Statistical Variability of Dispersion in the Convective Boundary Layer: Ensembles of Simulations and Observations

A Lagrangian particle dispersion model (LPDM) driven by velocity fields from large-eddy simulations (LESs) is used to determine the mean and variability of plume dispersion in a highly convective planetary boundary layer (PBL). The total velocity of a “particle” is divided into resolved and unresolved or random (subfilter scale, SFS) velocities with the resolved component obtained from the LES and the SFS velocity from a Lagrangian stochastic model. This LPDM-LES model is used to obtain an ensemble of dispersion realizations for calculating the mean, root-mean-square (r.m.s.) deviation, and fluctuating fields of dispersion quantities. An ensemble of 30 realizations is generated for each of three source heights: surface, near-surface, and elevated. We compare the LPDM calculations with convection tank experiments and field observations to assess the realism of the results. The overall conclusion is that the LPDM-LES model produces a realistic range of dispersion realizations and statistical variability (i.e., r.m.s. deviations) that match observations in this highly convective PBL, while also matching the ensemble-mean properties. This is true for the plume height or trajectory, vertical dispersion, and the surface values of the crosswind-integrated concentration (CWIC), and their dependence on downstream distance. One exception is the crosswind dispersion for an elevated source, which is underestimated by the model. Other analyses that highlight important LPDM results include: (1) the plume meander and CWIC fluctuation intensity at the surface, (2) the applicability of a similarity theory for plume height from a surface source to only the very strong updraft plumes—not the mean height, and (3) the appropriate variation with distance of the mean surface CWIC and the lower bound of the CWIC realizations for a surface source.     

The vertical structure of concentration fluctuation statistics in plumes dispersing in the atmospheric surface layer

This paper describes a study of the vertical structure of concentration fluctuations in a neutrally buoyant plume from an elevated point source in slightly convective to moderately stable meteorological conditions at ranges of between 12.5 and 100 m for a range of source heights between 1 and 5 m. Observations were made of concentration fluctuations in a dispersing plume using a vertical array of sixteen very fast-response photoionization detectors placed at heights between 0.5 and 16 m. Vertical profiles of a number of concentration statistics were extracted, namely, mean concentration, fluctuation intensity, intermittency factor, peak-to-mean concentration ratio, mean dissipation rate of concentration variance, and various concentration time and length scales of dominant motions in the plume (e.g., integral macro-scale, in-plume mid-scale and Taylor micro-scale). The profiles revealed a similarity to corresponding crosswind profiles for a fully elevated plume, but showed greater and greater departure from the latter shapes once the plume had grown in the vertical so that its lower dege began to interact progressively more strongly with the ground. The evolution of the concentration probability density function at a fixed range, but with decreasing height from the ground, is similar to that obtained at a fixed height but with increasing distance from the source. Concentration power spectra obtained at different heights all had an extensive inertial-convective subrange spanning at least two decades in frequency, but spectra measured near the ground had a greater proportion of the total concentration variance in the lower frequencies (energetic subrange), with a correspondingly smaller proportion in the higher frequencies (inertial-convective subrange). It is believed that these effects result from the increased mean shear near the surface, and blocking by the surface. The effect of enhanced shear-induced molecular diffusion on concentration fluctuations is examined.     

Statistical characteristics of concentration fluctuations in dispersing plumes in the atmospheric surface layer

Measurements have been made of concentration fluctuations in a dispersing plume from an elevated point source in the atmospheric surface layer using a recently developed fast-response photoionization detector. This detector, which has a frequency response (–6 dB point) of about 100 Hz, is shown to be capable of resolving the fluctuation variance contributed by the energetic subrange and most of the inertial-convective subrange, with a reduction in the fluctuation variance due to instrument smoothing of the finest scales present in the plume of at most 4%.Concentration time series have been analyzed to obtain the statistical characteristics of both the amplitude and temporal structure of the dispersing plume. We present alongwind and crosswind concentration fluctuation profiles of statistics of amplitude structure such as total and conditional fluctuation intensity, skewness and kurtosis, and of temporal structure such as intermittency factor, burst frequency, and mean burst persistence time. Comparisons of empirical concentration probability distributions with a number of model distributions show that our near-neutral data are best represented by the lognormal distribution at shorter ranges, where both plume meandering and fine-scale in-plume mixing are equally important (turbulent-convective regime), and by the gamma distribution at longer ranges, where internal structure or spottiness is becoming dominant (turbulent-diffusive regime). The gamma distribution provides the best model of the concentration pdf over all downwind fetches for data measured under stable stratification. A physical model is developed to explain the mechanism-induced probabilistic schemes in the alongwind development of a dispersing plume, that lead to the observed probability distributions of concentration. Probability distributions of concentration burst length and burst return period have been extracted and are shown to be modelled well with a powerlaw distribution. Power spectra of concentration fluctuations are presented. These spectra exhibit a significant inertial-convective subrange, with the frequency at the spectral peak decreasing with increasing downwind fetch. The Kolmogorov constant for the inertial-convective subrange has been determined from the measured spectra to be 0.17±0.03.     

A Comparison Of The Detailed Structure In Dispersing Tracer Plumes Measured In Grid-Generated Turbulence With A Meandering Plume Model Incorporating Internal Fluctuations

A meandering plume model that explicitly incorporatesinternal fluctuations has been developed and used to model the evolutionof concentration fluctuations in point-source plumes in grid turbulenceobtained from a detailed water-channel simulation. This fluctuating plumemodel includes three physical parameters: the mean plume spread in fixedcoordinates, which represents the outer plume length scale; the meaninstantaneous plume spread in coordinates attached to the instantaneousplume centroid, which represents the inner plume length scale; and, theconcentration fluctuation intensity in the meandering reference frame,which represents the in-plume fluctuation scale. These parameters arespecified in terms of a set of coupled dynamical equations that modeltheir development with downstream distance from the source. Explicitexpressions for the concentration moments of arbitrary integral orderand the concentration probability density function have been obtainedfrom the fluctuating plume model. Detailed comparisons of model predictionsagainst water-channel measurements for the first four concentrationmoments and the concentration probability distributions generally showvery good overall quantitative agreement. Exact quantitative conditions,expressed in terms of the physical parameters of the fluctuating plumemodel, have been derived for the emergence of off-centreline peaks inthe concentration variance profile. These quantitative conditions havebeen illustrated in terms of a diagram of states of the dispersing plume,and the qualitatively different regimes of plume concentration variancebehaviour on this state diagram have been identified and characterized.     

Comparison of Wind-tunnel and Water-channel Simulations of Plume Dispersion through a Large Array of Obstacles with a Scaled Field Experiment

We report on measurements of the near-field dispersion of contaminant plumes in a large array of building-like obstacles at three scales; namely, at full-scale in a field experiment, at 1:50 scale in a wind-tunnel simulation, and at 1:205 scale in a water-channel simulation. Plume concentration statistics extracted from the physical modelling in the wind-tunnel and water-channel simulations are compared to those obtained from a field experiment. The modification of the detailed structure of the plume as it interacts with the obstacles is investigated. To this purpose, measurements of the evolution of the mean concentration, concentration fluctuation intensity, concentration probability density function, and integral time scale of concentration fluctuations in the array plume obtained from the field experiment and the scaled wind-tunnel and water-channel experiments are reported and compared, as well as measurements of upwind and within-array velocity spectra. Generally, the wind-tunnel and water-channel results on the modification of the detailed plume structure by the obstacles were qualitatively similar to those observed in the field experiments. However, with the appropriate scaling, the water-channel simulations were able to reproduce quantitatively the results of the full-scale field experiments better than the wind-tunnel simulations.     

Wind-Tunnel Experiments for Gas Dispersion in an Atmospheric Boundary Layer with Large-Scale Turbulent Motion

Large-scale turbulent motions enhancing horizontal gas spread in an atmospheric boundary layer are simulated in a wind-tunnel experiment. The large-scale turbulent motions can be generated using an active grid installed at the front of the test section in the wind tunnel, when appropriate parameters for the angular deflection and the rotation speed are chosen. The power spectra of vertical velocity fluctuations are unchanged with and without the active grid because they are strongly affected by the surface. The power spectra of both streamwise and lateral velocity fluctuations with the active grid increase in the low frequency region, and are closer to the empirical relations inferred from field observations. The large-scale turbulent motions do not affect the Reynolds shear stress, but change the balance of the processes involved. The relative contributions of ejections to sweeps are suppressed by large-scale turbulent motions, indicating that the motions behave as sweep events. The lateral gas spread is enhanced by the lateral large-scale turbulent motions generated by the active grid. The large-scale motions, however, do not affect the vertical velocity fluctuations near the surface, resulting in their having a minimal effect on the vertical gas spread. The peak concentration normalized using the root-mean-squared value of concentration fluctuation is remarkably constant over most regions of the plume irrespective of the operation of the active grid.     

Predicting plume meandering and averaging time effects on mean and fluctuating concentrations in atmospheric dispersion simulated in a water channel

Plume meandering and averaging time effects were measured directly using a high spatial resolution, high frequency, linescan laser-induced fluorescence (LIF) technique for measuring scalar concentrations in a plume dispersing in a water channel. Post-processing of the collected data removed time dependent background dye levels and corrected for attenuation across the laser beam to produce accurate measurements over long sample times in both a rough surface boundary-layer shear flow and shear free grid-generated turbulent flow. The data were used to verify the applicability of a meandering plume model for predicting the properties of mean and fluctuating concentrations. The centroid position of the crosswind concentration profile was found to have a Gaussian probability density function and the instantaneous plume spread about the centroid fluctuated log-normally. A modified travel-time power law model for averaging time adjustment was developed and compared to the widely used, but much less accurate, 0.2 power-law model.     

Incorporation of internal fluctuations in a meandering plume model of concentration fluctuations

A meandering plume model that explicitly incorporates the effects of small-scale structure in the instantaneous plume has been formulated. The model requires the specification of two physically based input parameters; namely, the meander ratio,M, which is dependent on the ratio of the meandering plume dispersion to the instantaneous relative plume dispersion and, a relative in-plume fluctuation measure,k, that is related inversely to the fluctuation intensity in relative coordinates. Simple analytical expressions for crosswind profiles of the higher moments (including the important shape parameters such as fluctuation intensity, skewness, and kurtosis) and for the concentration pdf have been derived from the model. The model has been tested against some field data sets, indicating that it can reproduce many key aspects of the observed behavior of concentration fluctuations, particularly with respect to modeling the change in shape of the concentration pdf in the crosswind direction.List of Symbols C Mean concentration in absolute coordinates - C _r Mean concentration in relative coordinates - C₀ Centerline mean concentration in absolute coordinates - C _r,0 Centerline mean concentration in relative coordinates - f Probability density function of concentration in absolute coordinates - f _c Probability density function of plume centroid position - f _r Probability density function of concentration in relative coordinates - i Absolute concentration fluctuation intensity (standard deviation to mean ratio) - i _r Relative concentration fluctuation intensity (standard deviation to mean ratio) - k Relative in-plume fluctuation measure:k=1/i _r ² - K Concentration fluctuation kurtosis - M Meander ratio of meandering plume variance to relative plume variance - S Concentration fluctuation skewness - x Downwind distance from source - y Crosswind distance from mean-plume centerline - z Vertical distance above ground - Instantaneous (random) concentration - Crosswind dispersion ofnth concentration moment about zero - _ny Mean-plume crosswind (absolute) dispersion - _y Plume centroid (meandering) dispersion in crosswind direction - _y,c Instantaneous plume crosswind (relative) dispersion - Normalized mean concentration in absolute coordinates:C/C ₀ - Particular value taken on by instantaneous concentration,      

Convective plumes in the atmospheric boundary layer as observed with an acoustic Doppler sodar

The vertical velocity field and the convective plumes in the atmospheric boundary layer have been observed during morning hours with the acoustic Doppler sounder of the C.R.P.E. A method for plume determination using acoustic soundings in the well-mixed layer is presented. Using Telford's 1970 and Manton's 1975 models, a comparison is made between the predictions of the models and the plume properties as observed by the Doppler sodar. The mean plume velocity is found to be parabolic. It is shown, restricting Monin and Obukhov similarity to conditions inside plumes and using only vertical velocity within plumes, that the observed convective plumes carry nearly sixty percent of the sensible heat flux at the top of the surface layer.     

Simulating Concentration Fluctuation Time Series with Intermittent Zero Periods and Level Dependent Derivatives

Intermittent concentration fluctuation time series were produced with a stochastic numerical model derived from the assumption that the concentration fluctuations at a fixed receptor in a point-source plume can be modelled as a first order Markov process. The time derivative of concentration was assumed to be level-dependent and constrained by a stationary lognormal probability density function. The input parameters required to reconstruct the intermittent time series are the intermittency factor , the conditional fluctuation intensity i _p ² , and the time scale T _c . A clipped lognormal probability distribution was used to describe the fluctuation time series. Good agreement between the stochastic simulation and experimental water-channel data was demonstrated by comparing the time derivative of concentration and the upcrossing rates over a range of intermittency factors = 0.7 to 0.01 and fluctuation intensities i _w ² = 2.2 to 7.5.     

Resolved Versus Parametrized Boundary-Layer Plumes. Part II: Continuous Formulations of Mixing Rates for Mass-Flux Schemes

The conditional sampling of coherent structures in large-eddy simulations of the convective boundary layer (Couvreux et al. Boundary-layer Meteorol 134:441–458, 2010) is used to propose and evaluate formulations of fractional entrainment and detrainment rates for mass-flux schemes. The proposed formulations are physically-based and continuous from the surface to the top of clouds. Entrainment is related to the updraft vertical velocity divergence, while detrainment depends on the thermal vertical velocity, on buoyancy and on the moisture contrast between the mean plume and its environment. The proposed formulations are first directly evaluated in simulations of shallow clouds. They are then tested in single-column simulations with the thermal plume model, a mass-flux representation of boundary-layer thermals.     

Dispersion of Heavy Particles Emitted from Area Sources in the Unstable Atmospheric Boundary Layer

Reliable predictions of the daytime dispersal of heavy particles in the unstable atmospheric boundary layer are important in a variety of disciplines. For many applications, particles disperse from area sources near the ground, and corresponding theoretical solutions are desired to reveal insight into the physical processes. Here, theoretical solutions recently developed for neutral conditions are modified to include the effects of atmospheric instability. The Obukhov length L _O and convection velocity w _? are introduced to characterize the patterns of particle dispersion, in additional to friction velocity u _? and settling velocity w _s used in the neutral case. The major effects of atmospheric instability are accounted for by modifying the vertical velocity variance profile and considering the ratio of velocity scales w _?/u _?. Theoretical predictions including the mean concentration profile, plume height, and horizontal transport above the source, and ground deposition flux downwind from the source agree well with large-eddy simulation results while the particle plume is within the atmospheric surface layer. The deposition curve is characterized by a power-law decay whose exponent depends on u _?, w _s, and w _?. A second steeper power-law develops once the plume extends into the mixed layer. This effect is enhanced with increasing atmospheric instability, implying that particles disperse farther from the source.     

A Stochastic Time Series Model for Threshold Crossing Statistics of Concentration Fluctuations in non-Intermittent Plumes

A numerical stochastic model is developed for the upcrossing rate across a specified threshold concentration. The model assumes that the concentration time series at a given spatial point within a dispersing plume can be approximated as a first-order Markovian process designed to be consistent with a given time-invariant concentration probability density function (pdf). The model requires only the specification of a concentration pdf with a given mean and variance and a concentration fluctuation integral time scale. Predicted upcrossing rates are compared with atmospheric plume concentration data obtained from a point source near the ground. For this data set, a log-normal pdf is found to give better estimates of the threshold crossing rate than a gamma pdf.     

The Influence Of Vertical Wind Direction Shear On Dispersion In The Convective Boundary Layer, And Its Incorporation In Coastal Fumigation Models

The mean concentration distributionwithin a plume released from a point source in the atmosphericboundary layer can be greatly influenced by the systematic turningof wind with height (i.e. vertical wind direction shear). Such aninfluence includes a deflection of the plume centroid, with anassociated shearing of the vertical plume cross-section, and anenhancement of dispersion, in the horizontal plane. Wind directionshear is normally not accounted for in coastal fumigation models,although dispersion observations with shear acting as acontrolling parameter are not uncommon. A three-dimensionalLagrangian stochastic model is used to investigate the influenceof uniform wind direction shear on the diffusion of a point-sourceplume within the horizontally homogeneous convective boundarylayer, with the source located at the top of the boundary layer.Parameterisations are developed for the plume deflection andenhanced dispersion due to shear within the framework of aprobability density function (PDF) approach, and compared with theLagrangian model results. These parameterisations are thenincorporated into two applied coastal fumigation models: a PDFmodel, and a commonly used model that assumes uniform andinstantaneous mixing in the vertical direction. The PDF modelrepresents the vertical mixing process more realistically. A moreefficient version of the PDF model, which assumes a well-mixedconcentration distribution in the vertical at large times, isapplied to simulate sulfur dioxide data from the Kwinana CoastalFumigation Study. A comparison between the model results and thedata show that the model performs much better when the wind-sheareffects are included.     

The transport and dispersion of airborne contaminants in boundary layers over the ocean and an isolated island cape

A series of sixteen atmospheric tracer experiments using sulfur hexafluoride (SF₆), chemical smoke and meteorological balloons was conducted to explore the transport of airborne contaminants in the boundary layer over the ocean surface and in the separating boundary layer over an isolated island cape. The immediate objective of the tests was to determine the impact of local pollutant sources on a background air quality sampling program conducted in the South Pacific from elevated towers on Tutuila Island, American Samoa. In addition to satisfying this objective, the tests are of interest in that they illustrate the local behavior of pollutants in a complex natural atmospheric flow.Offshore tracer tests indicated that the crosswind dispersion of pollutants over the ocean surface can be approximately modeled using the simple Gaussian plume model. The observed crosswind dispersion of the tracer corresponded to that expected under neutrally stable atmospheric conditions, consistent with the near equilibration of the ocean surface and air temperature in the South Pacific. Local, or near-field, tests indicated that tracer released into the wake downwind of the leading edge of the cape mixed rapidly to a height of about 8 m above the surface (i.e., 30–40% of the cape height). Due to decoupling between the boundary layer over the cape and the freestream flow, however, very little of the tracer was observed above this height. This suggests that the impact of local pollutant sources (i.e., on the cape) would be minimized if the proposed sampling towers were elevated significantly above an 8 m altitude (e.g., twice that height).     

Similarity Scaling Of Surface-Released Smoke Plumes

Concentration fluctuation data from surface-layer released smokeplumes have been investigated with the purpose of finding suitable scaling parametersfor the corresponding two-particle, relative diffusion process.Dispersion properties have been measured at downwind ranges between 0.1 and 1 km from a continuous, neutrally buoyant ground level source. A combinationof SF₆ and chemical smoke (aerosols) was used as tracer. Instantaneous crosswind concentration profiles of high temporal (up to 55 Hz) and spatialresolution (down to 0.375 m) were obtained from aerosol-backscatter Lidar detectionin combination with simultaneous gas chromatograph (SF₆) reference measurements. The database includes detailed crosswind concentration fluctuation measurements. Each experiment, typically of 1/2-hour duration, containsplume mean and variance concentration profiles, intermittency profiles andexceedence and duration statistics. The diffusion experiments were accompanied by detailed in-situ micrometeorological mean and turbulence measurements. In this paper, a new distance-neighbour function for surface-released smoke plumes is proposed, accompanied by experimental evidence in its support. The new distance-neighbour function is found to scale with the surface-layer friction velocity,and not with the inertial subrange dissipation rate, over the range of distance-neighbour separations considered.     

Atmospheric chemistry of hydrogen fluoride

Although a large volume of monitoring and computer simulation data exist for global coverage of HF, study of HF in the troposphere is still limited to industry whose primary interest is the safety and risk assessment of HF release because it is a toxic gas. There is very limited information on atmospheric chemistry, emission sources, and the behavior of HF in the environment. We provide a comprehensive review on the atmospheric chemistry of HF, modeling the reactions and transport of HF in the atmosphere, the removal processes in the vertical layer immediately adjacent to the surface (up to approximately 500 m) and recommend research needed to improve our understanding of atmospheric chemistry of HF in the troposphere. The atmospheric chemistry, emissions, and surface boundary layer transport of hydrogen fluoride (HF) are summarized. Although HF is known to be chemically reactive and highly soluble, both factors affect transport and removal in the atmosphere, the chemistry can be ignored when the HF concentration is at a sufficiently low level (e.g., 10 ppmv). At a low concentration, the capability for HF to react in the atmosphere is diminished and therefore the species can be mathematically treated as inert during the transport. At a sufficiently high concentration of HF (e.g., kg/s release rate and thousands of ppm), however, HF can go through a series of rigorous chemical reactions including polymerization, depolymerization, and reaction with water to form molecular complex. As such, the HF species cannot be considered as inert because the reactions could intimately influence the plume’s thermodynamic properties affecting the changes in plume temperature and density. The atmospheric residence time of HF was found to be less than four (4) days, and deposition (i.e., atmosphere to surface transport) is the dominant mechanism that controls the removal of HF and its oligomers from the atmosphere. The literature data on HF dry deposition velocity was relatively high compared to many commonly found atmospheric species such as ozone, sulfur dioxide, nitrogen oxides, etc. The global average of wet deposition velocity of HF was found to be zero based on one literature source. Uptake of HF by rain drops is limited by the acidity of the rain drops, and atmospheric particulate matter contributes negligibly to HF uptake. Finally, given that the reactivity of HF at a high release rate and elevated mole concentration cannot be ignored, it is important to incorporate the reaction chemistry in the near-field dispersion close to the proximity of the release source, and to incorporate the deposition mechanism in the far-field dispersion away from the release source. In other words, a hybrid computational scheme may be needed to address transport and atmospheric chemistry of HF in a range of applications. The model uncertainty will be limited by the precision of boundary layer parameterization and ability to accurately model the atmospheric turbulence.     

Effect of Roughness on Surface Boundary Conditions for Large-Eddy Simulation

An important parameterization in large-eddy simulations (LESs) of high- Reynolds-number boundary layers, such as the atmospheric boundary layer, is the specification of the surface boundary condition. Typical boundary conditions compute the fluctuating surface shear stress as a function of the resolved (filtered) velocity at the lowest grid points based on similarity theory. However, these approaches are questionable because they use instantaneous (filtered) variables, while similarity theory is only valid for mean quantities. Three of these formulations are implemented in simulations of a neutral atmospheric boundary layer with different aerodynamic surface roughness. Our results show unrealistic influence of surface roughness on the mean profile, variance and spectra of the resolved velocity near the ground, in contradiction of similarity theory. In addition to similarity-based surface boundary conditions, a recent model developed from an a priori experimental study is tested and it is shown to yield more realistic independence of the results to changes in surface roughness. The optimum value of the model parameter found in our simulations matches well the value reported in the a priori wind-tunnel study.     

等熵面和湿等熵面倾斜发展的诊断分析

利用等压坐标系中的热力学方程和水汽方程推导出可以诊断分析等熵面（等位温面）和湿等熵面（等相当位温面） 倾斜变化的倾角方程。等熵面倾角的局地变化由倾角平流输送项、风速切变项和非绝热加热项共同决定,而影响湿等熵面倾角局地变化的强迫项除倾角平流输送项、风速切变项和非绝热加热项之外,还包括垂直热量通量切变项。NCEP/NCAR实时分析资料的分析结果表明,大气斜压性、相对垂直涡度与等熵面和湿等熵面的倾角密切相关,它们的正高值区互相重叠;垂直风速切变项,特别是垂直速度的经向切变项是影响等熵面倾斜发展的主要强迫项,而纬向和经向风速的垂直切变项对湿等熵面倾角演变的贡献最大。