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Comparison of PDFs, closure schemes and turbulence parameterisations in Lagrangian stochastic models
Abstract
Six one-dimensional models, based on the Ito-type stochastic equation, are presented and compared. Four of these take into account up to the fourth order moment of vertical velocity fluctuations, and two up to the third order moment. Four models make use of a bi-Gaussian probability density function (PDF) and the other two are based on a Gram-Charlier series expansion truncated to the third or fourth order. All the models were run with a parameterisation of input turbulence (i.e. w<SUP align=right>2</SUP> , w<SUP align=right>3</SUP> , and τ profiles). Concerning the fourth order moment w<SUP align=right>4</SUP> , two different parameterisations were considered. Comparisons are made between ground-level concentrations, plume height and plume width observed in the Willis and Deardorff water tank experiments and those predicted by the different models here considered. The goal of this study was to find the models that give greater confidence in their applicability in dispersion studies and to verify the importance of considering the fourth order moment. The main conclusions are: simulation results largely depend on the turbulence parameterisation chosen; the Gram-Charlier PDF gives the best agreement with observations; some combinations of models and turbulence parameterisations perform well in simulating the shape of the ground-level concentration (g.1.c.) trend but fail in correctly simulating the form of the plume (plume height and vertical width); in the case of the Gram-Charlier PDF, the fourth order model reproduced the vertical plume width better than the third order one, whereas the two schemes yielded similar g.1.c. distributions.
... When E; K m and e are not available, alternative parameterisations can be used, based, for instance, on the schemes by Hanna (1982). If needed, the third moment of the vertical velocity component is assigned following Chiba (1978) and the fourth moment is calculated from the method suggested by Ferrero and Anfossi (1998). Data are finally processed to prepare a meteorological file having the format and the temporal sequence appropriate to be used as input to SPRAY. ...
... SPRAY is a Lagrangian stochastic one-particle model designed to study the dispersion of passive pollutants in complex terrain (Tinarelli et al., 1994(Tinarelli et al., , 2000Ferrero and Anfossi, 1998), where the inhomogeneity of the variables that determine the dispersion process play an important role. It is based on a 3D form of the Langevin equation for the random velocity (Thomson, 1987). ...
... In conclusion, both this quantitative analysis and the previous discussion of the scatter plots shows that if the closure model contributes to a satisfactory reproduction of flow and turbulence, as it is with E2l and E2e closures, the only difference in the accuracy of the results depends on the parameterisation of the Lagrangian time scales. This result was also obtained by Ferrero and Anfossi (1998) examining flat terrain convective dispersion conditions. So far, we have shown the comparison between the 3D observed and prescribed field of concentrations. ...
When atmospheric pollutant dispersion is simulated over complex terrain, the turbulence input parameters are often prescribed according to standard parameterisation based on surface layer quantities. These last are available from literature. In the past, several different parameterisations for the first few moments of the turbulence velocity statistic and for the Lagrangian time scale have been developed and tested in different stability conditions.The main shortcomings for using these parameterisations are their inadequateness in predicting the turbulence field in horizontally non-homogeneous boundary layer (like for example in complex terrain or in urban heat island) and the essentially local nature of the prescribed turbulence. The purpose of this work is to suggest proper methods for predicting turbulence field for dispersion model over complex terrain and, more generally, in horizontally non-homogeneous conditions.The modelling system RMS (RAMS–MIRS–SPRAY) is applied to the present study. We introduced new non-local turbulence closures in the RAMS circulation model, which provides both mean wind and turbulence fields. Then, through the interface code (MIRS), the input quantities needed to the Lagrangian stochastic dispersion model (SPRAY) are computed. The model system is validated against a tracer experiment performed in a wind tunnel over a schematic two-dimensional valley.
... Ground level concentrations measured during Prairie Grass and Copenhagen tracer dispersion field experiments are used to evaluate the predictions of a Lagrangian dispersion model including both turbulent parameterizations. In the present study, the Lagrangian particle model LAMBDA (Ferrero et al., 1995;Ferrero and Anfossi, 1998a;Ferrero and Anfossi, 1998b) is used to reproduce the diffusion of passive contaminants. ...
... While in the two horizontal directions the E P is considered to be Gaussian in the vertical direction the PDF is assumed to be non-Gaussian (to deal with non-uniform turbulent conditions and/or convection). In this latter case, two different approaches can be adopted in order to calculate the Fokker-Planck equation: a bi-Gaussian one, truncated to the third order, and a Gram-Charlier one, truncated to the third or to the fourth order (Anfossi et al., 1997;Ferrero and Anfossi, 1998a;Ferrero and Anfossi, 1998b). The bi-Gaussian PDF is given by the linear combination of two Gaussians (Baerentsen and Berkowicz, 1984) and the Gram-Charlier PDF is a particular type of expansion that uses orthonormal functions in the form of Hermit polynomials. ...
Considering a Lagrangian stochastic particle dispersion model and diffusion experiments, two turbulence parameterizations have been tested. The parameters obtained from the Taylor turbulence parameterization are derived from observed spectral properties and characteristics of energy containing eddies. Taylor turbulence scheme provides continuous values for the turbulent parameters in the planetary boundary layer. Hanna turbulence parameterization is obtained from theoretical considerations and second-order closure models and it does not provide continuous vertical profiles for the turbulent parameters. The predicted values by a Lagrangian diffusion model utilizing Taylor turbulence parameterization and the Hanna turbulence scheme are compared with observed concentration data from diffusion experiments. The use of Taylor turbulence scheme resulted in better results.
... The second technique is based on solution of the Langevin equation through the Method of Successive Approximations or Picard's Iteration Method (Carvalho et al., 2004. Lagrangian particle models are obtained considering the Gram-Charlier Probability Density Function (PDF) of turbulent velocity, through which Gaussian and non-Gaussian turbulence conditions can be considered (Anfossi et al., 1997;Ferrero and Anfossi, 1998). The main objective of this paper is to present and discuss the results of a model evaluation between two semi-analytical techniques, focusing the quality and accuracy of these techniques in pollutant emitted from low and high sources. ...
... a depends on the Eulerian PDF of the turbulent velocity and is determined from the Fokker-Planck equation under steady conditions for the statistical momentum (Thomson, 1987;Rodean, 1996). A Gram-Charlier PDF, which is given by the series of Hermite polynomials, can be adopted (Anfossi et al., 1997;Ferrero and Anfossi, 1998). The Gram-Charlier PDF truncated to the fourth order is given by the following expression (Kendall and Stuart, 1977): ...
Neste artigo é realizada uma avaliação de duas técnicas semi-analíticas, considerando a qualidade e a exatidão destas técnicas em reproduzir valores de concentração ao nível da superfície de poluentes passivos emitidos a partir de fontes baixas e altas. A primeira técnica é um modelo Euleriano baseado na solução da equação advecção-difusão através da técnica de transformada de Laplace. A segunda é um modelo Lagrangiano baseado na solução da equação de Langevin através do Método Iterativo de Picard. Parâmetros da turbulência são calculados de acordo com uma parametrização capaz de gerar valores contínuos em todas as condições de estabilidade e em todas as alturas na camada limite planetária. Simulações numéricas e comparações mostram uma boa concordância entre valores de concentração previstos e observados. Comparações entre as duas técnicas revelam que o modelo Lagrangiano gera resultados mais precisos, mas o modelo Euleriano exige um menor tempo computacional.
... SPRAY (Tinarelli et al., 2000;Ferrero and Anfossi, 1998) is a Lagrangian stochastic particle model designed to study the dispersion of passive pollutants in complex terrain. It is based on the generalised Langevin equation (Thomson, 1987). ...
... While in the two horizontal directions the PDF is considered to be Gaussian, in the vertical direction, the PDF is assumed to be non-Gaussian (to deal with non-uniform turbulent conditions and/or convection). In this latter case, two different approaches can be adopted in order to calculate the Fokker-Planck equation: a bi-Gaussian one, truncated to the third order, and a Gram-Charlier one, truncated to the third or to the fourth order Ferrero and Anfossi, 1998). The bi-Gaussian PDF is given by the linear combination of two Gaussians and the Gram-Charlier PDF is given by the series expansion of Hermite polynomials. ...
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.
... SPRAY was used in this work as a regulatory model, according to the suggestion of the Regional Environmental Protection Agency (ARPA Piemonte). SPRAY ability to correctly prescribe g.l.c. was tested many times (see, for instance: Ferrero et al., 1997 and2001;Ferrero and Anfossi, 1998). ...
... The wind velocity standard deviations and the Lagrangian time scales were computed in MIRS according to the Hanna (1982) scheme. SPRAY was run in the inner grid and the following options were used: dynamic plume rise (Anfossi et al., 1993), variable time step, Gaussian PDF in the horizontal plane and a skewed Gram-Charlier PDF (Ferrero and Anfossi, 1998) in the vertical. Concentrations were computed in grid boxes having size to 250 x 250 x 15 m. ...
... The last group of five bits is related to the number of neurons in each layer. Because of the binary encoding scheme and the number of bits used, the number of neurons in each hidden layer is restricted to [0, 31] since 1 ? 2 ? 4 ? 8 ? ...
... In this work, we used a multilayer perceptron ANN to solve the problem of estimating air pollution sources (see [30]). We tested the methodology using data from the dispersal Lagrangian stochastic LAMBDA model for pollution dispersion (acronym for LAgrangean Model for Buoyant Dispersion in Atmosphere), developed to study the pollutants transport and diffusion on land plan (see [31, 32]). The meteorological data used by LAMBDA model to simulate the dispersion of particles by the wind are extracted from Copenhagen [30] and displayed in theTable 3 . ...
This article deals with evolutionary artificial neural network (ANN) and aims to propose a systematic and automated way to find out a proper network architec-ture. To this, we adapt four metaheuristics to resolve the problem posed by the pursuit of optimum feedforward ANN architecture and introduced a new criteria to measure the ANN performance based on combination of training and generalization error. Also, it is proposed a new method for estimating the computational complexity of the ANN architecture based on the number of neurons and epochs needed to train the network. We implemented this approach in software and tested it for the problem of identification and estimation of pollution sources and for three separate benchmark data sets from UCI repository. The results show the proposed computational approach gives better performance than a human specialist, while offering many advantages over similar approaches found in the literature.
... The Lagrangian particle model LAMBDA was developed to study the transport process and pollutants diffusion, starting from the Brownian random walk modeling78. In the LAMBDA code, full-uncoupled particle movements are assumed. ...
... The time step was maintained constant ( s t 1 = ∆ ). The PDF Gram-Charlier truncated to the third order was chosen [8]. One hundred particles were released at each time step during 2400 time steps for each source. ...
Pollutant dispersion problem in the atmosphere is a hard issue, because the atmosphere presents several stability conditions, implying different parameterisations for the atmospheric turbulence. In some practical situations, such as accident, it is important to have available a tool capable of identifying the pollutant source emission strength on the basis of measured concentrations only. Therefore, the goal here is to identify the strength of pollutant sources knowing the ground level concentrations, where two different sources, a linear and an areal, are simultaneously emitting. A Langrangian particle model, based on the Langevin equation, is used to simulate the forward problem, while the inverse problem is formulated as an optimization problem. Two optimizers are employed to obtain inverse solutions: quasi-Newton method, and simulated annealing. They are deterministic and stochastic approaches, respectively. Under certain conditions, the deterministic approach is unable to find a good inverse solution.
... PSPRAY is a 3D Lagrangian particle dispersion model (LPDM) [15], directly derived from the SPRAY code [16][17][18][19][20][21][22]. The dispersion of a pollutant (gas or fine aerosol) is simulated following the trajectories of a large number of numerical particles. ...
The number of cities, or parts of cities, where air quality has been computed using the PMSS 3D model now appears to be sufficient to allow assessment and understanding of performance. Two fields of application explain the growing number of sites: the first is the long-term air quality assessment required in urban areas for any building or road project. The geometric complexity found in such areas can justify the use of a 3D approach, as opposed to Gaussian ones. However, these studies have constraining rules that can make the modelling challenging: several scenarios are needed (current, future with project, future without project), the long-term impact implies a long physical time period to be computed, and the spatial extension of the domain can be large in order to cover the traffic impact zone of the project. The second type of application is dedicated to services and, essentially, to forecasting. As for impact assessments, the modelling can be challenging here because of the extension of the domain if the target area is a whole city. Forecast also adds the constraint of time, as results are requested early, and the constraint of robustness. The CPU amount needed to meet all these requirements is important. It is therefore crucial to optimize all possible parts of the modelling chain in order to limit cost and delay. The sites presented in the article have been modelled with PMSS for long periods. This allows feedback to be provided on different topics: (a) daily forecasts offer an opportunity to increase the robustness of the modelling chain; (b) quantitative validation at air quality measurement stations; (c) comparison of annual impact based on a whole year, and based on a sampling list of dates selected thanks to a classification process; (d) large calculation domains with widespread pollutant emissions offer a great opportunity to qualitatively check and improve model results on numerous geometrical configurations; (e) CPU time variations between different sites provide valuable information to select the best parametrizations, to predict the cost of the services, and to design the needed hardware for a new site.
... Particles are transported by mean wind (read from an external file) and turbulence, whose effect result in a stochastic component in particle velocities. The stochastic term is calculated according to Thomson (1987) with third-order Gram-Charlier (Ferrero and Anfossi, 1998). A plume rise algorithm was activated in order to take into account buoyancy (Anfossi et al., 1996). ...
Pollutants released by large industries are often a cause of major concern for local communities living nearby. Traditional monitoring consists of continuous emissions controlling systems (CEMS) and regular sampling of flue gas associated with monitoring stations positioned at best for checking on air quality where people reside. Sometimes a remote monitoring station is employed to set a background pollution reference value.
In the case of Persistent Organic Pollutants (POPs) this may not be the best planning strategy for monitoring exposure. In fact, direct exposure through inhalation forms just a minor contribution to the total people exposure. A much more relevant exposure is indirect, due to the ingestion of food, either vegetable or animal, which has been contaminated. For this reason, a great care should be put in placing monitoring instruments where deposition of POPs is larger, especially when industrial and rural areas are bordering.
As an example, we present the case of a steel foundry in an alpine valley, emitting PCDD/Fs and PCBs besides traditional air pollutants. Using all the available data registered by the CEMS installed on the main chimney, hourly concentration and deposition fields have been obtained by running a one year long simulation with the three dimensional lagrangian model SPRAY, capable of simulating both dry and wet deposition.
Due to the complexity of the local topography, a 250m horizontal spatial resolution grid has been used. Meteorological fields have been obtained at the same resolution by a downscaling procedure with a mass-consistent model (SWIFT). The statistical analysis of the results shows the relevance of secondary fallout patterns in remote areas, where vegetables could be grown for local consumption or dairy cattle could frequently pasture, thus suggesting the need of specific monitoring for remote areas in order to attain a wider assessment of human exposure.
... Another model used to study and predict the environmental impact is the stochastic Lagrangian dispersion model LAMBDA (Ferrero and Anfossi, 1998). Particle models are efficient and fundamental tools in the investigation and study of turbulent diffusion phenomenom in the planetary boundary layer. ...
The aim of this study is to compare the CALPUFF and LAMBDA models and evaluate the regulatory model CALPUFF accuracy in situations of line instant source emissions. Line source emissions exist in a variety of situations in the environmental field. Paved and unpaved roads are the most common examples of line sources. For instance, in the mining sector these two types of sources play an important role of anthropogenic influences in the environment. The OLAD experiment is appropriate to evaluate these models and check the accuracy of both. The CALPUFF results show in the simulations for short and long distances a systematic tendency of sub-prediction for the concentration. The LAMBDA model presented better accuracy in the prediction of natural pollutant dispersion even disregarding the spatial variability of meteorological field and topography. When the LAMBDA model is used the flow of pollutants to greater distances is less pronounced, especially because of the time step of one second adopted in the simulation.
... The coefficient a(z,w) must be determined by solving the Fokker-Planck equation for a given PDF that must be prescribed from the available measurements or parametrisations. In the present work, we used the Gram-Charlier PDF truncated to the third order [26]. The dispersion model is coupled with the circulation model, RAMS [27]. ...
... Differently to the Eulerian dispersion models, as the Gaussian and the GILTT, ref. [10] presented a turbulence parameterization for the planetary boundary layer (PBL) dispersion models in all stability conditions. The tracer dispersion was simulated by the Lagrangian particle model LAMBDA [11,12]. ...
In the literature there exists a variety of pollution of dispersion models and in general, Gaussian models are
used worldwide by environmental agencies in regulatory applications. The CALPUFF model is one of them. In this study,
the influence of decorrelation time scales in the CALPUFF modeling system under neutral conditions is evaluated. To do
this a new parameterization of decorrelation time scales is proposed. This method is based on the Eulerian velocity spectra
and a formulation of the evolution of the Lagrangian decorrelation timescales. To this end a spectral distribution of an
Eulerian velocity profile and a formulation of the evolution of Lagrangian decorrelation timescales under neutral conditions
is used as the forcing mechanisms (shear-dominated boundary layer) for the turbulent dispersion. The model performance
was established by comparing the levels of ground-level concentrations of the tracer gas with experimental results from the
Over-Land Alongwind Dispersion experiment. Comparing the two simulations using the CALPUFF model, the CALMET
CALPUFF simulations had better results only for samplers located near the line source. Is it possible this behaviour is
associated with the spatial variability of the fluid flow that is present in CALMET CALPUFF modeling mode. The new
parameterizations was evaluated in SURFACE and PROFILE mode, without spatial variability. Therefore, it can be used as
parameterization for regulatory modeling applications using CALPUFF. The simulation and the results suggests an increase
inaccuracy for long range turbulent transport of pollutants in both simulations. This behaviour it was evidenced from the
ratio between observed and predicted ground level concentration that show an increased inclination to greater distances. In
general the CALPUFF simulations clearly moving away from the line that contains ideal ratio between experimental and
predicted results. These findings show the necessity to correct the model. Moreover, the high correlation coefficients
determined with the observed data indicate how to fix the model predictions by a concentration dependent scale with
distance.
... In MicroSpray, the asymmetric PDF can be parameterized either by the bi-Gaussian PDF [Baerentsen and Berkowicz, 1984;Luhar and Britter, 1989;Weil, 1990] or by the Gram-Charlier PDF Ferrero andAnfossi, 1998a, 1998b]. Following results of numerical experiments [Ferrero and Anfossi, 1998b], in practical applications, the Gram-Charlier PDF showed major advantages for its computational efficiency and its ability to include information on the Eulerian moments directly. ...
In this paper, the MicroSpray 3-D Lagrangian particle dispersion model is presented and reviewed, and several validation studies are shown. Starting from its core, based on a 3-D form of the Langevin equation for the random velocity, the successive developments of different modules treating the main physical processes that determine the atmospheric pollutant dispersion are illustrated. Different prob- ability density functions are implemented to estimate the deterministic coefficient in the Langevin equation. Buoyancy effects are described through simplified plume rise formulations up to a complete set of equations for negatively and positively buoyant emissions, also including phase changes. MicroSpray is able to simulate different types of sources and emissions; it includes the treatment of obstacles and complex orography and offers several options to optimize the numerical runs. The model can be driven both by diagnostic and prognostic atmospheric models, and it has been used and validated in a variety of cases, from experimental to real conditions. Some significant examples of MicroSpray simulations are detailed and discussed.
... In MicroSpray, the asymmetric PDF can be parameterized either by the bi-Gaussian PDF [Baerentsen and Berkowicz, 1984;Luhar and Britter, 1989;Weil, 1990] or by the Gram-Charlier PDF Ferrero andAnfossi, 1998a, 1998b]. Following results of numerical experiments [Ferrero and Anfossi, 1998b], in practical applications, the Gram-Charlier PDF showed major advantages for its computational efficiency and its ability to include information on the Eulerian moments directly. ...
A new version of the Lagrangian dispersion model MicroSpray was developed to simulate the dispersion of two-phase aerosol clouds. The model extends the algorithms developed to take into account the effects of dense gas dynamics recently developed for the code, allowing the simulation of gas-aerosol jets forming from accidental release of toxic industrial chemicals (TIC) stored in liquid phase in a pressurized vessel or pipe. The mixture of contaminant liquid and vapor is considered as a single material and each particle tracked by the model simulates the contaminant liquid and vapor, water liquid and vapor and dry air taking into account all the possible phase transformations and the related effects on the dynamics of the plume. A system of differential equations is solved to follow at the same time the dynamics and the thermodynamics of the plume to evaluate the liquid and vapor mass fractions after the initial flashing, taking into account the presence of water initially in the mixture or entrained from the wet ambient air. The state of the contaminant at each time step is determined assuming homogeneous thermodynamic equilibrium. The equation of energy conservation is rewritten to include the latent heats of the liquid contaminant and atmospheric water.
A sensitivity analysis showing the dependence of the model output on the time-step chosen and the influence of water vapor entrainment in the emission temperature drop has been performed. Further, to evaluate the MicroSpray ability to simulate the dispersion of two-phase releases of heavy gases, the model has been coupled with the diagnostic MicroSwift model, that provides the 3-D wind field in presence of obstacles and orography, and its performances compared in detail to a chlorine railway accident (Macdona). The simulations results, with and without the aerosol module, are presented and the differences are discussed.
... This set must be big enough to guarantee a certain statistical accuracy. This calculation is made by the Lagrangian particle model LAMBDA [4]. Each particle trajectory can be described by the τ . ...
Atmospheric area pollutant sources are estimated using Particle Swarm Optimization (PSO). The forward problem is addressed by a Lagrangian particle model to simulate the pollutant dispersion. The inverse results are compared with a previous work that used a deterministic method (quasi-Newton approach). The PSO approach produced a good identification and no regularization operator was employed, showing the robustness and efficacy of the bio-inspired algorithm. PARTICLE SWARM OPTIMIZATION The particle swarm optimization is a relatively recent heuristic search method the uses the behavior of biological societies, like birds or fishes to drive the artificial particles in a search pattern that equalizes a global search with a local search, in a way that an optimum, or near to optimum, result is found [1]. There is a socio-cognitive theory that supports the particle swarm model, and it is quite simple. The cultural adaptive process encloses a high-level component, as seen in pattern formation trough the individual and the ability of problem solving, and a low-level component, the individual behavior, that can be summarized in three principles [2]: • Evaluate; • Compare; • Imitate. The tendency to evaluate stimuli, to classify them as positive or negative is, maybe, the behavioral characteristic more present in several living beings. The learning cannot occur unless the living being can evaluate, distinguish from what is good or not. The social comparison theory describes the behavior of people comparing each other as a pattern to find a way to improve each one quality. The imitation behavior gives the living beings the ability to learn through the observations of others attitudes. This behavior is not so much common in the nature as believed in common sense. The imitation behavior is more central to the human society, but it can be used in a way to improve the performance of bio-inspired algorithms. These three principles can be combined, even in simplified computational entities, providing them the ability to adapt their selves in complex and challenging environments, solving several classes of problems. PSO solves this problems searching for the optimum in an infinite (ℜ ∞) or a n-dimensional space of real numbers, symbolized as ℜ N . In a matter of fact, the infinite space is reduced to the computable space that can be reproduced in personal computers, this fact brings aboard the inconvenience of rounding errors.
... MicroSpray ) is a LPD model directly derived from SPRAY code (Tinarelli et al., 1994(Tinarelli et al., , 2000Ferrero and Anfossi, 1998), capable of taking into account the presence of obstacles. The dispersion of an airborne pollutant is simulated following the motion of a large number of fictitious particles, each representing a part of the emitted mass from sources of general shapes. ...
A Lagrangian particle dispersion model for dense gas dispersion is proposed. It is a new version of MicroSpray oriented to simulate dense gas dispersion in urban or industrial environment, and includes the treatment of obstacles, complex terrain and low wind. The dense gas descent is computed by a 3D dynamical plume rise/descent model, the gravity spreading and bottom boundary condition are accounted for by empirical formulations. The differences between simulations obtained with the new model and with the standard one are presented. The model is validated against tracer field data gathered in the Thorney Island experiment 8.
... In the vertical direction, the PDF is assumed to be non-Gaussian to describe non-uniform turbulent conditions. In this case, the Gram-Charlier series expansion is adopted (Anfossi et al. 1997;Ferrero and Anfossi 1998). The diffusion coefficient b ij (x, u) is obtained from the Lagrangian structure function and is related to the Kolmogorov's universal constant, C 0 (Du 1997), and to the dissipation rate of turbulent kinetic energy e, as the following equation: ...
The atmospheric impact of stack emissions from a power plant (tri-generator and boilers) that will be
installed in an urban area in the central Po valley (Northern Italy), characterized by calm wind events, is studied andcompared with the impact of the existing plant (conventionalboilers). Both the plants are supplied by methane gas. The atmospheric dispersion of NOx emitted is simulated, both in the current and future scenario, by the software package ARIA INDUSTRY. The NOx emission rates are set equal to the regulatory emission limits for existing and future boilers, while the tri-generation system emission
rates are set equal to the emission limits certified by the system manufacturer. The simulation periods focus over the 2010 winter season. The simulation estimates the impact of NOx emissions on air quality (vertical concentrationprofiles and concentration maps at the ground) in the urban area close to the plant. The future power plant impact on air quality results lower than the impact of the existing plant, even if the yearly total mass of pollutants emitted in atmosphere from the new power plant is higher than from the existing plant. The emissions of conventional boilers result the main responsible of the air pollution at the
ground in the future scenario.
... In MicroSpray, the asymmetric PDF can be parameterized either by the bi-Gaussian PDF [Baerentsen and Berkowicz , 1984; Luhar and Britter, 1989; Weil, 1990] or by the Gram-Charlier PDF [Anfossi et al., 1997; Ferrero and Anfossi, 1998a, 1998b]. Following results of numerical experiments [Ferrero and Anfossi, 1998b], in practical applications, the Gram-Charlier PDF showed major advantages for its computational efficiency and its ability to include information on the Eulerian moments directly. ...
A new original method for the dispersion of a positively and negatively
buoyant plume is proposed. The buoyant pollutant movement is treated
introducing a fictitious scalar inside the Lagrangian Stochastic
Particle Model SPRAY. The method is based on the same idea of
Alessandrini and Ferrero (Phys. A 388:1375-1387, 2009) for the treatment
of a background substance entrainment into the plume. In this
application, the fictitious scalar is the density and momentum
difference between the plume portions and the environment air that
naturally takes into account the interaction between the plume and the
environment. As a consequence, no more particles than those inside the
plume have to be released to simulate the entrainment of the background
air temperature. In this way the entrainment is properly simulated and
the plume sink is calculated from the local property of the flow. This
new approach is wholly Lagrangian in the sense that the Eulerian grid is
only used to compute the propriety of a portion of the plume from the
particles contained in every cell. No equation of the bulk plume is
solved on a fixed grid. To thoroughly test the turbulent velocity field
calculated by the model, the latter is compared with a water tank
experiment carried out in the TURLAB laboratory in Turin (Italy). A
vertical density driven current was created releasing a saline solution
(salt and water) in a water tank with no mean flow. The experiment
reproduces in physical similarity, based on the density Froud number,
the release of a dense gas in the planetary boundary layer and the
Particle Image Velocimetry technique has been used to analyze the
buoyancy generated velocity field. The high temporal and spatial
resolution of the measurements gives a deep insight to the problems of
the bouncing of the dense gas and of the creation of the outflow
velocity at the ground.
... While in the two horizontal directions the E P is considered to be Gaussian, in the vertical direction the PDF is assumed to be non- Gaussian (to deal with non-uniform turbulent conditions and/or convection). In this latter case, two different approaches can be adopted in order to calculate the Fokker-Planck equation: a bi-Gaussian equation, truncated to the third order, and a Gram-Charlier equation, truncated to the third or to the fourth order (ANFOSSI et al., 1997; FERRERO;). The bi-Gaussian PDF is given by the linear combination of two Gaussians (BAERENTSEN; BERKOWICZ, 1984 ) and the Gram- Charlier PDF is a particular type of expansion that uses orthonormal functions in the form of Hermit polynomials. ...
An Eulerian model and a Lagrangian particle model are used to study the dispersion of a contaminant released from a low height source in the Stable Boundary Layer (SBL). The Eulerian model is based on the solution of the advection-diffusion equation by the Laplace transform technique. The Lagrangian model is based on a generalized form of the Langevin equation. Turbulence inputs are parameterised according to two procedures capable of generating continuous values in all stability conditions and in all heights of Planetary Boundary Layer (PBL). Statistical indices were calculated to compare the predicted and observed values of ground-level concentration. According to the statistical analysis, predicted concentration values agree well with the observed ones.
... Thus, using the same model (i.e. in particular, the same numerical schemes) but, alternatively , Eqs. (6) or (7), the effects of the new parameterisation should clearly come out. In particular, the vertical component of the velocity fluctuation w 0 was in both cases computed as usual Q is the tracer emission rate, U 2 and U 4 are the hourly mean wind speed at 2 and 4 m and s W is the hourly standard deviation of wind direction at 4 m. in LAMBDA, that is by solving the Langevin equation (Thomson, 1987 p T Lw and a i ðz; w 0 Þ is computed by solving the Fokker–Planck equation associated to (8) using a PDF of Gram–Charlier type truncated to the thirdorder (Ferrero and Anfossi, 1998). The position of each particle, at each time step, is obtained by the numerical integration of Eqs. ...
The simulation of atmospheric dispersion in low wind speed conditions (LW) is still recognised as a challenge for modellers. Recently, a new system of two coupled Langevin equations that explicitly accounts for meandering has been proposed. It is based on the study of turbulence and dispersion properties in LW. The new system was implemented in the Lagrangian stochastic particle models LAMBDA and GRAL. In this paper we present simulations with this new approach applying it to the tracer experiments carried out in LW by Idaho National Engineering Laboratory (INEL, USA) in 1974 and by the Graz University of Technology and CNR-Torino near Graz in 2003. To assess the improvement obtained with the present model with respect to previous models not taking into account the meandering effect, the simulations for the INEL experiments were also performed with the old version of LAMBDA. The results of the comparisons clearly indicate that the new approach improves the simulation results.
... From Prairie Grass runs we select the most convective cases. Ferrero and Anfossi (1998a) and Ferrero and Anfossi (1998b) provide a detailed presentation and discussion of LAMBDA dispersion model. The current version of the LAMBDA dispersion model is based on the generalized Langevin equation, whose coefficients are obtained by solving the Fokker-Planck equation, and satisfies the well-mixed condition (Thomson, 1987). ...
A new formulation for the vertical turbulent velocity third statistical moment in a convective boundary layer is proposed. The parameterization is based directly on the definition of this higher order moment, with velocity skewness and variance being calculated from large eddy simulation data. The formulation, included in a Lagrangian stochastic dispersion model, has been tested and compared with expressions for the third moment obtained from experimental data and reported in the literature, using concentration data from field experiments. The application of a statistical evaluation shows that the proposed parameterization has one of the best overall adjustments to the data.
... In Gaussian or non-Gaussian turbulence, a Gram–Charlier PDF can be adopted [1,18]. The Gram–Charlier PDF truncated to the fourth order is given by the following expression [25]: ...
In this work we present an alternative hybrid method to solve the Langevin equation and we apply it to simulate air pollution dispersion in inhomogeneous turbulence conditions. The method solves the Langevin equation, in semi-analytical manner, by the method of successive approximations or Picard's Iterative Method. Solutions for Gaussian and non-Gaussian turbulence conditions, considering Gaussian, bi-Gaussian and Gram–Charlier probability density functions are obtained. The models are applied to study the pollutant dispersion in all atmospheric stability and in low-wind speed condition. The proposed approach is evaluated through the comparison with experimental data and results from other different dispersion models. A statistical analysis reveals that the model simulates very well the experimental data and presents results comparable or even better than ones obtained by the other models.
... a(z,w) must be determined by solving the Fokker-Planck equation for the velocity probability density function (PDF), that must be prescribed from the available measurements or parameterisations. In the present work, we have used the Gram-Charlier PDF (Ferrero and Anfossi, 1998). The second modelling system used is the CALMET-CALPUFF chain. ...
In this work the comparisons between measured and numerically simulated tracer experiments are presented for two different datasets. Different versions of the model system RMS, including the Regional Atmospheric Modelling System (RAMS) and the dispersion model SPRAY, accounting for alternative turbulence closures are used. These last are the Mellor and Yamada model level 2.5 and two versions of the E-l model, the standard isotropic and anisotropic versions. Moreover, simulations performed with the CALPUFF dispersion model coupled with RAMS are also presented. The wind fields and the ground level concentrations produced by the two model systems are shown and compared.
... is the PDF that must be prescribed from the available measurements or parameterisations. In the present work, we used the Gram-Charlier PDF (Ferrero and Anfossi, 1998). The model makes use of the Gaussian assumption in the horizontal directions. ...
A Lagrangian stochastic (single particle) model is modified in order to account for simple chemistry reactions and tested against measured wind tunnel data. These data refers to a reactive plume generated by a single point source of NO inside a turbulent grid flow doped with ozone. The comparisons were made at different distances from the emission considering all the substances involved in the experiment. The cross correlation terms between the concentrations of the different chemical compounds are neglected or parameterised. Despite this simplification the results are rather satisfactory and seem to encourage practical applications in real atmosphere.
... To examine the performance of Eq. (12) in dispersion model turbulent parameterizations, we simulate the Prairie Grass tracer experiment [20] using the Lagrangian particle model LAMBDA [21,22]. LAMBDA is a Lagrangian stochastic particle model based on a three-dimensional form of the Langevin equation for the random velocity [5]. ...
The classical statistical diffusion theory and the binomial autocorrelation function are used to obtain a new formulation for the turbulence dissipation rate ε. The approach employs the Maclaurin series expansion of a logarithm function contained in the dispersion parameter formulation. The numerical coefficient of this new relation for ε is 100% larger than the numerical coefficient of the classical relation derived from the exponential autocorrelation function. A similar approach shows that the dispersion parameter obtained from the even exponential autocorrelation function does not result in a relation for ε and, therefore, is not suitable for application in dispersion models. In addition, a statistical comparison to experimental ground-level concentration data demonstrates that this newly derived relation for ε as well as other formulations for the turbulence dissipation rate are suitable for application in Lagrangian stochastic dispersion models. Therefore, the analysis shows that there is an uncertainty regarding the turbulence dissipation rate function form and the autocorrelation function form.
... SPRAY dispersion simulations were performed in the 40 × 40 km 2 smallest domain centred on the incinerator location. The following options were adopted: dynamic plume rise (Anfossi et al., 1993), variable time step, Gaussian PDF in the horizontal plane and a skewed Gram-Charlier PDF (Ferrero and Anfossi, 1998) in the vertical, five particles emitted per second. This number is obtained imposing that sufficient particles are released per time step to give meaningful accuracy of the predicted concentrations: in our case each particle contributes with 0.5 µg/m 3 to the concentration computed in the model cell. ...
A numerical modelling study for the assessment of the air quality impact of a waste incinerator to be built in the city of Turin is presented, aimed at evaluating the ground level concentration distribution during adverse dispersion conditions, causing severe pollution episodes. The pollutant impact of the incinerator is evaluated with the three-dimensional modelling system RMS. This class of models is essential to get reliable simulations in 3-D complex conditions. A comparison vs. observed wind data is presented and various parameters elaborated from the concentration values are discussed for three episodes, in critical meteorological conditions from the pollutant dispersion viewpoint.
... The interface code MIRS (Trini Castelli and , uses the RAMS outputs (wind speed, turbulent kinetic energy -TKE, diffusion coefficients, potential temperature, model SPRAY, not directly given by the RAMS, i.e.: the convective velocity scale the fourth moment it uses the following relationship: (Ferrero and Anfossi, 1998). For the PBL height, three methods are considered: McNider and Pielke (1981), Maryon and Buckland (1994) and Kalthoff et al. (1998). ...
The main objectives of this study was to carry out the link between the meteorological model RAMS and the Lagrangian particles
model SPRAY in order to simulate the transport and diffusion processes and to verify its ability to describe the dispersion
of a tracer emitted during the TRACT experiment. According to the results here presented, it is possible to state that such
goals were reached. In particular, the comparisons of modelled and observed meteorological variables show that RAMS simulates
very well the TRACT experiment. The model system correctly reproduces the general behaviour of the contaminant plume, the
temporal and spatial distribution of the concentration and the location of the concentration maximum. It is also shown that
the connection between RAMS and SPRAY, through MIRS, is fully operative.
... During convective conditions , the velocity distribution is non-Gaussian due the skewness generated by the organized updrafts and downdrafts motion. In this latter case, two different approaches can be adopted to calculate the Fokker–Planck equation: a bi-Gaussian equation, truncated to the third order, and a Gram–Charlier equation, truncated to the third or to the fourth order (Anfossi et al., 1997; Ferrero and Anfossi, 1998). The bi-Gaussian PDF is given by the linear combination of two Gaussians (Baerentsen and Berkowicz, 1984) and the Gram-Charlier PDF is a particular type of expansion that uses orthonormal functions in the form of Hermit polynomials. ...
An Eulerian model and a Lagrangian particle model are used to study the dispersion of a contaminant released from a low source in the Stable Boundary Layer (SBL) using two different turbulence parameterisations. The Eulerian model is based on the solution of the advection–diffusion equation by the Laplace transform technique. The Lagrangian model is based on a generalized form of the Langevin equation. The first parameterisation, Degrazia et al. (2000), is based on Taylors statistical diffusion theory and the observed spectral properties, supposes a linear combination between shear and buoyancy turbulence. The second, Hanna (1982), is based on observed spectral properties from Minnesota Planetary Boundary Layer (PBL) observations and is widely used in pollutant dispersion models. Considering that these simulations are in the SBL, the analysis of the results shows a reasonably good agreement between the values computed by the models against the experimental ones for the two turbulence parameterisations.
... All these data are on an hourly basis. The tracer dispersion was simulated by the Lagrangian particle model LAMBDA (Ferrero et al., 1995; Ferrero and Anfossi, 1998a, b). For a detailed presentation and discussion of LAMBDA we refer to the quoted papers. ...
In the atmospheric dispersion models turbulence parameterization is a key parameter. In the present paper, accounting for the current knowledge of the PBL structure and characteristics, a new set of turbulence parameterization to be used is such models has been derived. That is, expressions for the vertical profiles of the velocity standard deviations σi
, Lagrangian length scale l
Li
, time scale TLi
and diffusion coefficient K
i
, where i = 1, 2, 3 are proposed. The classical statistical diffusion theory, the observed spectral properties and observed characteristics of energy containing eddies are used to estimate these parameters. These parameterizations give continuous values for the PBL at all elevations ((z
0≤ z ≤ h) and all stability conditions from unstable to stable (-∞ < L < ∞), where h is the neutral or stable PBL height, z
0the aerodynamic roughness length and L the Monin-Obukhov length
In 2015, 2016, nine chlorine releases experiments took place at Dugway Proving Ground (Utah, USA). Five trials conducted in 2015 featured a grid of CONEX shipping containers around the release tank to simulate an idealized urban area. The trials were a great occasion to collect data describing the dynamics of “high molecular weight” species in an idealized urban environment.
This paper proposes a comparison of the PMSS (Parallel Micro-Swift Micro-Spray) suite against the experimental data from four of the trials, following the choice made by an international model inter-comparison team. PMSS combines two MPI parallelized urban modelling subsystems: (1) PSWIFT phenomenologically accounts for 3D wind flow and turbulence around buildings, and (2) PSPRAY simulates air-based contaminant dispersion in urban areas using a stochastic Lagrangian Particle Dispersion Model.
For this comparison, PMSS is deployed first on a hypothetic configuration and compared to the Code_Saturne CFD model, and then using the data of the trials 1, 5, 6 and 7 performed during JRII (Jack Rabbit II) 2015 and 2016. The initial momentum due to the tank discharge and the dense gas and droplet effects of the pressurized chlorine release are modelled using a dedicated radial source term jet and the Glendening equations. In trials 1 and 5, the influence of the CONEX shipping containers on the wind flow and the dispersion is explicitly considered. While spread through a large interval, the chlorine concentrations are computed both in the near field and in the far field (up to 11 km) using PMSS nesting capabilities. The results of the model are compared with the experimental data and sensitivity tests are also presented.
The meteorological model RAMS and the Lagrangian particle model SPRAY are coupled to simulate the transport and diffusion of tracer released during the project TRACT, realized in the Rhine valley, Central Europe. The simulation results generated by the model system are evaluated against observational data measured in the TRACT experiments. Analysis of the results and the application of statistical indices show that the considered models reproduce well the general behaviour of the contaminant plume, the temporal and spatial distribution of the concentration and the location of the concentration maxima.
In stably stratified flows, the flux Richardson number Ri f is a measure of the ratio between buoyancy destruction and shear production of turbulent kinetic energy (TKE). In flows with local equilibrium between shear production, buoyancy destruction and dissipation of TKE, the critical Ri f,c ≈0.21 corresponds to the limit above which Kolmogorov turbulence can no longer be sustained. Analysis of the TKE and velocity variance budget equations shows that the critical Ri f,c is increased by the presence of positive turbulent transport of TKE. This situation is observed, for example, in the roughness sublayer above plant canopies, as demonstrated using field data from the Amazon rainforest.
Turbulent wind data measured by sonic anemometers installed at various heights on a 140-m-tall micrometeorological tower located at a coastal site are used to obtain vertical profiles of the velocity standard deviations σi, Lagrangian decorrelation local time scales TLi, and eddy diffusivities Kα for distinct stability conditions. The novelty of the study lies in the use of turbulent data directly measured over the extension of the atmospheric surface layer at a coastal site for that purpose. Furthermore, the approach employs the Hilbert-Huang transform to determine the wind energy spectral peak frequencies. These are applied to the asymptotic spectral equation from Taylor statistical diffusion theory to obtain the turbulent dispersion parameters, which are shown to generally agree well with those provided by a classical autocorrelation approach. For neutral and stable situations the vertical profiles of momentum eddy diffusivities agree well with those derived from the spectral and autocorrelation method. Additionally, the turbulent integral time scales and eddy diffusivities determined by the method at a coastal location are found to overestimate those predicted from analytical expressions based on continental field observations. The turbulence parameters found are suitable to be employed in air pollution dispersion models.
Environmental impact of aircraft emissions can be addressed in two ways. Air quality impact occurs during landings and takeoffs while in-flight impact during climbs and cruises influences climate change, ozone and UV-radiation. The aim of this paper is to investigate airports related local emissions and fuel consumption (FC). It gives flight path optimization model linked to a dispersion model as well as numerical methods. Operational factors are considered and the cost function integrates objectives taking into account FC and induced pollutant concentrations. We have compared pollutants emitted and their reduction during LTO cycles, optimized flight path and with analysis by Dopelheuer. Pollutants appearing from incomplete and complete combustion processes have been discussed. Because of calculation difficulties, no assessment has been made for the soot, H_2O and PM_{2.5}. In addition, because of the low reliability of models quantifying pollutant emissions of the APU, an empirical evaluation has been done. This is based on Benson`s fuel flow method. A new model, giving FC and predicting the in-flight emissions, has been developed. It fits with the Boeing FC model. We confirm that FC can be reduced by 3% for takeoffs and 27% for landings. This contributes to analyze the intelligent fuel gauge computing the in-flight fuel flow. Further research is needed to define the role of which is emitted during the combustion process derived from the ambient air, not the fuel. Models are needed for analyzing the effects of fleet composition and engine combinations on emission factors and fuel flow assessment.
In this work, a Lagrangian particle model able to account for simple chemical reactions between NO and O<sub align="right"> 3 </sub> has been improved to consider the photolysis of NO<sub align="right"> 2 </sub>. A system of chemical equations is numerically solved on a Eulerian grid, while the particle trajectories are moved in a Lagrangian frame. The NO<sub align="right"> x </sub> emissions of a power plant in real atmosphere, situated in a complex topography environment, have been considered as a test case. The simulated episodes refer to the diurnal time, when the ultraviolet radiation activates the NO<sub align="right"> 2 </sub>. Comparisons between NO/NO<sub align="right"> 2 </sub>'s concentrations ratio are presented in terms of scatter plots and statistical indexes analysis.
A Lagrangian stochastic particle model is utilized to simulate the dispersion and the transport of contaminants under low wind stable conditions in the tracer experiment carried in the Idaho National Engineering Laboratory (INEL). In this work a new parameterization for the parameters representing the frequencies associated to the meandering phenomenon is tested. The new parameterization is expressed in terms of a non-dimensional quantity that controls the frequencies of the meandering oscillation and of the time scale associated to a coherent structure in a fully developed turbulence. The simulations show that the considered Lagrangian model, incorporating this new parameterization, reproduces correctly the diffusion of passive scalars in a low wind speed stable atmospheric boundary layer.
A Lagrangian stochastic particle dispersion model composed of two coupled Langevin equations, employing a new transport parameterization is used to study the meandering enhanced dispersion in a low wind speed stable atmospheric boundary layer (ABL). The meandering parameterization introduced into the Lagrangian stochastic dispersion model is expressed in terms of a characteristic phenomenological meandering period and of the horizontal local turbulent time scales associated with a fully developed turbulence. The results of this new method are shown to agree with the field observations of Idaho experiments and also with other different meandering dispersion models. The major advance shown throughout this paper is as it follows: For air quality modeling it is highly necessary to include a parameterization that allows a correct description of the dispersion caused by the low-frequency horizontal wind oscillations.
In this article is carried out a comparison between Lagrangian and Eulerian modelling of the turbulent transport of pollutants within the Planetary Boundary Layer (PBL). The Lagrangian model is based on a three-dimensional form of the Langevin equation for the random velocity. The Eulerian analytical model is based on a discretization of the PBL in N sub-layers; in each of the sub-layers the advection-diffusion equation is solved by the Laplace transform technique. In the Eulerian numerical model the advective terms are solved using the cubic spline method while a Crank-Nicholson scheme is used for the diffusive terms. The models use a turbulence parameterization that considers a spectrum model, which is given by a linear superposition of the buoyancy and mechanical effects. Observed ground-level concentrations measured in a dispersion field experiment are used to evaluate the simulations.
Dispersion in low wind speed conditions is governed by meandering that disperses plumes over wide angular sectors, thus g.l.c. are lower than predicted by Gaussian models. It was proposed to model these dispersion situations in homogeneous conditions with two coupled Langevin equations, based on low wind speed turbulence analysis. Their parameters were derived from the autocorrelation functions of horizontal wind that exhibit an oscillations and large negative lobes. We propose a new equation system for: general case of inhomogeneous turbulence; total velocity; for the windy situations (based on the ''Thomson simplest solution'') and verify that these new solutions satisfy the ''well-mixed condition''.
The aim of the work presented here is to study experimentally and numerically the dispersion characteristics of vehicular exhaust plume at an idle condition in an idealized and simplified environment. The gaseous and particulate concentrations in the exhaust plume of three idling motor vehicles were measured in an isolated environment under calm weather conditions. Despite the difference in the initial concentrations, the pollutants decayed exponentially in all directions.The CFD code PHOENICS 3.3, with the k–ε eddy dissipation sub-model, was used for the numerical simulation. The simulated results match very well with the experimental results close to the source of emission but decay to the ambient concentrations much slower. The effects of the initial emission concentration, exit velocity, exit direction and crosswind intensity have been investigated parametrically. The initial pollutant concentration will increase the local concentrations but the pattern of dispersion remains the same. The exit velocity will increase the momentum of the jet, resulting in a deeper penetration downstream. The exit angle has a stronger influence on pollutant dispersion than both initial pollutant concentration and exit velocity. When the exit angle is 15°, the pollutants tend to spread on the ground region. Crosswind shows a significant effect on the dispersion of the exhaust plume also. It will divert the plume to disperse in the same direction of the wind with limited penetration in the downstream direction.
Accounting for the current knowledge of the stable atmospheric boundary layer (ABL) turbulence structure and characteristics, a new formulation for the meandering parameters to be used in a Lagrangian stochastic particle turbulent diffusion model has been derived. That is, expressions for the parameters controlling the meandering oscillation frequency in low wind speed stable conditions are proposed. The classical expression for the meandering autocorrelation function, the turbulent statistical diffusion theory and ABL similarity theory are employed to estimate these parameters. In addition, this new parameterization was introduced into a particular Lagrangian stochastic particle model, which is called Iterative Langevin solution for low wind, validated with the data of Idaho National Laboratory experiments, and compared with others diffusion models. The results of this new approach are shown to agree with the measurements of Idaho experiments and also with those of the other atmospheric diffusion models. The major advance shown in this study is the formulation of the meandering parameters expressed in terms of the characteristic scales (velocity and length scales) describing the physical structure of a turbulent stable boundary layer. These similarity formulas can be used to simulate meandering enhanced diffusion of passive scalars in a low wind speed stable ABL.
A parameterization for the transport processes in a shear driven planetary boundary layer (PBL) has been established employing turbulent statistical quantities measured during the north wind phenomenon in southern Brazil. Therefore, observed one-dimensional turbulent energy spectra are compared with a spectral model based on the Kolmogorov arguments. The good agreement obtained from this comparison leads to well defined formulations for the turbulent velocity variance, local decorrelation time scale and eddy diffusivity. Furthermore, for vertical regions in which the wind shear forcing is relevant, the eddy diffusivity derived from the north wind data presents a similar profile to those obtained from the non-extensive statistical mechanics theory. Finally, a validation for the present parameterization has been accomplished, using a Lagrangian stochastic dispersion model. The Prairie Grass data set, which presents high mean wind speed, is simulated. The analysis developed in this study shows that the turbulence parameterization constructed from wind data for north wind flow cases is able to describe the diffusion in a high wind speed, shear-dominated PBL.
A Lagrangian particle model is used to study the dispersion of pollutants released in two different tracer experiments: Prairie Grass and Copenhagen. The model is based on a generalized form of the Langevin equation. Turbulence inputs are parameterized according to a scheme able to generate continuous values in all stability conditions and in all heights in the planetary boundary layer. Predicted values of ground-level concentration agree quite well with observed ones. The major progress of this paper is as follows: For air quality modeling it is highly necessary to include a parameterization that allows a correct description of the turbulent transport of contaminants released simultaneously from low and tall sources. Ein Lagrange'sches Partikelmodell wird bei zwei verschiedenen Tracer-Experimenten zur Untersuchung der Dispersion von Luftschadstoffen verwendet: Pra¨riegrass und Kopenhagen. Das Modell fußt auf einer generalisierten Form der Langevin-Gleichung. Der turbulente Input wird nach einem Prinzip parameterisiert, dass es ermo¨glicht, kontinuierliche Werte fu¨r alle Stabilita¨tsbedingungen und die gesamte Planetare Grenzschicht zu erzeugen. Die vorhergesagten Werte der bodennahen Konzentration stimmen recht gut mit den beobachteten u¨berein. Der große Fortschritt, den diese Arbeit aufzeigt, ist der folgende: Zur Modellierung der Luftqualita¨t ist es in hohem Maße notwendig eine Parameterisierung einzufu¨gen, die eine zutreffende Beschreibung derjenigen turbulenten Transporte der Schadstoffe ermo¨glicht, die gleichzeitig von niedrigen und hohen Quellen freigesetzt werden.
Considering the convective boundary layer physical structure and their characteristics, a derivation for the Lagrangian decorrelation timescales to be used in Lagrangian stochastic particle models has been developed. That is, expressions for the Lagrangian decorrelation timescales depending on source distance for inhomogeneous turbulence are proposed. The classical statistical diffusion theory, the observed spectral properties and observed characteristics of energy-containing eddies are used to estimate these parameters. In addition, these decorrelation timescales were introduced in an Lagrangian stochastic particle model and validated with the data of Copenhagen experiments. The results of this new method are shown to agree very well with the measurements of Copenhagen. Furthermore, the present study suggests that the inclusion of the memory effect, important in near regions from an elevated continuous point source, improves the description of the turbulent transport process of atmospheric contaminants. The major advance shown in this paper is the necessity of including the downwind distance-dependent decorrelation timescales in air quality modeling, and it is demonstrated that such theory would suggest that it should yield better results than the asymptotic solution alone. It in fact does yields better results in the near and intermediate fields.
The study of the pollutant dispersion in the atmosphere disposes nowadays of a new computational model: the stochastic Lagrangian model. The theory related to these models has been constructed in the last two centuries. In this work we present this theory that integrate this important model, which has been full used. INTRODUÇÃO No estudo dos processos de transporte e difusão de poluentes na atmosfera, adotam-se dois tipos de modelos: modelo Euleriano e modelo Lagrangeano. A diferença básica entre as aproximações Euleriana e Lagrangeana é que o sistema de referência Euleriano encontra-se fixo em relação a terra, enquanto o sistema de referência Lagrangeano segue o movimento atmosférico médio. No modelo Euleriano descreve-se o andamento temporal da concentração de uma substância em relação a um sistema de referência fixo em relação à terra. O processo dispersivo é então formulado por uma equação diferencial de conservação de massa. No modelo Lagrangeano, calcula-se a concentração de uma substância através da determinação da trajetória de massas de ar ou de partículas, que seguem passivamente o escoamento. Nestes modelos, as grandezas físicas que descrevem as trajetórias são especificadas em termos probabilísticos. Um dos tipos de modelos Lagrangeanos mais utilizados é o modelo estocástico de partículas Lagrangeano. Neste tipo de modelo Lagrangeano, a dispersão de um poluente é simulada através do movimento de partículas fictícias (partículas marcadas), cujas trajetórias permitem o cálculo do campo de concentração. Essas partículas devem ser pequenas o bastante para poderem seguir o movimento dos menores turbilhões (da ordem da escala de Kolmogorov) e ao mesmo tempo grandes o suficiente para conterem um número elevado de moléculas. Para descrever tal comportamento, as velocidades das partículas estão sujeitas a um forçante aleatório. Os modelos de partículas Lagrangeanas são baseados na equação de Langevin. A equação de Langevin é derivada a partir da hipótese que a velocidade da partícula, em determinado intervalo de tempo, é dada pela soma de um termo determinístico e um termo aleatório (termo estocástico). Nesta equação, a evolução do movimento de uma partícula difundindo-se na atmosfera forma um processo de Markov (um processo estocástico no qual o passado e o futuro são estatisticamente independentes quando o presente é conhecido). A equação de Langevin foi derivada por Paul Langevin em 1908 para estudar o movimento Browniano e a difusão molecular como um método alternativo ao proposto por Einsten em 1905. No que segue, serão apresentadas as definições que formam as bases teóricas dos modelo estocásticos de partículas Lagrangenos. Por fim, apresenta-se a derivação do modelo de Langevin para dispersão em três dimensões, considerando condições de turbulência não-homogênea.
The increasing concentration of greenhouse effect gases is a central issue nowadays, mainly with regard to the anthropogenic
production gases, such as methane (CH4) and carbon dioxide (CO2). Despite the ratification of the Kyoto Protocol, the expectation is the releases of CO2 and CH4 into the atmosphere will continue to increase in next decade (IPCC, 2007). One essential strategy is to monitor the concentration of these gases in the atmosphere. However, in order to understand
the bio-geochemical cycle of these gases, it is necessary to estimate the surface emission rates. One procedure to do that
is to employ an inverse problem methodology. Here, the artificial neural network is employed to compute the inverse solution
with good results.
Eulerian turbulence observations, madein the surface layer under unstable conditions (z/L > 0),by a sonic anemometer were used to estimatethe Lagrangian structure function constant O. Twomethods were considered. The first one makes use of arelationship, widely used in the Lagrangian stochasticdispersion models, relating O to the turbulent kineticenergy dissipation rate , wind velocity variance andLagrangian decorrelation time. The second one employsa novel equation, connecting O to the constant of thesecond-order Eulerian structure function. Beforeestimating O, the measurements were processed in orderto discard non-stationary cases at least to a firstapproximation and cases in which local isotropy couldnot be assumed. The dissipation was estimated eitherfrom the best fit of the energy spectrum in theinertial subrange or from the best fit of the third-orderlongitudinal Eulerian structure function. Thefirst method was preferred and applied to the subsequentpart of the analysis. Both methods predict thepartitioning of O in different spatial components as aconsequence of the directional dependence of theEulerian correlation functions due to the isotropy.The O values computed by both methods are presented anddiscussed. In conclusion, both methods providerealistic estimates of O that compare well withprevious estimations reported in the literature, evenif a preference is to be attributed to the second method.
This work presents the computational fluid dynamic modeling of an exhaust plume dispersed from the exhaust pipe of a class-8 tractor truck powered by 330 hp Cummins M11 electronically controlled diesel engine. This effort utilizes an advanced CFD technique to accurately predict the variation of carbon dioxide concentration inside a turbulent plume using a k–ε eddy dissipation model. The simulation includes the “real-world” operation of a truck and its exhaust plume in a NASA, Langley aircraft testing wind tunnel, that had an effective volume of 226, 535 m3 (8,000,000 ft3). The predicted results show an excellent agreement with the experimentally measured values of CO2 concentrations, dilution ratios, and the temperature variations inside the plume. A specific goal of this effort was to study the effect of recirculation region near the truck walls on dispersion of the plume. For this purpose, growth of the plume from the center of the exhaust pipe is also presented and discussed. This work also shows the benefits of CFD modeling in applications where dispersion correlations are not required a priori, instead the dispersion coefficients are calculated precisely by solving the turbulent kinetic energy and dissipation equations.
An alternative formulation for the turbulence dissipation rate ε is presented. The development consists on a binomial expansion of an algebraic relation for the lateral dispersion parameter σy, originated from the fitting of experimental data. The new formulation keeps the same physical premises contained on the classical, largely used one, but the numerical coefficient increases by a factor of 50%. The new expression leads to dissipation rate values, which are shown to be in good agreement with those previously determined in the convective boundary layer. Furthermore, a statistical comparison to observed concentration data shows that the alternative relation for the dissipation rate is suitable for application in Lagrangian stochastic dispersion models. Motivated by these results, a new form for the autocorrelation function has also been obtained. Once the procedures that originated both the new and classical formulations are similar, only starting from a different expression for σy, this study shows that there is no universal certainty regarding the dissipation rate functional form and the autocorrelation function exponential form.
A semi-analytical Lagrangian particle model to simulate the pollutant dispersion during low wind speed conditions is presented and tested. The method relies to a stochastic integral equation whose solution is obtained using ILS method, which consists in the iterative solution of Langevin equation by the Picard's iteration method. To consider the low wind speed effect, the solution for the horizontal components of the turbulent velocity takes account the Eulerian autocorrelation function as suggested by Frenkiel [1953. Advances in Applied Mechanics 3, 61–107]. The model results are shown to agree very well with the field tracer data collected during stable conditions at Idaho National Engineering Laboratory (INEL) and during convective conditions from the series of field experiments at Indian Institute of Technology (IIT). A statistical analysis reveals that the model simulates very well the experimental data and presents results comparable or even better than ones obtained with other models used as comparison. The analytical feature of the ILS method and the inclusion of the Eulerian autocorrelation function suggested by Frenkiel (1953) allow generating more accurate results.
It is determined how long a time series must be to estimate covariances and moments up to fourth order with a specified statistical significance. For a given averaging time T there is a systematic difference between the true flux or moment and the ensemble average of the time means of the same quantities. This difference, referred to here as the systematic error, is a decreasing function of T tending to zero for T → ∞. the variance of the time mean of the flux or moment, the so-called error variance, represents the random scatter of individual realizations, which, when T is much larger than the integral time scale τ of the time series, is also a decreasing function of T. This makes it possible to assess the minimum value of T necessary to obtain systematic and random errors smaller than specified values. -from Authors
Vertical velocity fluctuations were measured in theatmospheric surface layer by means of an ultrasonic anemometer andhigher order correlations were calculated on two time series, recordedin unstable and neutral conditions, and selected for the wholemeasurement period on the basis of the inversion test (stationaritytest). Comparisons have been made between observed and predictedcorrelations by considering Gaussian joint-PDF and Gram-Charlierseries expansions truncated to the fourth and sixth order as doneearlier by Frenkiel and Klebanoff. A bi-Gaussian PDF, given by amixture of two Gaussian PDFs, has also been considered. This lasthas been constructed assuming that either the first three or the firstfour moments are given, and the relationships between correlationfunctions of different order are derived. The departure from Gaussianbehaviour in both stability conditions is derived. Though Gram-Charlier series expansions show a good correspondence toexperimental reality, their use as non-Gaussian probabilitydistributions cannot be suggested in theoretical approaches andshould be considered with care in practical applications, due topossible occurrences of small negative probabilities. The resultsshown in this paper support the applicability of the bi-Gaussian PDFcreated using up to the fourth moment.
Two Lagrangian particle models, developed by Luhar and Britter (Atmos. Environ., 23 (1989) 1191) and Weil (J. Atmos. Sci., 47 (1990) 501), satisfying the "well-mixed" condition as prescribed by Thomson (J. Fluid. Mech., 180 (1987) 529), are compared. They differ in the closure scheme used in calculating the probability density function of the random forcing in a convective boundary layer. Four different turbulent parameterizations were used as input to both models. Their performances are evaluated against one of the well-known Willis and Deardorff water tank experiments (Atmos. Environ., 12 (1978) 1305). Predicted and measured ground-level concentrations (g.l.c.), maximum g.l.c. distance, mean plume height and plume vertical spread are presented and discussed.
Lagrangian stochastic (LS) dispersion models often use trajectory reflection to limit the domain accessible to a particle. It is shown how the well-mixed condition (Thomson) can he expressed in the Chapman-Kolmogorov equation for a discrete-time LS model to provide a test for the validity of a reflection algorithm. By that means it is shown that the usual algorithm (perfect reflection) is exactly consistent with the wmc when used to bound Gaussian homogeneous turbulence, but that no reflection scheme can satisfy the wmc when applied at a location where the probability distribution for the normal velocity is asymmetric, or locally inhomogeneous. Thus, there is no well-mixed reflection scheme for inhomogeneous or skew turbulence.
Higher-order correlations were measured in a turbulent boundary layer using the LDA measuring technique. In the paper, comparisons are made between the measured and predicted correlations obtained by utilizing the properties of truncated Gram-Charlier series expansions. Several theoretically derived relationships between correlations of different orders were confirmed by the experimental data. The experimental and theoretical results support the applicability of truncated Gram-Charlier series expansions for a refined statistical analysis of the conservation equations for higher-order moments of turbulent property fluctuations.
A Lagrangian stochastic model of particle trajectories is used to investigate the asymmetry in vertical diffusion from area sources at the bottom and top of an inhomogeneous turbulent boundary layer. Such an asymmetry was discovered in the large-eddy simulations (LES) of the convective boundary layer (CBL) by Wyngaard and Brost (1984) and Moeng and Wyngaard (1984).For inhomogeneous Gaussian turbulence, a diffusion asymmetry results from the vertical asymmetry in the vertical velocity variance about the midplane of the boundary layer. For small turbulence time scales, this is predictable from eddy-diffusion (K) theory. However, for large time scales, K theory is inapplicable as evidenced by countergradient flux regions and K singularities. The fundamental causes of the K model breakdown are the memory (large time scale) and vertical inhomogeneity of the turbulence, which lead to a mean vertical acceleration of particles away from the source and a `drift' velocity.A positive skewness in vertical velocity enhances the drift velocity for a bottom source and suppresses it for a top source, thus leading to a greater diffusion asymmetry than in Gaussian turbulence; this is independent of the variance profile. The asymmetry due to skewness is caused by the bias in the probability density function of vertical velocity (w)-larger positive w values and smaller negative ones than in Gaussian turbulence. The results for inhomogeneous skewed turbulence are in good agreement with the LES results for the CBL.
A Monte Carlo model and computer code (MC-LAGPAR) for simulating atmospheric transport and diffusion of plumes are described. The turbulent diffusion is simulated by the semi-random motion of Lagrangian particles. The particles are emitted by a point source and dispersed in a computational domain by pseudo-velocities derived from vertical profiles of meteorological variables.The MC-LAGPAR code includes the implementation of special algorithms for the simulation of a dynamic plume rise, chemical decay, deposition and resuspension effects. Furthermore, computer-graphics displays have been developed. The model, here used in its two dimensional version, is validated in the well-known case of homogeneous and stationary turbulence. In this case, we compared the concentration fields obtained by our model with those calculated by the known analytical solution. In both computations, the standard deviations of wind velocities are calculated according to the Taylor formulas.In the nonhomogeneous case, the vertical structure of turbulence is parameterized according to the scheme suggested by Hanna. As an example of the non-homogeneous case, we present numerical simulations in convective (unstable) conditions in which the influence of updraughts and downdraughts is empirically taken into account.
Higher‐order time‐correlations and the associated skewnesses and flatnesses were measured in a turbulent field downstream of a grid using high‐speed computing techniques. The results were obtained using samples of 160 020 digitized data recorded at time intervals of 1∕12 800 sec during time periods of approximately 12.5 sec. Comparison is made between the measured correlations and the higher‐order correlation curves corresponding to a Gaussian probability density distribution of turbulent velocities. The departures from Gaussianity are shown, and non‐Gaussian probability distributions are proposed which correspond considerably better to experimental reality. Several relations between correlation coefficients of different orders are obtained for the non‐Gaussian probability distributions and confirmed by comparison with the measured correlations, skewnesses, and flatnesses.
The cumulant-discard approach is used to predict the third- and fourth-order moments and the probability density of turbulent Reynolds shear stress fluctuations uv, the streamwise and normal velocity fluctuations being represented by u and v respectively. Measurements of these quantities in a turbulent boundary layer are presented, with the required statistics of uv obtained by the use of a high-speed digital data-acquisition system. Including correlations between u and u up to the fourth order, the cumulant-discard predictions are in close agreement with the measurements in the inner region of the layer but only qualitatively follow the experimental results in the outer intermittent region. In this latter region, predictions for the third- and fourth-order moments of uv are also obtained by assuming that the properties of both turbulent and irrotational fluctuations are Gaussian and by using some of the available conditional averages of u,
v and uv.
Many different random-walk models of dispersion in inhomogeneous or unsteady turbulence have been proposed and several criteria have emerged to distinguish good models from bad. In this paper the relationships between the various criteria are examined for a very general class of models and it is shown that most of the criteria are equivalent. It is also shown how a model can be designed to satisfy these criteria exactly and to be consistent with inertial-subrange theory. Some examples of models that obey the criteria are described. As an illustration some calculations of dispersion in free-convective conditions are presented.
An experimental investigation of the two-dimensional incompressible mixing layer was carried out. The measurements provide new information on the development of the mean and turbulent fields towards a self-preserving state and on the higher-order statistical characteristics of the turbulent field. The relevance of initial conditions to the development of the flow is discussed in the light of both present and previous data. Measurements of spectra, probability densities and moments to eighth order of all three velocity-component fluctuations at various transverse positions across the flow were carried out using an on-line digital data acquisition system. The probability density distributions of the derivative and the squared derivative of the longitudinal and lateral velocity fluctuations were also determined. Direct measurements of moments to eighth order of the velocity derivatives were attempted and are discussed in the light of the simultaneously measured histograms. The problems in obtaining higher-order statistical data are considered in some detail. Estimates of the integral time scale of many of the higher-order statistics are presented. The high wave-number structure was found to be locally anisotropic according to both spectral and turbulent velocity-gradient moment requirements. Higher-order spectra to fourth order of the longitudinal velocity fluctuations were measured and are discussed. Finally the lognormality of the squared longitudinal and lateral velocity-derivative fluctuations was investigated and the universal lognormal constant μ was evaluated.
Dispersion in one dimension is simulated by the Langevin equation dW = −(W/TL)dt + dμ, where W is the velocity of the particle (hypothetical fluid element), TL the Lagrangian time scale and dμ the random velocity increment induced by forces exerted by the turbulence on the particle during dt. The moments of dμ in the Langevin equation in inhomogeneous conditions can be determined, by requiring that for large times the density distribution of the particles is the same as that of the air. In our numerical experiment the Langevin equation with the above-defined moments is applied to diffusion in the convective boundary layer. Profiles of the moments of the vertical turbulence velocities, U(z), n = 1, 2, 3, are based on measurements and scaled by convective scaling; TL is assumed constant. Particles are released at several heights, with an initial velocity distribution that has the same moments as the Eulerian turbulence velocity distribution at that height. At the boundaries reflection conditions are imposed. Our results are extensively compared with water-tank experiments of Willis and Deardorff, wind-tunnel experiments of Poreh and Cermak, field experiments by Briggs and a model of Baerentsen and Berkowicz. The mean height and variance of the particles, the concentration field as a function of down-wind distance and height, and ground level concentrations are presented. They agree very well with observations of dispersion in the convective boundary layer.
A laboratory model of the convective planetary boundary layer has provided information concerning the evolution of concentration distributions downwind from a simulated continuous point source located near the ground. Results indicate that a Gaussian plume formulation adequately describes the model γ-concentration distributions, but is useful in predicting the z-concentration distributions only to a distance downstream of about x = 0.5zi/(w*/U), where zi is the mixed layer depth and w*/U is a dimensionless stability parameter. Near this distance an elevated concentration maximum appears at a height above the source release height. The elevated maximum rises to a height of about 0.8zi at x = 1.7zi/(w*/U) and retains its identity until the pollutants become vertically well mixed farther downstream. Use of the stability parameter w*/U permits the model results to be applied to a range of atmospheric conditions encompassing the Pasquill-Gifford stability classes A and B. Close agreement is found between the laboratory data and the atmospheric observations of ground-level lateral spread of Islitzer (1961) and Islitzer and Dumbauld (1963), where the latter measurements extended out to x≃ 3 km.
We report a two-dimensional (alongwind u, vertical w) trajectory-simulation model, consistent with Thomson's (1987) well-mixed criteria, that allows for the non-Gaussian turbulence typical of flow within a plant canopy. The effect of non-Gaussian turbulence was examined by formulating a non-Gaussian u, w joint probability density function (PDF) as the sum of two Gaussian joint-PDFs. The resultant PDF reproduced the desired means, variances, skewnesses, and kurtoses, and the correct covariance. In prediction of the location of maximum concentration downwind of a line source in homogeneous, slightly non-Gaussian turbulence, it proved advantageous to incorporate skewness and kurtosis. However, in the case of inhomogeneous, highly non-Gaussian turbulence, the addition of skewness and kurtosis in the model resulted in substantially worse agreement with measurements than the results of the model using Gaussian PDFs. This may be due to inaccuracy in our PDF formulation. Dispersion predictions from the model with Gaussian PDFs were generally not statistically different from measurements. These results indicate that a two-dimensional Gaussian trajectory-simulation approach is adequate to predict mean concentrations and fluxes resulting from sources within plant canopies.
Dispersion from an elevated source has been studied by means of a laboratory model of the convective planetary boundary layer. Results are presented in terms of a continuous point source located within a thermally convecting field and in the presence of a simulated uniform mean wind. Quantities measured in this study are nondimensionalized through the use of free-convection similarity scaling. From a source height of , where h is the height of the convectively mixed layer, the average plume concentration maximum descends to ground level at a downstream distance , and remains there for a comparable distance before being carried high up into the mixed layer. (The convective velocity scale divided by the mean wind U serves as a dimensionless stability parameter.) It is shown that a Gaussian plume formulation cannot adequately describe this evolving vertical concentration distribution. However, the Gaussian formulation provides an adequate estimate of the vertically-integrated cross-wind concentration distribution. The ground-level concentration field in the X-Y plane indicates that the mean plume first reaches ground level at and attains its maximum concentration near . Power-law formulations for the Gaussian diffusion parameters are made for small downstream distances.
Dispersion from a non-buoyant source of height 0.49 times the mixed-layer depth has been studied by means of a laboratory model of the convective planetary boundary layer. Results are presented in terms of a continuous point source within a thermally convective field and in the presence of a simulated uniform mean wind. Quantities are non-dimensionalized through the use of free-convection similarity scaling. The plume concentration maximum is found to descend to ground level at a downstream distance , just twice the distance found earlier for a source of half this height, and with a magnitude of (h is the height of the convectively mixed layer, is the mixed-layer convective velocity scale, S is the source strength and is the mean wind). Farther downstream the maximum is carried upward while broadening and weakening. Mappings of the dimensionless concentration are presented, along with lateral and vertical spreading rates.
When a probability density function (pdf) is to be formed on the basis of incomplete information, the “maximum missing information” (mmi) pdf (Jaynes, Phys. Rev.106, 620–630, 1957) is theoretically preferable. We compare the performance of Lagrangian stochastic (LS) models of vertical dispersion in the convective boundary layer, satisfying Thomson's (J. Fluid Mech.180, 529–556, 1987) well-mixed condition, that derive from the often-used bi-Gaussian pdf (eg. Weil, J. atmos. Sci.47, 501–515, 1990) and from the mmi pdf. The bi-Gaussian based LS model, which we tailor to reproduce velocity moments to fourth order, is less complex than the corresponding mmi based model, and gives similar (good) predictions, which are arguably slightly superior (as regards agreement with convection tank data) to those stemming from the original bi-Gaussian based model (Luhar and Britter, Atmospheric Environment23, 1911–1924, 1989), wherein knowledge of the kurtosis was forsaken.
Recently, Thomson and Montgomery (1994, Atmospheric Environment28, 1981–1987) stated the correct method of treating the reflection of particle velocity at the boundaries in Lagrangian particle diffusion models for non-Gaussian turbulence. Unfortunately, this method does not have an analytical solution. Two different approximated analytical solutions are proposed and compared. It is concluded that both of them satisfy the well-mixed condition and do not appreciably depart from the correct solution. The one consuming less time is proposed.
Lagrangian stochastic dispersion models make use of the probability density function (PDF) of the Eulerian vertical turbulent velocities. For convective conditions, the PDF is often assumed to have a bi-Gaussian form. Using new laboratory measurements of velocity PDFs in the convective boundary layer (CBL), we propose a new closure for constructing this bi-Gaussian PDF and compare results with three other closure schemes in current use. Of the three existing closures, two utilize the second and third moments of the vertical velocity as inputs, while the third one also incorporates the fourth moment. The new closure is defined with the desirable property that it collapses to a simple Gaussian in the limit of zero skewness. The value of an adjustable parameter in this closure scheme is selected using laboratory data for the third and fourth velocity moments. We determine the parameters in the PDF expression obtained using the four closures, and compare them with those derived by fitting velocity PDF data from the convection tank experiments. Significant differences are found between the values of the PDF parameters from the various closures and the water tank data. The performance of the closure schemes is compared by using a Lagrangian stochastic model to compute ground-level crosswind-integrated concentrations from particles released at four source heights. It is shown that the differences between the concentration estimates obtained using various closures increase as the source height increases. Using, as the benchmark, the dispersion results calculated from the Lagrangian stochastic model incorporating the laboratory velocity data without any closure, we recommend our new closure scheme. The results highlight the importance of turbulence observations in the CBL for accurate dispersion modelling.