single vertical fracture to the source region determines its effects on tracer transport, especially if the fracture diverts fluid flowing from the source region into the matrix.     

Multidimensional, multicomponent, subsurface reactive transport in nonuniform velocity fields: code verification using an advective reactive streamtube approach

High performance computing has made possible the development of high resolution, multidimensional, multicomponent reactive transport models that can be used to analyze complex geochemical environments. However, as increasingly complex processes are included in these models, the accuracy of the numerical formulation coupling the nonlinear processes becomes difficult to verify. Analytical solutions are not available for realistically complex problems and benchmark solutions are not generally available for specific problems. We present an advective reactive streamtube (ARS) transport technique that efficiently provides accurate solutions of nonlinear multicomponent reactive transport in nonuniform multidimensional velocity fields. These solutions can be compared with results from Eulerian-based advection-dispersion-reaction models to evaluate the accuracy of the numerical formulation used. The ARS technique includes mixed equilibrium and kinetic complexation and precipitation-dissolution reactions subject to the following assumptions: (1) transport is purely advective (i.e., no explicit diffusion or dispersion), and (2) chemistry is described by a canonical system of reactions that evolves with time and is unaffected by position in space. Results from the ARS technique are compared with results from the massively parallel, multicomponent reactive transport model MCTRACKER on a test problem involving irreversible oxidation of organic carbon and reaction of the oxidation products with two immobile mineral phases, gypsum and calcite, and fifteen aqueous complexes. Truncation error, operator splitting error, and the nonlinear transformation of these errors in the high-resolution reactive transport model are identified for this problem.     

Numerical simulation of scalar dispersion downstream of a square obstacle using gradient-transport type models

We present a numerical study of scalar transport released from a line source downstream of a square obstacle to investigate the capabilities and limitations of gradient-transport modeling in predicting atmospheric dispersion. The standard k–? and k–ω models and a Reynolds Stress Transport closure are employed and compared to predict the time-averaged turbulent flow field, while a standard gradient–diffusion model is initially adopted to relate the scalar flux to mean gradients of the concentration field. The analysis of two algebraic closures for turbulent scalar fluxes based on the generalized-gradient–diffusion hypothesis and its quadratic extension is also presented. In spite of the rather simple flow setup, where both the flow and the scalar fields can be assumed homogeneous in the spanwise direction, the analysis clarifies several critical issues concerning gradient-transport type models. We established the dominant role of predicted turbulent kinetic energy on scalar dispersion when a scalar diffusivity is employed, irrespectively of the Reynolds stress closure adopted for the averaged momentum equation. Moreover, the standard gradient–diffusion hypothesis failed to predict the streamwise component of the scalar flux, which is characterized by a counter-gradient-transport mechanism. Although the resulting contribution in the averaged scalar transport equation is small in the present flow configuration, this limitation can become severe for strongly inhomogeneous flows in the presence of point sources, where the spread of the scalar plume is essentially three-dimensional. The predictive capabilities of gradient-transport type modeling are found clearly improved using algebraic closures, which appear to represent a promising tool for predicting atmospheric dispersion in complex flows when unsteady transport mechanisms are not dominant.     

Evaluation of the Meteo-France response in ETEX release 1

During ETEX Meteo-France applied part of its emergency response system for critical events developped in the framework of the World Meteorological Organization environmental emergency response program. The atmospheric transport model used to forecast the evolution of a passive tracer is an eulerian model called MEDIA. In real time this model is driven by meteorological data from ARPEGE, the operational numerical weather prediction model available at the Meteo-France operation center. The overall evaluation of the results show that the model can reproduce the cloud displacement, but there exists a stretching in the transport direction. In the ATMES-II phase, the results are closer to the observations when meteorological data from the European Center for Medium range Weather Forecast are used. A simulation using analyzed meteorological data from ARPEGE every 6 h slightly improve the results comparing with the real-time experiment. All the simulations we performed reveal that the quality of the atmospheric transport model is strongly dependent on the quality of the driving numerical weather prediction model.     

Predictive modelling of dispersion controlled reactive plumes at the laboratory-scale

A model-based interpretation of laboratory-scale experimental data is presented. Hydrolysis experiments carried out using thin glass tanks filled with glass beads to construct a hypothetical and inert, homogeneous porous medium were analysed using a 2D numerical model. A new empirical formula, based upon results for non-reactive (tracer) experiments is used to calculate transversal dispersivity values for a range of grain sizes and any flow velocities. Combined with effective diffusion coefficients calculated from Stokes-Einstein type equations, plume lengths arising from mixing between two solutes can be predicted accurately using numerical modelling techniques. Moreover, pH and ion concentration profiles lateral to the direction of flow of the mixing species can be determined at any given point downstream, without the need for result fitting. In our case, this approach does not lead to overpredictions of lateral mixing, as previously reported when using parameters derived from non-reactive tracer experiments to describe reactive solute transport. The theory is based on the assumption of medium homogeneity.     

Characterization of flow and transport processes within the unsaturated zone of Yucca Mountain, Nevada, under current and future climates

This paper presents a large-scale modeling study characterizing fluid flow and tracer transport in the unsaturated zone of Yucca Mountain, Nevada, a potential repository site for storing high-level radioactive waste. The study has been conducted using a three-dimensional numerical model, which incorporates a wide variety of field data and takes into account the coupled processes of flow and transport in the highly heterogeneous, unsaturated fractured porous rock. The modeling approach is based on a dual-continuum formulation of coupled multiphase fluid and tracer transport through fractured porous rock. Various scenarios of current and future climate conditions and their effects on the unsaturated zone are evaluated to aid in the assessment of the proposed repository's system performance using different conceptual models. These models are calibrated against field-measured data. Model-predicted flow and transport processes under current and future climates are discussed.     

An experimental study of flow and transport in fractured slate

A series of laboratory tracer migration experiments in a single rock fracture have been performed, and the breakthrough curves have been interpreted using mathematical modelling. Discrepancies were observed between the experimental data and the predictions made using a simple advection-dispersion model. The potential reasons for these discrepancies have been investigated by applying more complex models: one model incorporates channelling of flow within the fracture, the other couples dispersion and advection in the fracture with rock-matrix diffusion. It is concluded that chanelling of flow can adequately explain the observed spreading behaviour; rock-matrix diffusion is not a significant mechanism influencing transport in these experiments.     

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).     

Application of a model system for the study of transport and diffusion in complex terrain to the TRACT experiment

The transport and diffusion processes of a tracer gas released near the ground in the Rhine valley region, in Central Europe, during the 1992 TRACT field experiment, are simulated by a computational model system for complex terrain. This system (RMS) is composed of the prognostic mesoscale model RAMS, the Lagrangian stochastic dispersion model SPRAY and the interface code MIRS, which links RAMS to SPRAY. Three flow simulations were performed, with different initialisations and the one showing the best agreement with the measured flow was selected for the simulation of the TRACT tracer experiment. Tracer concentrations measured by an array of samplers at ground level and by an airplane aloft, are used to evaluate the 3-D concentration field simulated by the model system. The analysis of the simulation results generated by RMS shows that our model system very well reproduces the general behaviour of the contaminant plume, the temporal and spatial distribution of the concentration and the location of the concentration maxima.     

Effective rates of heavy metal release from alkaline wastes--quantified by column outflow experiments and inverse simulations

Column outflow experiments operated at steady state flow conditions do not allow the identification of rate limited release processes. This requires an alternative experimental methodology. In this study, the aim was to apply such a methodology in order to identify and quantify effective release rates of heavy metals from granular wastes. Column experiments were conducted with demolition waste and municipal waste incineration (MSWI) bottom ash using different flow velocities and multiple flow interruptions. The effluent was analyzed for heavy metals, DOC, electrical conductivity and pH. The breakthrough-curves were inversely modeled with a numerical code based on the advection–dispersion equation with first order mass-transfer and nonlinear interaction terms. Chromium, Copper, Nickel and Arsenic are usually released under non-equilibrium conditions. DOC might play a role as carrier for those trace metals. By inverse simulations, generally good model fits are derived. Although some parameters are correlated and some model deficiencies can be revealed, we are able to deduce physically reasonable release-mass-transfer time scales. Applying forward simulations, the parameter space with equifinal parameter sets was delineated. The results demonstrate that the presented experimental design is capable of identifying and quantifying non-equilibrium conditions. They show also that the possibility of rate limited release must not be neglected in release and transport studies involving inorganic contaminants.     

Simplified contaminant source depletion models as analogs of multiphase simulators

Four simplified dense non-aqueous phase liquid (DNAPL) source depletion models recently introduced in the literature are evaluated for the prediction of long-term effects of source depletion under natural gradient flow. These models are simple in form (a power function equation is an example) but are shown here to serve as mathematical analogs to complex multiphase flow and transport simulators. The spill and subsequent dissolution of DNAPLs was simulated in domains having different hydrologic characteristics (variance of the log conductivity field=0.2, 1 and 3) using the multiphase flow and transport simulator UTCHEM. The dissolution profiles were fitted using four analytical models: the equilibrium streamtube model (ESM), the advection dispersion model (ADM), the power law model (PLM) and the Damkohler number model (DaM). All four models, though very different in their conceptualization, include two basic parameters that describe the mean DNAPL mass and the joint variability in the velocity and DNAPL distributions. The variability parameter was observed to be strongly correlated with the variance of the log conductivity field in the ESM and ADM but weakly correlated in the PLM and DaM. The DaM also includes a third parameter that describes the effect of rate-limited dissolution, but here this parameter was held constant as the numerical simulations were found to be insensitive to local-scale mass transfer. All four models were able to emulate the characteristics of the dissolution profiles generated from the complex numerical simulator, but the one-parameter PLM fits were the poorest, especially for the low heterogeneity case.     

Global-scale environmental transport of persistent organic pollutants

In order to realistically simulate both chemistry and transport of atmospheric organic pollutants, it is indispensable that the applied models explicitly include coupling between different components of the global environment such as atmosphere, hydrosphere, cryosphere and soil system. A model with such properties is presented.

The atmospheric part of the model is based on the equations in a general contravariant form which permits easy changes of the coordinate system by redefining the metric tensor of a specifically employed coordinate system. Considering a need to include explicitly the terrain effects, the terrain following spherical coordinate system is chosen from among many possible coordinate systems. This particular system is a combination of the Gal-Chen coordinates, commonly employed in mesoscale meteorological models, and the spherical coordinates, typical for global atmospheric models.

In addition to atmospheric transport, the model also simulates the exchange between air and different types of underlying surfaces such as water, soil, snow, and ice. This approach permits a realistic representation of absorption and delayed re-emission of pollutants from the surface to the atmosphere and, consequently, allows to capture hysteresis-like effects of the exchange between the atmosphere and the other components of the system. In this model, the most comprehensive numerical representation of the exchange is that for soil. In particular, the model includes a realistic soil module which simulates both diffusion and convection of a tracer driven by evaporation from the soil, precipitation, and gravity.

The model is applied to a long-term simulation of the transport of pesticides (hexachlorocyclohexanes in particular). Emission fluxes from the soil are rigorously computed on the basis of the realistic data of the agricultural application. All four modelled systems, i.e. atmosphere, soil, hydrosphere and cryosphere, are driven by objectively analysed meteorological data supplemented, when necessary, by climatological information. Therefore, the verification against the observed data is possible. The comparison of the model results and the observations taken at remote stations in the Arctic indicates that the presented global modelling system is able to capture both trends and short-term components in the observed time series of the concentrations, and therefore, provides a useful tool for the evaluation of the source–receptor relationships.     

Non-dissipative cloud transport in Eulerian grid models by the volume-of-fluid (VOF) method

The formation of clouds is coupled to the vapour saturation condition. Cloud modelling is therefore dramatically disturbed by dilution processes, which are induced by recurrent interpolations on the fixed (Eulerian) grid. The numerical diffusion gives rise to degeneration and premature disappearance of the modelled clouds. The difficulties increase, if sectional mass representation in the drop microphysics and aerosol chemistry is considered. To tackle this problem, stringently defined and tracked phase boundaries are required.The numerical diffusion of clouds can be totally suppressed by the volume-of-fluid (VOF) method, which is applied here in connection with an atmospheric model. The cloud phase is distinguished by prognosing the partial cloud volume in all grid cells near the cloud boundary. Adopting elementary geometrical forms for the intracellular cloud volume and simple diagnostic rules of their alignment, the standard transport fluxes can be used in the new equation. Separate variables for the cloud and environmental phase complete the transport scheme.The VOF method and its realisation are described in detail. Advection, condensation, evaporation, and turbulent diffusion are considered within the VOF framework. The variation of the grid resolution and turbulence conditions for a rising thermal leads to striking arguments in favour of the VOF method, resulting in higher intensity, lifting, and lifetime as well as clear boundaries of the simulated clouds (even for low grid resolution).     

Chemical transport models

Background, aim, and scope  Improving the parameterization of processes in the atmospheric boundary layer (ABL) and surface layer, in air quality and chemical transport models. To do so, an asymmetrical, convective, non-local scheme, with varying upward mixing rates is combined with the non-local, turbulent, kinetic energy scheme for vertical diffusion (COM). For designing it, a function depending on the dimensionless height to the power four in the ABL is suggested, which is empirically derived. Also, we suggested a new method for calculating the in-canopy resistance for dry deposition over a vegetated surface. Materials and methods  The upward mixing rate forming the surface layer is parameterized using the sensible heat flux and the friction and convective velocities. Upward mixing rates varying with height are scaled with an amount of turbulent kinetic energy in layer, while the downward mixing rates are derived from mass conservation. The vertical eddy diffusivity is parameterized using the mean turbulent velocity scale that is obtained by the vertical integration within the ABL. In-canopy resistance is calculated by integration of inverse turbulent transfer coefficient inside the canopy from the effective ground roughness length to the canopy source height and, further, from its the canopy height. Results  This combination of schemes provides a less rapid mass transport out of surface layer into other layers, during convective and non-convective periods, than other local and non-local schemes parameterizing mixing processes in the ABL. The suggested method for calculating the in-canopy resistance for calculating the dry deposition over a vegetated surface differs remarkably from the commonly used one, particularly over forest vegetation. Discussion  In this paper, we studied the performance of a non-local, turbulent, kinetic energy scheme for vertical diffusion combined with a non-local, convective mixing scheme with varying upward mixing in the atmospheric boundary layer (COM) and its impact on the concentration of pollutants calculated with chemical and air-quality models. In addition, this scheme was also compared with a commonly used, local, eddy-diffusivity scheme. Simulated concentrations of NO₂ by the COM scheme and new parameterization of the in-canopy resistance are closer to the observations when compared to those obtained from using the local eddy-diffusivity scheme. Conclusions  Concentrations calculated with the COM scheme and new parameterization of in-canopy resistance, are in general higher and closer to the observations than those obtained by the local, eddy-diffusivity scheme (on the order of 15–22%). Recommendations and perspectives  To examine the performance of the scheme, simulated and measured concentrations of a pollutant (NO₂) were compared for the years 1999 and 2002. The comparison was made for the entire domain used in simulations performed by the chemical European Monitoring and Evaluation Program Unified model (version UNI-ACID, rv2.0) where schemes were incorporated.     

Determination of spatially-resolved porosity, tracer distributions and diffusion coefficients in porous media using MRI measurements and numerical simulations

This work is focused on measuring the concentration distribution of a conservative tracer in a homogeneous synthetic porous material and in heterogeneous natural sandstone using MRI techniques, and on the use of spatially resolved porosity data to define spatially variable diffusion coefficients in heterogeneous media. The measurements are made by employing SPRITE, a fast MRI method that yields quantitative, spatially-resolved tracer concentrations in porous media. Diffusion experiments involving the migration of H(2)O into D(2)O-saturated porous media are conducted. One-dimensional spatial distributions of H(2)O-tracer concentrations acquired from experiments with the homogeneous synthetic calcium silicate are fitted with the one-dimensional analytical solution of Fick's second law to confirm that the experimental method provides results that are consistent with expectations for Fickian diffusion in porous media. The MRI-measured concentration profiles match well with the solution for Fick's second law and provide a pore-water diffusion coefficient of 1.75×10(-9)m(2)s(-1). The experimental approach was then extended to evaluate diffusion in a heterogeneous natural sandstone in three dimensions. The relatively high hydraulic conductivity of the sandstone, and the contrast in fluid density between the H(2)O tracer and the D(2)O pore fluid, lead to solute transport by a combination of diffusion and density-driven advection. The MRI measurements of spatially distributed tracer concentration, combined with numerical simulations allow for the identification of the respective influences of advection and diffusion. The experimental data are interpreted with the aid of MIN3P-D - a multicomponent reactive transport code that includes the coupled processes of diffusion and density-driven advection. The model defines local diffusion coefficients as a function of spatially resolved porosity measurements. The D(e) values calculated for the heterogeneous sandstone and used to simulate diffusive and advective transport range from 5.4×10(-12) to 1.0×10(-10)m(2)s(-1). These methods have broad applicability to studies of contaminant migration in geological materials.     

Computational fluid dynamics analysis of the effects of reactor configuration on disinfection efficiency.

The efficacy of disinfection processes in water purification systems is governed by several key factors, including reactor hydraulics, disinfectant chemistry, and microbial inactivation kinetics. The objective of this work was to develop a computational fluid dynamics (CFD) model to predict velocity fields, mass transport, chlorine decay, and microbial inactivation in a continuous flow reactor. The CFD model was also used to evaluate disinfection efficiency in alternative reactor designs. The CFD reactor analysis demonstrates that disinfection efficiency is affected by both kinetics and mixing state (i.e., degree of micromixing or segregation). Residence time distributions (RTDs) derived from tracer analysis do not describe intrinsic mixing conditions. The CFD-based disinfection models account for reactor mixing patterns by resolution of the reactor velocity field and thus provide a better prediction of microbial inactivation than models that use an RTD.