Variable K-theory model for the dispersion of air pollutants in low-wind conditions in the surface-based inversion

A variable K-model has been proposed for the dispersion in low winds in the surface-based inversion by expressing the eddy diffusivities as a linear function of downwind distance from the source. The resulting partial differential equation with variable coefficients along with the physically relevant boundary conditions is solved analytically. For the accuracy of the so-obtained solution, an analysis of the convergence and error estimation has been carried out. It is shown that the series converges absolutely. An upper bound for the error based on the partial sum of the series is estimated and it is described that the error tends to zero as the number of terms in the expansion are sufficiently large.The solution has been used to simulate the field tracer data sets collected from Hanford and IIT diffusion experiments in stable and unstable conditions, respectively. It predicts 41% cases in stable and 35% cases in unstable conditions within a factor of two to observations.     

A multi-layer model for pollutant dispersion with dry deposition to the ground

This paper presents a semi-analytical solution for the steady advection–diffusion equation that allows simulating the vertical turbulent dispersion of air pollution with deposition to the ground. The performances of the solution, with a proper parameterization of the vertical profiles of wind and eddy diffusivity, were evaluated against Hanford diffusion experiment dataset using two tracers (Doran and Horst, 1985): a non-depositing gas (SF₆) and depositing particles (ZnS). Results show that the dispersion model with the K-parameterization included produces a good fitting of the measured ground-level concentration data and there are no big differences between the parameterizations taken from literature. A comparison with other models was shown and discussed.     

A statistical approach for estimating uncertainty in dispersion modeling: An example of application in southwestern USA

A method based on a statistical approach of estimating uncertainty in simulating the transport and dispersion of atmospheric pollutants is developed using observations and modeling results from a tracer experiment in the complex terrain of the southwestern USA. The method takes into account the compensating nature of the error components by representing all terms, except dispersion error and variance of stochastic processes. Dispersion error and the variance of the stochastic error are estimated using the maximum likelihood estimation technique applied to the equation for the fractional error. Mesoscale Model 5 (MM5) and a Lagrangian random particle dispersion model with three optional turbulence parameterizations were used as a test bed for method application. Modeled concentrations compared well with the measurements (correlation coefficients on the order of 0.8). The effects of changing two structural components (the turbulence parameterization and the model grid vertical resolution) on the magnitude of the dispersion error also were examined. The expected normalized dispersion error appears to be quite large (up to a factor of three) among model runs with various turbulence schemes. Tests with increased vertical resolution of the atmospheric model (MM5) improved most of the dispersion model statistical performance measures, but to a lesser extent compared to selection of a turbulence parameterization. Method results confirm that structural components of the dispersion model, namely turbulence parameterizations, have the most influence on the expected dispersion error.     

A model study for ambient air quality analysis using routine meteorological observations

In the present study, more realistic and easily adaptable input parameters have been used with a view to investigating the long-range air quality analysis for the dispersion of air pollutants emitted from an area source with a multiple box model. The model formulation has been discussed at length for the ground level sources when convective conditions prevail. The routine meteorological observations have been used for the computation of sensible surface heat flux, friction velocity and mixing depth. A radiation model provides the estimates of the sensible surface heat flux. Based on the similarity theory, an iterative procedure has been adopted for the estimation of friction velocity which provides a coupling of radiation computation and the surface layer of the planetary boundary layer through surface heat flux expression. The important parameters—wind speed and eddy diffusivity profiles—have been derived and have been used to obtain the concentration patterns as hourly averages. The procedure could be easily adopted where observed meteorological parameters may be used for studying the dispersal of pollutants from the ground level sources.     

An efficient Lagrangian stochastic model of vertical dispersion in the convective boundary layer

We consider the one-dimensional case of vertical dispersion in the convective boundary layer (CBL) assuming that the turbulence field is stationary and horizontally homogeneous. The dispersion process is simulated by following Lagrangian trajectories of many independent tracer particles in the turbulent flow field, leading to a prediction of the mean concentration. The particle acceleration is determined using a stochastic differential equation, assuming that the joint evolution of the particle velocity and position is a Markov process. The equation consists of a deterministic term and a random term. While the formulation is standard, attention has been focused in recent years on various ways of calculating the deterministic term using the well-mixed condition incorporating the Fokker–Planck equation. Here we propose a simple parameterisation for the deterministic acceleration term by approximating it as a quadratic function of velocity. Such a function is shown to represent well the acceleration under moderate velocity skewness conditions observed in the CBL. The coefficients in the quadratic form are determined in terms of given turbulence statistics by directly integrating the Fokker–Planck equation. An advantage of this approach is that, unlike in existing Lagrangian stochastic models for the CBL, the use of the turbulence statistics up to the fourth order can be made without assuming any predefined form for the probability distribution function (PDF) of the velocity. The main strength of the model, however, lies in its simplicity and computational efficiency. The dispersion results obtained from the new model are compared with existing laboratory data as well as with those obtained from a more complex Lagrangian model in which the deterministic acceleration term is based on a bi-Gaussian velocity PDF. The comparison shows that the new model performs well.     

Transport and Diffusion Calculations during Time- and Space-Varying Meteorological Conditions Using a Microcomputer

Small computers can now solve complex transport and diffusion problems. Making such calculations rapidly and on the spot would be very useful for decision makers during emergencies. This paper describes a microcomputer model that can simulate nonsteady state transport and diffusion and calculate mass-consistent flow fields in uneven terrain. Transport and diffusion calculations use a Puff model approach to simulate dispersion from a continuous point source. Three-dimensional wind fields are generated from linear combinations of solutions that are obtained ahead of time on a larger machine. A computer code has been written in BASIC and successfully run on an Apple II personal computer.     

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.     

A new urban boundary layer and dispersion parameterization for an emergency response modeling system: Tests with the Joint Urban 2003 data set

A new urban parameterization for a fast-running dispersion prediction modeling system suitable for emergency response situations is introduced. The parameterization represents the urban convective boundary layer in the dispersion prediction system developed by the National Atmospheric Release Advisory Center (NARAC) at Lawrence Livermore National Laboratory. The performance of the modeling system is tested with data collected during the field campaign Joint Urban 2003 (JU03), held in July 2003 in Oklahoma City, Oklahoma. Tests were performed using data from three intense operating periods held during daytime slightly unstable to unstable conditions. The system was run in operational mode using the meteorological data that would be available operationally at NARAC to test its effectiveness in emergency response conditions. The new parameterization considerably improves the performance of the original modeling system, by producing a better degree of pattern of correspondence between predictions and observations (as measured by Taylor diagrams), considerably reducing bias, and better capturing directional effects resulting in plume predictions whose shape and size better resemble the observations (via the measure of effectiveness). Furthermore, the new parameterization shows similar skills to urban modeling systems of similar or greater complexity. The parameterization performs the best at the three JU03 sensor arcs (1, 2, and 4 km downwind the release points), with fractional bias values ranging from 0.13 to 0.4, correlation values from 0.45 to 0.71, and centered root-mean-square error being reduced more than 50% in most cases. The urban parameterization has been tested with grid increments of 125, 250, 500 and 1000 m, performing best at 250 and 500 m. Finally, it has been found that representing the point source by a Gaussian distribution with an initial spread of particles leads to a better representation of the initial spread induced by near-source buildings, resulting in lower bias and improved correlation in downtown Oklahoma City.     

Validation of the UK Met. Office’s name model against the ETEX dataset

The ETEX 1 data set has been used to assess the performance of the UK Met Office’s long-range dispersion model NAME. In terms of emergency response modelling the model performed well, successfully predicting the overall spread and timing of the plume across Europe. However, in common with most other models, NAME overpredicted the observed concentrations. This is in contrast with other NAME validation studies which indicate either no significant bias or a tendency to underpredict concentrations. This suggests the reasons for overpredicting are specific to the ETEX situation. Explanations include inadequate vertical diffusion or transport, possible venting by convective activity, and experimental errors. An assessment of a range of advection schemes of varying complexity indicated no clear advantage, at present, in using more sophisticated random walk techniques at long range, a simple diffusion coefficient based scheme providing some of the best results. A brief look is also taken at a simulation of the more problematical ETEX 2 release.     

The assessment of electromigration as a new technique to study diffusion of radionuclides in clayey soils

For the performance assessment study of a geological disposal of High Level Waste (HLW) in clayey formations, migration studies are essential. For low permeability soils (clays), classical diffusion studies take a very long time. In order to reduce the experimental time, we propose an electrical field as driving force to accelerate the migration of ionic species. This paper reports the assessment of the electromigration technique as a powerful new and fast technique for migration studies. The apparent molecular diffusion coefficient can be derived by two independent methods using the migration parameters obtained from an electromigration experiment, namely the apparent dispersion coefficient and the apparent convection velocity. First, it can be calculated from the velocity of the migrating species by the Einstein relation. But, corrections are necessary for electroosmotic flow. The apparent electroosmotic mobility is experimentally determined as 2.2·10⁻⁹ m²/Vs. Second, it can be calculated from the relation between the apparent dispersion coefficient and the total apparent convection velocity. But it is necessary to know the dispersion length of the medium. The dispersion length for Boom Clay is experimentally determined as 8·10⁻⁵ m. Because of the serious reduction in time, it becomes possible to run series of experiments at different electrical fields to obtain averaged values for the apparent molecular diffusion coefficient according to the two methods. Experiments at different electrical fields have another advantage: the intercept of the linear relationship between the total apparent convection velocity and the apparent dispersion coefficient gives the apparent molecular diffusion coefficient. The apparent molecular diffusion coefficients obtained for ⁸⁵Sr, ¹³¹I and HTO are respectively 0.8·10⁻¹¹, 15·10⁻¹¹, and 24·10⁻¹¹ m²/s. These values are confirmed by pure diffusion experiments. The excellent agreement with the apparent molecular diffusion coefficients obtained by classical diffusion tests clearly demonstrates the feasibility of the electromigration technique for the determination of diffusion coefficients.     

Free tropospheric ozone production after deep convection of dispersing tropical urban plumes

Ozone generation is computed in a one-dimensional photochemistry code following convective redistribution of tropical urban effluent into the free troposphere. Simulations are run at several stages of pollutant dilution by surrounding surface air. A threshold boundary layer NO_x concentration of 300 pptv is established for significant production enhancements at upper levels. Areas defined by the 300 pptv level are examined in the Gaussian dispersion framework based on a wet season plume event observed in Amazonia. Pollution travels slowly in the sluggish winds of the equatorial trough. Daily storms are likely to interrupt the effluent while coverages are still on the order of few thousand square kilometers and NO_x concentrations are above the threshold. Dry season plume sizes are difficult to assess because local concentration data are scarce, but it is conceivable that the faster trade winds lead to a several fold extension.     

Stability studies with the help of acoustic sounding

A Monostatic acoustic sounder has been operating at the National Physical Laboratory, New Delhi (India) for several years. Analytical studies of the data on the atmospheric boundary layer obtained at Delhi for the period May 1977 to April 1982 are reported. A systematic classification of the observed structure has also been proposed to give information on the prevailing Pasquill stability category which determines pollution dispersion, This was done by comparing the echo structure type with observations of fluctuations in the horizontal wind direction,     

A wind tunnel study of the effect of roadway configurations on the dispersion of traffic-related pollution

In this paper we examine the effect of different roadway configurations, including noise barriers and roadway elevation or depression relative to the surrounding terrain, on the dispersion of traffic-related pollutants for winds perpendicular to the roadway. A wind tunnel experiment modeling 12 different configurations was performed to study the flow fields and the concentration distributions resulting from emissions from a simulated six-lane highway. All of the configurations examined here reduced the downwind ground-level concentrations relative to that for a flat, unobstructed roadway; however, the degree to which the concentrations were reduced varied widely depending on the particular situation.Ground-level concentration data from the cases considered in this research indicate that a constant entrainment velocity can be used over the region beginning downwind of any initial disturbance to the flow resulting from the roadway configuration (e.g., a recirculation region behind a noise barrier) and extending at least to the end of our measurements. For example, for the case of a single noise barrier on the downwind side of the road, this region extends from approximately four barrier heights downwind of the roadway to 40 barrier heights. It was also found that the virtual origin concept is useful in describing the initial mixing created by the particular roadway configuration. To effectively model the influence of the roadway configuration on the dispersion, a combination of a virtual origin and an entrainment velocity may be effective. The magnitude of the virtual origin shift appears to depend on the particular roadway configuration, while the entrainment velocity appears to be a function of the friction velocity and the roadway geometry. These results suggest that road configuration must be taken into account in modeling near-road air quality.     

The influence of mass transfer on solute transport in column experiments with an aggregated soil

The spreading of concentration fronts in dynamic column experiments conducted with a porous, aggregated soil is analyzed by means of a previously documented transport model (DFPSDM) that accounts for longitudinal dispersion, external mass transfer in the boundary layer surrounding the aggregate particles, and diffusion in the intra-aggregate pores. The data are drawn from a previous report on the transport of tritiated water, chloride, and calcium ion in a column filled with Ione soil having an average aggregate particle diameter of 0.34 cm, at pore water velocities from 3 to 143 cm/h. The parameters for dispersion, external mass transfer, and internal diffusion were predicted for the experimental conditions by means of generalized correlations, independent of the column data. The predicted degree of solute front-spreading agreed well with the experimental observations. Consistent with the aggregate porosity of 45%, the tortuosity factor for internal pore diffusion was approximately equal to 2. Quantitative criteria for the spreading influence of the three mechanisms are evaluated with respect to the column data. Hydrodynamic dispersion is thought to have governed the front shape in the experiments at low velocity, and internal pore diffusion is believed to have dominated at high velocity; the external mass transfer resistance played a minor role under all conditions. A transport model such as DFPSDM is useful for interpreting column data with regard to the mechanisms controlling concentration front dynamics, but care must be exercised to avoid confounding the effects of the relevant processes.     

Evaluation of a long-range lagrangian dispersion model with ETEX

Performance of a Lagrangian dispersion model was examined in connection with its dependency on the boundary layer modelling and the input data resolution. The European Tracer Experiment (ETEX) data were used as reference. According to the sensitivity analysis of the model performance, the long-range dispersion model with the sparse input data was not noticeably different from that with the finer resolution data. The assumption of the prescribed constant mixing depth did not largely degrade the prediction results as compared with the simulation results with the temporally changing boundary layer. It is, therefore, concluded that the model is practical, considering the limited input data in the operational mode. However, it was also pointed out that the parameterization for the horizontal and vertical diffusion processes used in the present model enhanced the growth of plume. The improvement of input data resolution in time and space caused further dispersion of tracer deterministically. These resulted in the underestimation of the maximum concentration and the unfocussed concentration distribution map although the mean concentration was predicted fairly well.     

A note on subgrid-scale processes in photochemical modelling

The effects of including a parameterization of subgrid-scale dispersion and chemical processes in the Eulerian-Lagrangian transport model of Hess are investigated. A case chosen to maximize the subgrid-scale effects is studied, and it is found that the predicted change in maximum O₃ when subgrid-scale processes are included is small (∼5%) compared with predictions based on direct injection of point emissions. It is also found for this model that the parameterization of subgrid-scale processes is not necessary to provide numerical stability in calculating the chemical kinetics.     

Simulation and analysis of solute transport in 2D fracture/pipe networks: the SOLFRAC program

The Time Domain Random Walk (TDRW) method has been recently developed by Delay and Bodin [Delay, F. and Bodin, J., 2001. Time domain random walk method to simulate transport by advection-dispersion and matrix diffusion in fracture networks. Geophys. Res. Lett., 28(21): 4051-4054.] and Bodin et al. [Bodin, J., Porel, G. and Delay, F., 2003c. Simulation of solute transport in discrete fracture networks using the time domain random walk method. Earth Planet. Sci. Lett., 6566: 1-8.] for simulating solute transport in discrete fracture networks. It is assumed that the fracture network can reasonably be represented by a network of interconnected one-dimensional pipes (i.e. flow channels). Processes accounted for are: (1) advection and hydrodynamic dispersion in the channels, (2) matrix diffusion, (3) diffusion into stagnant zones within the fracture planes, (4) sorption reactions onto the fracture walls and in the matrix, (5) linear decay, and (6) mass sharing at fracture intersections. The TDRW method is handy and very efficient in terms of computation costs since it allows for the one-step calculation of the particle residence time in each bond of the network. This method has been programmed in C++, and efforts have been made to develop an efficient and user-friendly software, called SOLFRAC. This program is freely downloadable at the URL (labo.univ-poitiers.fr/hydrasa/intranet/telechargement.htm). It calculates solute transport into 2D pipe networks, while considering different types of injections and different concepts of local dispersion within each flow channel. Post-simulation analyses are also available, such as the mean velocity or the macroscopic dispersion at the scale of the entire network. The program may be used to evaluate how a given transport mechanism influences the macroscopic transport behaviour of fracture networks. It may also be used, as is the case, e.g., with analytical solutions, to interpret laboratory or field tracer test experiments performed in single fractures.     

Simulation of the evolution of particle size distributions containing coarse particulate in the atmospheric surface layer with a simple convection-diffusion-sedimentation model

The Fugitive Dust Model (FDM) and Industrial Source Complex (ISC), widely used coarse particulate dispersion models, have been shown inaccurate due to the neglect of vertical variations in atmospheric wind speed and turbulent diffusivity (Vesovic et al., 2001), omission of the gravitational advection velocity, and an underestimation of the ground deposition velocity (Kim and Larson, 2001). A simple, transient two-dimensional convection-diffusion-sedimentation model is proposed to simulate the evolution in particle size distribution of an aerosol ‘puff’ containing coarse particulate in the atmospheric surface layer. Monin-Okhubov similarity theory, accompanied by empirical observations made by Businger et al. (1971), is adopted to characterize the surface layer wind speed and turbulent diffusivity profiles over a wide range of atmospheric conditions. A first order analysis of the crossing trajectories effect suggests simulation data presented here are not significantly affected by particle inertia. The model is validated against Suffield experimental data in which coarse particulate deposition was measured out to a distance of 800 m from the source (Walker, 1965). Good agreement is found for the decay in ground deposits with distance from the source for stable atmospheres. Deposition data was also simulated for unstable atmospheric stratification and the current model was determined to modestly underestimate the peak concentration with increasing accuracy further downwind of the release. The current model's effective deposition velocity was compared to that suggested by Kim et al. (2000) and shows improvement with respect to FDM. Lastly, the model was used to simulate the dispersion of nine lognormal aerosol puffs in the lowest 50 m of the atmospheric surface layer for four classes of atmospheric stability. The simulated mass median aerodynamic diameters (MMAD) at multiple downwind sampling locations were calculated and plotted with distance from the source. The first 50 m from the source was found to have a substantial impact on the evolution of MMAD for stable atmospheric conditions. Away from the source, it was observed that particle size distributions were truncated by removal of all particles larger than about 60 μm. A particle Peclet number was also defined to quantify the relative importance of turbulent dispersion and sedimentation on particle motion in the vertical direction.     

Climate simulations using the GCRC 2-D zonally averaged statistical dynamical climate model

The two-dimensional statistical dynamical climate model, recently developed at the Global Change Research Center (GCRC 2D climate model) is presented and discussed. The model solves the 2-D primitive equations in finite difference form (mass continuity, Newton's second law, and the first law of thermodynamics) for the prognostic variables zonal mean density, zonal mean zonal velocity, zonal mean meridional velocity, and zonal mean temperature on a grid that has 18 nodes in latitude and 9 vertical nodes (plus the surface). The equation of state, p = ρRT and an assumed hydrostatic atmosphere, δp = −ρgδz, are used to diagnostically calculate the zonal mean pressure and vertical velocity for each grid node, and the moisture balance equation is used to estimate the precipitation rate.

The performance of the model at simulating the two-dimensional temperature, zonal winds, and mass stream function is discussed here. The strengths and weaknesses of the model are highlighted and plans for future model experiments and improvements are given. The parameterization of the transient eddy fluxes of heat and momentum developed by Stone and Yao (1987 and 1990) are used with small modifications. These modifications are shown to improve the performance of the model at simulating the observed climate system as well as increase the model's computational stability.     

A statistical evaluation and comparison of coastal point source Dispersion Models

Fumigation caused by elevated sources in coastal areas has been simulated by two base models: the CRSTER Shoreline Fumigation Model (CSFM) and the Shoreline Dispersion Model (SLDM). This study consisted of evaluating the two base models along with variations of the SLDM model.The statistical evaluation procedures involved the use of scatterplots, variances, total root mean square error and systematic root mean square error. In addition, an index of agreement value (d) was used in place of the standard statistical correlation coefficient (r) because of the restrictive nature of the correlation coefficient.The 2-y comprehensive Nanticoke, Canada power plant study was used for evaluation purposes. The 13 test cases taken from the data base met the criteria of daytime onshore flow and sufficient land-water temperature difference.The statistical evaluation indicated that the SLDM model performed better than the CSFM base model. This decision was based on (among other factors) the comparatively high index of agreement values (0.76 vs 0.46) for the SLDM model. Reasons for the comparatively poor performance of the CSFM model are given in terms of the Pasquill-Gifford curves vs the convective velocity scaling approach of the SLDM model and also the point source vs areal type dispersion approach. Two variations of the SLDM model were then evaluated. This evaluation indicated that the SLDM/downdraft model outperformed the SLDM/empirical model but was not better than the base SLDM model.