Testing kernel density reconstruction for Lagrangian photochemical modelling

In recent years, a number of pioneering works have shown as Lagrangian models can be of great interest when dealing with photochemistry, provided that special care is given in the reconstruction of chemicals concentration in the atmosphere. Density reconstruction can be performed through the so-called “box counting” method: an Eulerian grid for chemistry is introduced and density is computed counting particles in each box. In this way one of the main advantages of the Lagrangian approach, the grid independence, is lost. In this paper, a new approach to Lagrangian photochemical modelling is investigated and the chemical module of the Photochemical Lagrangian Particle Model (PLPM) is described and fully tested for stability, reliability and computational weight. Photochemical reactions are treated in PLPM by means of the complex chemical mechanism SAPRC90 and four density reconstruction methods have been developed, based on the kernel density estimator approach, in order to obtain grid-free accurate concentrations.     

A fluctuating plume model for concentration fluctuations in a plant canopy

A one-particle Lagrangian model for continuous releases in the non-Gaussian inhomogeneous turbulence of a canopy layer is derived based on the fluctuating plume model of Franzese [2003. Lagrangian stochastic modeling of a fluctuating plume in the convective boundary layer. Atmos. Environ. 37, 1691–1701.]. The model equations are filtered by a time-dependent low-pass filter applied to the turbulent kinetic energy in order to obtain a fluctuating plume model able to simulate the vertical meandering of the cloud centroid through non-stationary Lagrangian equations. The model satisfies the well-mixed condition. The relative dispersion of particles and the concentration fluctuation statistics of a passive tracer inside a modeled vegetal canopy are studied. The probability density function of the concentration relative to the plume centroid is parameterized and the mean and variance fields of concentration are simulated and compared with wind-tunnel data and numerical simulations. A skewed, reflected probability density function for the vertical position of the plume centroid is considered.     

A concentration correction scheme for Lagrangian particle model and its application in street canyon air dispersion modelling

Pollutant dispersion in street canyons with various configurations was simulated by discharging a large number of particles into the computation domain after developing a time-dependent wind field. Trajectory of the released particles was predicted using a Lagrangian particle model developed in an earlier study. A concentration correction scheme, based on the concept of “visibility”, was adopted for the Lagrangian particle model to correct the calculated pollutant concentration field in street canyons. The corrected concentrations compared favourably with those from wind tunnel experiments and a linear relationship between the computed concentrations and wind tunnel data were found. The developed model was then applied to four simulations to test for the suitability of the correction scheme and to study pollutant distribution in street canyons with different configurations. For those cases with obstacles presence in the computation domain, the correction scheme gives more reasonable results compared with the one without using it. Different flow regimes are observed in the street canyons, which depend on building configurations. A counter-clockwise rotating vortex may appear in a two-building case with wind flow from left to right, causing lower pollutant concentration at the leeward side of upstream building and higher concentration at the windward side of downstream building. On the other hand, a stable clockwise rotating vortex is formed in the street canyon with multiple identical buildings, resulting in poor natural ventilation in the street canyon. Moreover, particles emitted in the downstream canyon formed by buildings with large height-to-width ratios will be transported to upstream canyons.     

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

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

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

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

A simple and fast model to compute concentration moments in a convective boundary layer

Recently, a modified meandering plume model for concentration fluctuations in a convective boundary layer has been formulated (Atmos. Environ. 34 (2000) 3599). This model is based on a hybrid Eulerian–Lagrangian approach and it accounts for the skewed and inhomogeneous turbulence characteristics of the convective flow. Using the same hypotheses, but eliminating the need for Lagrangian particle model, we propose a generalised approach, that only requires the knowledge of mean concentration field. The proposed model is independent from the method used to obtain the mean concentration field. The evaluation of the concentration fluctuation field needs a computational time of only few seconds on a standard PC. Therefore, the model is suitable for practical applications.     

Validation of the lagrangian particle dispersion model FLEXPART against large-scale tracer experiment data

A comprehensive validation of FLEXPART, a recently developed Lagrangian particle dispersion model based on meteorological data from the European Centre for Medium-Range Weather Forecasts, is described in this paper. Measurement data from three large-scale tracer experiments, the Cross-Appalachian Tracer Experiment (CAPTEX), the Across North America Tracer Experiment (ANATEX) and the European Tracer Experiment (ETEX) are used for this purpose. The evaluation is based entirely on comparisons of model results and measurements paired in space and time. It is found that some of the statistical parameters often used for model validation are extremely sensitive to small measurement errors and should not be used in future studies. 40 cases of tracer dispersion are studied, allowing a validation of the model performance under a variety of different meteorological conditions. The model usually performs very well under undisturbed meteorological conditions, but it is less skilful in the presence of fronts. The two ETEX cases reveal the full range of the model’s skill, with the first one being among the best cases studied, and the second one being, by far, the worst. The model performance in terms of the statistical parameters used stays rather constant with time over the periods (up to 117 h) studied here. It is shown that the method used to estimate the concentrations at the receptor locations has a significant effect on the evaluation results. The vertical wind component sometimes has a large influence on the model results, but on the average only a slight improvement over simulations which neglect the vertical wind can be demonstrated. Subgrid variability of mixing heights is important and must be accounted for.     

Numerical simulation of smoke plumes from large oil fires

A large eddy simulation (LES) model of smoke plumes generated by large outdoor pool fires is presented. The plume is described in terms of steady-state convective transport by a uniform ambient wind of heated gases and particulate matter introduced into a stably stratified atmosphere by a continuously burning fire. The Navier-Stokes equations in the Boussinesq approximation are solved numerically with a constant eddy viscosity representing dissipation on length scales below the resolution limits of the calculation. The effective Reynolds number is high enough to permit direct simulation of the large-scale mixing over two to three orders of magnitude in length scale. Particulate matter, or any non-reacting combustion ;product, is represented by Lagrangian particles which are advected by the fire-induced flow field. Background atmospheric motion is described in terms of the angular fluctuation of the prevailing wind, and represented by random perturbations to the mean particle paths. Results of the model are compared with two sets of field experiments.     

Mathematical Modeling of Photochemical Smog Using the PICK Method

A new method for solving the turbulent atmospheric diffusion equation has been developed based on Lagrangian mass points, or particles moving through an Eulerian grid. The method is one of a family of Particle-/n-Cell techniques but is a unique extension to incorporate the effects of turbulent diffusion based on K-theory; thus the acronym PICK.

In the three-dimensional computer-aided model, NEXUS (Numerical EXamination of Urban Smog), this method has been applied to simulation of carbon monoxide (CO) in Los Angeles. For CO the NEXUS simulation was within 20% of observed day-averaged concentrations at 12 stations and the hour-averages were also in good agreement. This model was extended to include the effects of photochemical smog in Los Angeles. The results of the photochemical simulation were also qualitatively correct due to rapid NO to NO₂ conversion in the simulation.     

旋风除尘器流场及浓度场实验与模拟

在研究旋风除尘器内气固两相的运动状况及分离机理方面,计算机模拟替代部分实验的方法能够优化设计旋风除尘器结构参数,提高其对微细颗粒的捕集效率,减少运行压力损失。本研究采用RSM模型和随机轨道模型对旋风除尘器内流场及浓度场进行模拟及实验。研究表明,旋风除尘器压力损失模拟结果与实验结果吻合较好,对于大于5μm的颗粒其捕集效率模拟结果与实验结果基本吻合;旋风除尘器外壁的颗粒浓度呈螺旋带状分布;如将排气管管径减少至原直径0.8倍,可使其对2μm颗粒捕集效率提高6.6%,但压力损失提高36.5%;颗粒的凝并作用有利于提高旋风除尘器微细颗粒的捕集效率。     

Erratum to “Continuous four-dimensional source attribution for the Berlin area during two days in July 1994. Part I: The new Euler–Lagrange-model system LaMM5”: [Atmospheric Environment 35 (32) (2001) 5497]

The multiple nested three-dimensional (3D) mesoscale Eulerian grid point model MM5 was directly coupled with a Lagrangian particle trajectory model in order to perform a 4D source attribution for the area of Berlin based on the import probability density (IPD) distribution of the according receptor box. Within the resulting model system LaMM5 introduced here, the IPD distributions are not based on backward trajectories, which lack the recognition of the turbulent environment, but on the forward integration of a huge amount (order of million per day) of particle releases according to an emission scenario which is approximately continuous in space and time. Hence, the receptor import yields an accordingly continuous IPD distribution. Much attention has been paid on spatial and temporal resolution at the interface between both model parts (online-coupling) and the interface itself has been extended by the turbulent quantities resulting from the higher-order turbulence closure of the Eulerian model part. LaMM5 is applied on an episode with high photochemical activity across Berlin at two consecutive days (25 and 26 July 1994) with varying meteorological conditions leading to an accordingly different source attribution. The main results are:

• •The decay of the Berlin IPD with increasing source-receptor distance and time appears in an exponential manner if only sources out of a constant level (z=25 m) are regarded.
• •Heterogeneous wind fields in time and space enhance the contributions (emissions) of nearby sources to the total import of the receptor in contrast to stationary wind fields which increase the scope of the IPD distribution in upstream direction.

There are further results from several additional sensitivity studies presented in a companion paper B (Part II).     

Continuous four-dimensional source attribution for the Berlin area during two days in July 1994. Part I: the new Euler–Lagrange-model system LaMM5

The multiple nested three-dimensional mesoscale Eulerian grid point model MM5 was directly coupled with a Lagrangian particle trajectory model in order to perform a four-dimensional source attribution for the area of Berlin based on the import probability density (IPD) distribution of the according receptor box. Within the resulting model system LaMM5 introduced here, the IPD distributions are not based on backward trajectories, which lack the recognition of the turbulent environment, but on the forward integration of a huge amount (order of Million per day) of particle releases according to an emission scenario which is approximately continuous in space and time. Hence the receptor import record yields an accordingly continuous IPD distribution. Much attention has been paid on spatial and temporal resolution at the interface between both model parts (online-coupling) and the interface itself has been extended by the turbulent quantities resulting from the higher-order turbulence closure of the Eulerian model part. LaMM5 is applied on an episode with high photochemical activity across Berlin at two consecutive days (25th and 26th of July in 1994) with varying meteorological conditions leading to an accordingly different source attribution. The main results are:

• •The decay of the Berlin IPD with increasing source-receptor distance and time appears in an exponential manner if only sources out of a constant level (z=25 m) are regarded.
• •Heterogeneous wind fields in time and space enhance the contributions (emissions) of nearby sources to the total import of the receptor in contrast to stationary wind fields which increase the scope of the IPD distribution in upstream direction.

There are further results from several additional sensitivity studies presented in a companion paper B (Part II).     

Relation between particle mass and number for submicrometer airborne particles

The relationship between particle mass and the number of ambient air particles for the submicrometer size range was examined using a tapered element oscillating microbalance (TEOM) to determine the mass concentration, and a scan-ning mobility particle sizer (SMPS) to determine the volume concentration and total number of particles. The techniques were validated through their application to the estimation of submicrometer particle density for two laboratory generated aerosols of known bulk density (sodium chloride and di-2-ethylhexyl-sebacate). Further evaluation was done with the submicrometer fraction of laboratory generated environmental tobacco smoke (ETS), for which the estimated density of 1.18±0.06 g/cm³ was very close to the previously reported literature value of 1.12 g cm³. Finally, ambient air particles were examined and an estimate of the average submicrometer particle densities for these aerosols was found to vary from 1.2 to 1.8 g cm^-3 depending on the time of day. This high variation in the density of the ambient air submicrometer particles, makes it hard to estimate the mass concentration from the SMPS number concentration with better than 60% uncertainty, based on an assumed density value.     

Calculation of concentration of aerosol particles around a slot sampler

A mathematical model and numerical procedure are proposed for investigation of aspiration efficiency and the particle concentration field around a slot sampler in a moving gas. A potential-flow model for the carrier gas and a Lagrangian method for calculation of particle trajectories and concentration are employed. The particle concentration patterns around the slot and at the sampler inlet are studied. The dependence of the aspiration efficiency on the ratio of the wind and sampling velocities is analyzed. It is shown that the local aspiration efficiency calculated on the symmetry axis of the slot gives satisfactory approximation for the integral aspiration efficiency.     

A comparison of operational Lagrangian particle and adaptive puff models for plume dispersion forecasting

Transport and dispersion of pollutants in the lower atmosphere are predicted by using both a Lagrangian particle model (LPM) and an adaptive puff model (APM2) coupled to the same mesoscale meteorological prediction model PMETEO. LPM and APM2 apply the same numerical solutions for plume rise; but, for advection and plume growth, LPM uses a stochastic surrogate to the pollutant conservation equation, and APM2 applies interpolated winds and standard deviations from the meteorological model, using a step-wise Gaussian approach. The results of both models in forecasting the SO₂ ground level concentration (glc) around the 1400 MWe coal-fired As Pontes Power Plant are compared under unstable conditions. In addition, meteorological and SO₂ glc numerical results are compared to field measurements provided by 17 fully automated SO₂ glc remote stations, nine meteorological towers and one Remtech PA-3 SODAR, from a meteorological and air quality monitoring network located 30 km around the power plant.     

Evaluation of the effect of meteorological data resolution on Lagrangian particle dispersion simulations using the ETEX experiment

This paper presents results from a series of numerical experiments designed to evaluate operational long-range dispersion model simulations, and to investigate the effect of different temporal and spatial resolution of meteorological data from numerical weather prediction models on these simulations. Results of Lagrangian particle dispersion simulations of the first tracer release of the European Tracer Experiment (ETEX) are presented and compared with measured tracer concentrations. The use of analyzed data of higher resolution from the European Center for Medium-Range Weather Forecasts (ECMWF) model produced significantly better agreement between the concentrations predicted with the dispersion model and the ETEX measurements than the use of lower resolution Navy Operational Global Atmospheric Prediction System (NOGAPS) forecast data. Numerical experiments were performed in which the ECMWF model data with lower vertical resolution (4 instead of 7 levels below 500 mb), lower temporal resolution (12 h instead of 6 h intervals), and lower horizontal resolution (2.5° instead of 0.5°) were used. Degrading the horizontal or temporal resolution of the ECMWF data resulted in decreased accuracy of the dispersion simulations. These results indicate that flow features resolved by the numerical weather prediction model data at approximately 45 km horizontal grid spacing and 6 h time intervals, but not resolved at 225 km spacing and 12 h intervals, made an important contribution to the long-range dispersion.     

Calculation of the Charging Rate of Fine Particles by Unipolar Ions

Theories of particle charging based on boundary value solutions to the diffysional equation may not be applicable to electrostatic precipitators where the ion density is rarely more than an order of magnitude greafer than the particle concentration. A new charging equation, based on kinetic theory, is presented which evaluates the charging rate in terms of the probability of collisions between the flust particles and ions. In the presence of an external electric field, the surface of the particle is divided into three charging regions, and separate charging rates are calculated for each region. The total charging rate is the sum of these three individual rates. For large particles and high electric fields, this theory predicts essentially the same charging rate as the classical field charging equation of Rohmann and Pauthenier. For low electric fields, the theory reduces to White’s diffusional charging equation. Agreement is within 25% of Hewitt’s experimental results over the entire range of variables where data are available. For practical charging times, agreement is within 15%.