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Comparison among empirical probability density functions of the vertical velocity in the surface layer based on higher order correlations
Abstract and Figures
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.
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... In the vertical direction the PDF is assumed to be non-Gaussian, to deal with non-uniform turbulent conditions and/ or convection. Two different approaches can be adopted in order to calculate the Fokker-Planck equation: a bi-Gaussian one [17] and a Gram-Charlier one [4], truncated to the third or fourth order. The diffusion term b ij ðx; u; tÞ is obtained from the Lagrangian structure function and is related to the Kolmogorov constant, C 0 , for the inertial subrange. ...
... The release started at 18:30 local time and the source emission was at 1.8 m height within the obstacles, categorized as a 'wide alley' location, between containers K8 and L8 (Fig. 1). We considered the observation fields averaged over a reference period between 300 s and 500 s after the start of the observational period, as suggested in the experiment's documentation by Yee and Biltoft [4,35] to handle the intrinsic unsteadiness of field meteorological data. The 200-s quasi-steady period within the 15-min release experiment was selected because it was greater than the plume travel time but at the same time it ensured the least variation for the mean wind speed and direction. ...
Three different modelling techniques to simulate the pollutant dispersion in the atmosphere at the microscale and in presence of obstacles are evaluated and compared. The Eulerian and Lagrangian approaches are discussed, using RAMS6.0 and MicroSpray models respectively. Both prognostic and diagnostic modelling systems are considered for the meteorology as input to the Lagrangian model, their differences and performances are investigated. An experiment from the Mock Urban Setting Test field campaign observed dataset, measured within an idealized urban roughness, is used as reference for the comparison. A case in neutral conditions was chosen among the available ones. The predicted mean flow, turbulence and concentration fields are analysed on the basis of the observed data. The performances of the different modelling approaches are compared and their specific characteristics are addressed. Given the same flow and turbulence input fields, the quality of the Lagrangian particle model is found to be overall comparable to the full-Eulerian approach. The diagnostic approach for the meteorology shows a worse agreement with observations than the prognostic approach but still providing, in a much shorter simulation time, fields that are suitable and reliable for driving the dispersion model.
... 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 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.
Describing the effects of wind meandering motions on the dispersion of scalars is a challenging task, since this type of flow represents a physical state characterized by multiple scales. In this study, a Lagrangian stochastic diffusion model is derived to describe scalar transport during the horizontal wind meandering phenomenon that occurs within a planetary boundary layer. The model is derived from the linearization of the Langevin equation, and it employs a heuristic functional form that represents the autocorrelation function of meandering motion. The new solutions, which describe the longitudinal and lateral wind components, were used to simulate tracer experiments that were performed in low-wind speed conditions. The results of the comparison indicate that the new model can effectively reproduce the observed concentrations of the contaminants, and therefore, it can satisfactorily describe enhanced dispersion effects due to the presence of meandering.
The dispersion of airborne pollutant in the planetary boundary layer (PBL) is governed, schematically, by the transport, operated by the mean wind, and by the atmospheric turbulence due to the presence of eddies having different spatial and temporal scales.
It is known (Thomson, 1987) that Ito’s type stochastic models (LS) satisfy the well-mixed condition and hence are physically consistent. An Eulerian probability density function (PDF) of the turbulent velocities, as close as possible to the actual atmospheric PDF, must be prescribed in order to specify the model. Unfortunately these models have a unique solution in one-dimension only (Sawford and Guest, 1988). For this reason the present study will focus on one-dimensional diffusion simulation.
The AIRCITY project, partly funded by the European Union, is now successfully achieved. It aimed at developing a 4D innovative numerical simulation tool dedicated to the dispersion of traffic-induced air pollution at local scale on the whole urban area of PARIS. AIRCITY modeling system is based on PMSS (Parallel-Micro-SWIFT-SPRAY) software, which has been developed by ARIA Technologies in close collaboration with CEA and MOKILI. PMSS is a simplified CFD solution which is an alternative to micro-scale simulations usually carried out with full-CFD. Yet, AIRCITY challenge was to model the flow and pollutant dispersion with a 3 m resolution over the whole city of Paris covering a 14 km × 11,5 km domain. Thus, the choice was to run a mass-consistent diagnostic flow model (SWIFT) associated with a Lagrangian Particle Dispersion Model (SPRAY) on a massively parallel architecture. With a 3 m resolution on this huge domain, parallelization was applied to the computation of both the flow (by domain splitting) and the Lagrangian dispersion (management of particles is split over several processors). This MPI parallelization is more complex but gives a large flexibility to optimize the number of CPU, the available RAM and the CPU time. So, it makes possible to process arbitrarily large domains (only limited by the memory of the available nodes). As CEA operates the largest computing center in Europe, with parallel machines ranging from a few hundred to several thousand cores, the modeling system was tested on huge parallel clusters. More usual and affordable computers with a few tens of cores were also utilized during the project by ARIA Technologies and by AIRPARIF, the Regional Air Quality Management Board of Paris region, whose role was also to build the end-users requirements. These computations were performed on a simulation domain restricted to the hypercenter of Paris with dimensions around 2 km × 2 km (at the same resolution of 3 m).
The focus was on the improvements needed to adapt simulation codes initially designed for emergency response to urban air quality applications:
• Coupling with the MM5 / CHIMERE operational photochemical model at AIRPARIF (as the forecast background),
• Turbulence generated by traffic / coupling with traffic model,
• Inclusion of chemical reactions / Interaction with background substances (especially NO / NO2).
Finally, in-depth validation of the modeling system was undertaken using both the routine air quality measurements in Paris (at four stations influenced by the road traffic) and a field experiment specially arranged for the project, with LIDARs provided by LEOSPHERE Inc. Comparison of PMSS and measurements gave excellent results concerning NO / NO2 and PM10 hourly concentrations for a monthly period of time while the LIDAR campaign results were also promising. In the paper, more details are given regarding the modeling system principles and developments and its validation.
Perspectives of the project will also be discussed as AIRCITY system. The TRL must now be elevated from a demonstration to a robust and systematically validated modeling tool that could be used to predict routinely the air quality in Paris and in other large cities around the world.
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.
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.
The results of numerical simulations of tracer dispersion in an urban stable boundary layer are presented. Both Gaussian approximation and fourth order closure are considered and a Gram-Charlier probability density function is used in our Lagrangian stochastic model. Different parameterisations for the boundary-layer height and different values of kurtosis are tested. The model is based on the generalised Langevin equation, whose coefficients are solution of the Fokker-Planck equation and plume rise is taken into account. The model accuracy is assessed by means of a model evaluation based on the predicted and observed crosswind integrated concentrations, maximum on the arc and standard deviation of the crosswind concentration distribution on the arc.
The development of physically sound low-order models (LOMs) of convective flow is discussed. LOMs are constructed in the form of coupled three-mode systems known in mechanics as Volterra gyrostats. This structure ensures energy conservation, a property of fundamental importance sometimes missing in atmospheric LOMs. In addition, the gyrostatic form makes it possible to reduce an LOM to one with the minimal number of modes that still describes the effect of interest. The approach is illustrated with two important LOMs. One is the modification of the Howard–Krishnamurti model of convection with shear that restores conservation of both energy and total vorticity to the original model. The other is the Charney–DeVore model of a barotropic atmosphere over topography. In each case, the ''minimal'' LOM is extracted that possesses conservation properties and demonstrates the effect of interest: tilting of convection cells and vacillation between high-index and low-index regimes, respectively.
Understanding the mass balance of the many chemical constituents either emitted to the atmosphere from anthropogenic or biogenic sources or formed within the atmosphere belongs to the most challenging problems in atmospheric sciences. Depending of the size of the volume for which a system with open boundaries is defined, different processes come into play determining the local distribution and temporal variation of the concentrations within the system.
The present paper provides a summary of a literature survey on
statistical properties of wall boundary layer flows. Existing knowledge
on the subject and the authors' own investigations are described that
were initially carried out to yield mean and fluctuating flow properties
in turbulent wall boundary layers at high Reynolds numbers. From these
investigations instantaneous velocity information resulted which was
processed to yield local velocity information in form of mean velocity
and of probability density distributions of the turbulent velocity
fluctuations. It is shown that the latter obey a general analytical
distribution law. Hence, it is possible to describe probability density
distributions in turbulent boundary layer flows in an analytical form.
In the sublayer as well as in the wake-region of the boundary layer, a
simple form of the general distribution, known as the hyperbolic
function, describes the probability density distributions of the
velocity fluctuations very well. The latter curve contains four
parameters whereas the general distribution requires seven parameters
for describing the entire probability density distribution of turbulent
velocity fluctuations.