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.     

An Eulerian model for scavenging of pollutants by raindrops

An Eulerian model for simulating the coupled processes of gas-phase depletion and aqueousphase accumulation of the pollutant species during a rain event has been formulated. The model is capable of taking into account any realistic vertical profile of pollutant species concentrations and time-dependent initial aqueous-phase concentrations at the cloud base. The model considers the processes of single species absorption and dissociation in the aqueous phase. The coupled partial differential equations constituting the model are discretized into a set of ordinary differential equations by using the Galerkin method with chapeau functions as the basis functions. These equations are solved to obtain the pollutant concentrations of the gas phase and raindrops as well as the pH of raindrops as a function of time and distance below cloud-base.Simulations are performed for scavenging of gaseous HNO₃, H₂O₂, SO₂, formaldehyde and NH₃. For the case of highly soluble HNO₃ and H₂O₂, raindrops are far from equilibrium with the gas phase and their capacity for absorption of these gases is undiminished even as they reach ground level. The gas-phase concentrations for these species decrease exponentially with time and the washout is determined primarily by the rain intensity and mass-transfer coefficient of the gaseous species to the raindrops. The pollutant species concentrations in raindrops are an almost linear function of the distance below the cloud base. For the simulation conditions considered in this study, the half-life periods of these gases for removal from the atmosphere range from 15 to 40 min.For SO₂ and formaldehyde, the aqueous-phase concentrations approach equilibrium as the drops fall to ground level and the gas-phase concentrations show large gradients in the vertical. Half-life periods for SO₂ range from 1.3 to 13 h depending on the initial raindrop pH and rain intensity. For formaldehyde, the half-life ranges from 19 to 63 min.Solubility of NH₃ is a strong function of the raindrop pH. As NH₃ is absorbed, the raindrop pH increases and NH₃ solubility decreases. For pre-acidified drops (pH = 4.6), ammonia solubility is very high and the drops are far from equilibrium with the gas phase throughout the falling period. The half-life for ammonia ranges from 11 min to over 3 h in our simulations.     

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).     

Study of expiratory droplet dispersion and transport using a new Eulerian modeling approach

Understanding of droplet nuclei dispersion and transport characteristics can provide more engineering strategies to control transmission of airborne diseases. Droplet dispersion in a room under the conventional well-mixed and displacement ventilation is simulated. Two droplet nuclei sizes, 0.01 and 10 μm, are selected as they represent very fine and coarse droplets. The flow field is modeled using k–ε RNG model. A new Eulerian drift-flux methodology is employed to model droplet phase. Under the conventional ventilation scheme, both fine and coarse droplets are homogeneously dispersed within approximately 50 s. Droplet nuclei exhibit distinctive dispersion behavior, particularly for low airflow microenvironment. After 270 s of droplet emission, gravitational settling influences the dispersion for 10 μm droplets, and concentration gradient can still be observed for displacement ventilation.     

Source apportion of atmospheric particulate matter: a joint Eulerian/Lagrangian approach

PM_2.5 samples were collected during an annual monitoring campaign (January 2012–January 2013) in the urban area of Naples, one of the major cities in Southern Italy. Samples were collected by means of a standard gravimetric sampler (Tecora Echo model) and characterized from a chemical point of view by ion chromatography. As a result, 143 samples together with their ionic composition have been collected. We extend traditional source apportionment techniques, usually based on multivariate factor analysis, interpreting the chemical analysis results within a Lagrangian framework. The Hybrid Single-Particle Lagrangian Integrated Trajectory Model (HYSPLIT) model was used, providing linkages to the source regions in the upwind areas. Results were analyzed in order to quantify the relative weight of different source types/areas. Model results suggested that PM concentrations are strongly affected not only by local emissions but also by transboundary emissions, especially from the Eastern and Northern European countries and African Saharan dust episodes.     

Issues to consider in the derivation of water quality benchmarks for the protection of aquatic life

While water quality benchmarks for the protection of aquatic life have been in use in some jurisdictions for several decades (USA, Canada, several European countries), more and more countries are now setting up their own national water quality benchmark development programs. In doing so, they either adopt an existing method from another jurisdiction, update on an existing approach, or develop their own new derivation method. Each approach has its own advantages and disadvantages, and many issues have to be addressed when setting up a water quality benchmark development program or when deriving a water quality benchmark. Each of these tasks requires a special expertise. They may seem simple, but are complex in their details. The intention of this paper was to provide some guidance for this process of water quality benchmark development on the program level, for the derivation methodology development, and in the actual benchmark derivation step, as well as to point out some issues (notably the inclusion of adapted populations and cryptic species and points to consider in the use of the species sensitivity distribution approach) and future opportunities (an international data repository and international collaboration in water quality benchmark development).     

Sensitivity analysis of the atmospheric reaction-diffusion equation

A general and computationally efficient methodology for the sensitivity analysis of space-time atmospheric reaction-diffusion problems is presented. For cases where the parameters or initial conditions vary spatially the elementary sensitivity analysis is based on sensitivity densities. Procedures are discussed to calculate these sensitivities directly as well as those integrated over a finite disturbance region. In addition, the analysis of the system Green's function is shown to be very useful in interpreting the spatial and temporal variation of the sensitivity densities. The techniques are illustrated by analyzing a one-dimensional time-dependent atmospheric transport-chemistry problem where an initial distribution of pure NO is injected into a homogeneous background of O₃.     

Sensitivity analysis of the atmospheric diffusion equation

A sensitivity analysis is performed on a representative mathematical model describing atmospheric diffusion. Basic characteristics of the spread of pollutants in the diffusion field are determined using the concentration moment method. A new variational approach yields a functional sensitivity relationship between the concentration moments and the spatially-varying parameters. It is demonstrated that this approach can be effectively used to compute general sensitivity measures for the spread of pollutants. The results of the analysis identify the key parameters influencing atmospheric diffusion. It is concluded that the analysis can provide useful insight into the effect of parameter variations in the atmospheric diffusion equation.     

Modeling the long-term transport and accumulation of radionuclides in the landscape for derivation of dose conversion factors

To evaluate the radiological impact of potential releases to the biosphere from a geological repository for spent nuclear fuel, it is necessary to assess the long-term dynamics of the distribution of radionuclides in the environment. In this paper, we propose an approach for making prognoses of the distribution and fluxes of radionuclides released from the geosphere, in discharges of contaminated groundwater, to an evolving landscape. The biosphere changes during the temperate part (spanning approximately 20,000 years) of an interglacial period are handled by building biosphere models for the projected succession of situations. Radionuclide transport in the landscape is modeled dynamically with a series of interconnected radioecological models of those ecosystem types (sea, lake, running water, mire, agricultural land and forest) that occur at present, and are projected to occur in the future, in a candidate area for a geological repository in Sweden. The transformation between ecosystems is modeled as discrete events occurring every thousand years by substituting one model by another. Examples of predictions of the radionuclide distribution in the landscape are presented for several scenarios with discharge locations varying in time and space. The article also outlines an approach for estimating the exposure of man resulting from all possible reasonable uses of a potentially contaminated landscape, which was used for derivation of Landscape Dose Factors.     

A nomographic solution of the Gaussian diffusion equation

The Gaussian diffusion equation for a surface receptor and a nondepositing surface or elevated source is solved by a single nomogram. A table and another nomogram allow adjustment for plume depletion and deposition for depositing particulate matter and reactive gases.     

Revisions to the derivation of the Australian and New Zealand guidelines for toxicants in fresh and marine waters

The Australian and New Zealand Guidelines for Fresh and Marine Water Quality are a key document in the Australian National Water Quality Management Strategy. These guidelines released in 2000 are currently being reviewed and updated. The revision is being co-ordinated by the Australian Department of Sustainability, Environment, Water, Population and Communities, while technical matters are dealt with by a series of Working Groups. The revision will be evolutionary in nature reflecting the latest scientific developments and a range of stakeholder desires. Key changes will be: increasing the types and sources of data that can be used; working collaboratively with industry to permit the use of commercial-in-confidence data; increasing the minimum data requirements; including a measure of the uncertainty of the trigger value; improving the software used to calculate trigger values; increasing the rigour of site-specific trigger values; improving the method for assessing the reliability of the trigger values; and providing guidance of measures of toxicity and toxicological endpoints that may, in the near future, be appropriate for trigger value derivation. These changes will markedly improve the number and quality of the trigger values that can be derived and will increase end-users’ ability to understand and implement the guidelines in a scientifically rigorous manner.     

The sensitivity of a 3-dimensional Eulerian model to uncertainties in emissions and dry deposition velocities

A 3-dimensional STEM-I Eulerian, regional scale transport/chemistry model for SO₂ and sulfate is used to investigate the relationships between model predictions and the resolution and uncertainty in the emissions and dry deposition velocities. Model results for conditions of 4 July 1974 where the emissions are time modulated, where the emissions are increased and decreased, and where the dry deposition velocities are increased and decreased are presented and discussed.     

Comparison of a new Eulerian model with a modified Lagrangian approach for particle distribution and deposition indoors

Understanding of aerosol dispersion characteristics has many scientific and engineering applications. It is recognized that Eulerian or Lagrangian approach has its own merits and limitations. A new Eulerian model has been developed and it adopts a simplified drift–flux methodology in which external forces can be incorporated straightforwardly. A new near-wall treatment is applied to take into account the anisotropic turbulence for the modified Lagrangian model. In the present work, we present and compare both Eulerian and Lagrangian models to simulate particle dispersion in a small chamber. Results reveal that the standard k–ε Lagrangian model over-predicts particle deposition compared to the present turbulence-corrected Lagrangian approach. Prediction by the Eulerian model agrees well with the modified Lagrangian model.     

Measuring the fractal dimension of diesel soot agglomerates by fractional Brownian motion processor

This work explores the application of fractional Brownian motion (FBM) analysis to SEM micrographs of soot aggregates exhausted by a model dynamometer. By directly quantifying the surface texture of fractal-like aggregates to extract their Hurst coefficients (H), the FBM analysis was successful in parameterizing fractal dimension (D_f) values, from which the relative aggregate structure variables could easily be determined. For two microscopic magnification scales (×50,000 and ×10⁵), the soot aggregate D_f fell in the range of 1.6–1.7. The experimental results closely agreed with the main conclusions derived from previous studies. An alternative approach is to clarify the impact of image properties on D_f measurements due to digital image processing and data recording. A twofold change in SEM magnification size gave rise to a 7% deviation, and scaling up from the original image increased the discrepancy compared to miniaturization. In conclusion, texture characterization is useful for estimating the fractal properties of most chain-like or cluster soot aggregates.     

A possible simplification of the Goss-modified Abraham solvation equation

Abraham solvation equations find widespread use in environmental chemistry and pharmaco-chemistry. Recently Goss proposed a modified Abraham solvation equation. For various partitioning processes, the present study investigates the consequences for the fit when the Abraham solvation parameter V is left out of this modified solvation equation. For air-organic solvent partition, the Abraham solvation parameter V can be omitted from the Goss-modified Abraham solvation equation without any loss of statistical quality. For air–water partitioning, organic biphasic system partitioning, as well as water-organic solvent partitioning, omitting the V parameter from the Goss-modified Abraham solvation equation leads to only a small deterioration of statistic quality.     

Prediction of two-phase capillary pressure-saturation relationships in fractional wettability systems

Capillary pressure/saturation data are often difficult and time consuming to measure, particularly for non-water-wetting porous media. Few capillary pressure/saturation predictive models, however, have been developed or verified for the range of wettability conditions that may be encountered in the natural subsurface. This work presents a new two-phase capillary pressure/saturation model for application to the prediction of primary drainage and imbibition relations in fractional wettability media. This new model is based upon an extension of Leverett scaling theory. Analysis of a series of DNAPL/water experiments, conducted for a number of water/intermediate and water/organic fractional wettability systems, reveals that previous models fail to predict observed behavior. The new Leverett–Cassie model, however, is demonstrated to provide good representations of these data, as well as those from two earlier fractional wettability studies. The Leverett–Cassie model holds promise for field application, based upon its foundation in fundamental scaling principles, its requirement for relatively few and physically based input parameters, and its applicability to a broad range of wetting conditions.     

A comparison of numerical methods for solving the advection equation

Six algorithms for solving the advection equation have been compared as to their accuracy, speed and storage requirements, the purpose being to determine the suitability of the algorithms for use in photochemical grid models. The algorithms tested are a flux-correction method, a multidimensional fluxcorrection method, an orthogonal-collocation method, a second-moment method, a pseudospectral method and a chapeau-function method. For some of these, more than one variant of the method has been examined. Also, some improvements are suggested in the second-moment method. The test problem was the rotation of a hill of concentration in a two-dimensional, circular velocity field, and the methods were tested at three or four time steps (Courant numbers). The flux-correction and orthogonal-collocation methods are the least accurate and would not be good choices for photochemical models. The pseudospectral method is the most accurate, but it and the second-moment method require the longest execution time. The chapeau-function and multidimensional flux-correction methods appear the most appropriate for photochemical grid models.