Footprints in Homogeneously and Heterogeneously Driven Boundary Layers Derived from a Lagrangian Stochastic Particle Model Embedded into Large-Eddy Simulation

A Lagrangian stochastic (LS) model, which is embedded into a parallelised large-eddy simulation (LES) model, is used for dispersion and footprint evaluations. For the first time an online coupling between LES and LS models is applied. The new model reproduces concentration patterns, which were obtained in prior studies, provided that subgrid-scale turbulence is included in the LS model. Comparisons with prior studies show that the model evaluates footprints successfully. Streamwise dispersion leads to footprint maxima that are situated less far upstream than previously reported. Negative flux footprints are detected in the convective boundary layer (CBL). The wide range of applicability of the model is shown by applying it under neutral and stable stratification. It is pointed out that the turning of the wind direction with height leads to a considerable dependency of source areas on height. First results of an application to a heterogeneously heated CBL are presented, which emphasize that footprints are severely affected by the inhomogeneity.     

ON THE PDF MODELS FOR ATMOSPHERIC DIFFUSION IN BOUNDARY LAYER

In this paper, taking its turbulent exchange coefficient as a function of the Lagrangian timescale and standard variance of the turbulence in atmosphere, the atmospheric dispersion PDFmodels are obtained on the basis of atmospheric diffusion K-theory. In the model the statistics ofwind speed are directly used as its parameters instead of classic dispersion parameters. The bi-Gaussian PDF is derived in convective boundary layer (CBL), from the statistics of verticalvelocity in both of the downdraft and updraft regions that are investigated theoretically in the otherpart of this paper. Giving the driven parameters of the CBL (including the convective velocity scalew* and the mixing depth h_i) and the time-averaged wind speed at release level, the PDF model isable to simulate the distribution of concentration released at any levels in the CBL. The PDF'ssimulations are fairly consistent with the measurements in CONDORS experiment or the resultsbrought out by some numerical simulations.     

A Large-Eddy Simulation and Lagrangian Stochastic Study of Heavy Particle Dispersion in the Convective Boundary Layer

Large-eddy simulation and Lagrangian stochastic dispersion models were used to study heavy particle dispersion in the convective boundary layer (CBL). The effects of various geostrophic winds, particle diameters, and subgrid-scale (SGS) turbulence were investigated. Results showed an obvious depression in the vertical dispersion of heavy particles in the CBL and major vertical stratification in the distribution of particle concentrations, relative to the passive dispersion. Stronger geostrophic winds tended to increase the dispersion of heavy particles in the lower CBL. The SGS turbulence, particularly near the surface, markedly influenced the dispersion of heavy particles in the CBL. For reference, simulations using passive particles were also conducted; these simulation results agreed well with results from previous convective tank experiments and numerical simulations.     

Large-Eddy Simulation of air Pollution Dispersion in the Nocturnal Cloud-Topped Atmospheric Boundary Layer

Effects of stratocumulus clouds on the dispersion of contaminants are studied in the nocturnal atmospheric boundary layer. The study is based on a large-eddy simulation (LES) model with a bulk parametrization of clouds. Computations include Lagrangian calculations of atmospheric dispersion of a passive tracer released from point sources at various heights above the ground. The results obtained show that the vertical diffusion is non-Gaussian and depends on the location of a source in the boundary layer.     

Flux Footprints in the Convective Boundary Layer: Large-Eddy Simulation and Lagrangian Stochastic Modelling

We investigated the flux footprints of receptors at different heights in the convective boundary layer (CBL). The footprints were derived using a forward Lagrangian stochastic (LS) method coupled with the turbulent fields from a large-eddy simulation model. Crosswind-integrated flux footprints shown as a function of upstream distances and sensor heights in the CBL were derived and compared using two LS particle simulation methods: an instantaneous area release and a crosswind linear continuous release. We found that for almost all sensor heights in the CBL, a major positive flux footprint zone was located close to the sensor upstream, while a weak negative footprint zone was located further upstream, with the transition band in non-dimensional upwind distances −X between approximately 1.5 and 2.0. Two-dimensional (2D) flux footprints for a point sensor were also simulated. For a sensor height of 0.158 z _i, where z _i is the CBL depth, we found that a major positive flux footprint zone followed a weak negative zone in the upstream direction. Two even weaker positive zones were also present on either side of the footprint axis, where the latter was rotated slightly from the geostrophic wind direction. Using CBL scaling, the 2D footprint result was normalized to show the source areas and was applied to real parameters obtained using aircraft-based measurements. With a mean wind speed in the CBL of U = 5.1 m s⁻¹, convective velocity of w _* = 1.37 m s⁻¹, CBL depth of z _i = 1,000 m, and flight track height of 159 m above the surface, the total flux footprint contribution zone was estimated to range from about 0.1 to 4.5 km upstream, in the case where the wind was perpendicular to the flight track. When the wind was parallel to the flight track, the total footprint contribution zone covered approximately 0.5 km on one side and 0.8 km on the other side of the flight track.     

A Three-Dimensional Backward Lagrangian Footprint Model For A Wide Range Of Boundary-Layer Stratifications

We present a three-dimensional Lagrangian footprint model with the ability to predict the area of influence (footprint) of a measurement within a wide range of boundary-layer stratifications and receptor heights. The model approach uses stochastic backward trajectories of particles and satisfies the well-mixed condition in inhomogeneous turbulence for continuous transitions from stable to convective stratification. We introduce a spin-up procedure of the model and a statistical treatment of particle touchdowns which leads to a significant reduction of CPU time compared to conventional footprint modelling approaches. A comparison with other footprint models (of the analytical and Lagrangian type) suggests that the present backward Lagrangian model provides valid footprint predictions under any stratification and, moreover, for applications that reach across different similarity scaling domains (e.g., surface layer to mixed layer, for use in connection with aircraft measurements or with observations on high towers).     

Simulating Dispersion in the Evening-Transition Boundary Layer

We investigate dispersion in the evening-transition boundary layer using large-eddy simulation (LES). In the LES, a particle model traces pollutant paths using a combination of the resolved flow velocities and a random displacement model to represent subgrid-scale motions. The LES is forced with both a sudden switch-off of the surface heat flux and also a more gradual observed evolution. The LES shows ‘lofting’ of plumes from near-surface releases in the pre-transition convective boundary layer; it also shows the subsequent ‘trapping’ of releases in the post-transition near-surface stable boundary layer and residual layer above. Given the paucity of observations for pollution dispersion in evening transitions, the LES proves a useful reference. We then use the LES to test and improve a one-dimensional Lagrangian Stochastic Model (LSM) such as is often used in practical dispersion studies. The LSM used here includes both time-varying and skewed turbulence statistics. It is forced with the vertical velocity variance, skewness and dissipation from the LES for particle releases at various heights and times in the evening transition. The LSM plume spreads are significantly larger than those from the LES in the post-transition stable boundary-layer trapping regime. The forcing from the LES was thus insufficient to constrain the plume evolution, and inclusion of the significant stratification effects was required. In the so-called modified LSM, a correction to the vertical velocity variance was included to represent the effect of stable stratification and the consequent presence of wave-like motions. The modified LSM shows improved trapping of particles in the post-transition stable boundary layer.     

THE EFFECTS OF HIGHER EULERIAN VELOCITY MOMENTS ON THE MEAN CONCENTRATION DISTRIBUTION

In this paper, we present a well-mixed Lagrangian stochasticmodel for vertical dispersion, that can accommodate a Eulerianprobability density function of vertical velocity derived from themaximum missing information (or maximum entropy) principle. Withthis model, we study the effects of skewness (S) and kurtosis (K) ofvertical velocity on the spacial distribution of the mean concentrationdue to sources in the convective boundary layer. Model calculationsshow that the maximum ground-level concentration increases withincreasing S and decreasing K, but the downstream distance to thelocation of the maximum ground-level concentration is ratherinsensitive to S and K. Some earlier predictions of vertical dispersionfor short travel time are examined.     

Determination of the Atmospheric Boundary Layer Height from Radiosonde and Lidar Backscatter

The height of the atmospheric boundary layer is derived with the help of two different measuring systems and methods. From radiosoundings the boundary layer height is determined by the parcel method and by temperature and humidity gradients. From lidar backscatter measurements a combination of the averaging variance method and the high-resolution gradient method is used to determine boundary layer heights. In this paper lidar-derived boundary layer heights on a 10 min basis are presented. Datasets from four experiments – two over land and two over the sea – are used to compare boundary layer heights from both methods. Only the daytime boundary layer is investigated because the height of the nighttime stable boundary layer is below the range of the lidar. In many situations the boundary layer heights from both systems coincide within ±200 m. This corresponds to the standard deviation of lidar-derived 10-min values within a 1-h interval and is due to the time and space variability of the boundary layer height. Deviations appear for certain situations and depend on which radiosonde method is applied. The parcel method fails over land surfaces in the afternoon when the boundary layer stabilizes and over the ocean when the boundary layer is slightly stable. An automatic radiosonde gradient method sometimes fails when multiple layers are present, e.g. a residual layer above the growing convective boundary layer. The lidar method has the advantage of continuous tracing and thus avoids confusion with elevated layers. On the other hand, it mostly fails in situations with boundary layer clouds     

Modelling Mean and Turbulence Fields in the Dry Convective Boundary Layer with the Eddy-Diffusivity/Mass-Flux Approach

The treatment of turbulence closure in atmospheric models is examined in the context of the dry convective boundary layer (CBL) and the eddy-diffusivity/mass-flux (EDMF) approach. The EDMF approach is implemented into a model called TAPM to use a coupled two-equation prognostic turbulence closure and the mass-flux approach to represent turbulence in the CBL. This work also extends the range of turbulence variables that can be derived from the mass-flux component of the model and uses these along with their values from the prognostic scheme to provide total turbulence fields that can be used to compare to data and/or to feed into other components of TAPM, including those needed to drive Eulerian and Lagrangian air pollution dispersion modules. Model results are presented for the afternoon of a simulated summer day and are compared to both laboratory and field observations in a mixed-layer scaled framework. The results show that the EDMF approach works well within TAPM and can provide good predictions of mean and turbulence fields, including in the upper levels of the CBL. The EDMF approach has several attractive features, including the potential to be one approach to unify the treatment of turbulence and dry and moist convection in atmospheric models.     

A Lagrangian Decorrelation Time Scale in the Convective Boundary Layer

A new method for deriving the Lagrangian decorrelation time scales for inhomogeneous turbulence is described. The expression for the time scales here derived for the convective boundary layer is compared to those estimated by Hanna during the Phoenix experiment. Then the values of C₀, the Lagrangian velocity structure function constant, and of B_i, the Lagrangian velocity spectrum constant, were evaluated from the Eulerian velocity spectra and from the Lagrangian time scales derived, under unstable conditions, from Taylor's statistical diffusion theory. The numerical coefficient of the lateral and vertical Lagrangian spectra in the inertial subrange was found equal to 0.21, in good agreement with previous experimental estimates.     

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.     

An Advanced Puff Model Based On A Mixed Eulerian/Lagrangian Approach For Turbulent Dispersion In The Convective Boundary Layer

An advanced model aimed at describing the problem of dispersion in theconvective boundary layer is proposed. The pollutant particles are groupedin clusters and modelled as Gaussian puffs. The expansion of each puff ismodelled according to the concept of relative dispersion and expressed interms of the spectral properties of the energy containing eddies of the turbulent field. The centre of mass of each puff is moved along a stochastic trajectory, obtained using a Lagrangian stochastic model and filtering the velocity with a recursive Kalman filter. At any instant, a filtering procedure, depending both on travel time and on puff size, acts to select spectral components involved in the expansion and in the meandering of the puff. Such an approach requires only a moderate number of puff releases, so that the proposed model is faster to run than a standard Lagrangian model. On the other hand, unlike the traditional puff model, it allows us to simulate both expansion and meandering of the puff. Therefore, it is well suited to simulate dispersion when the turbulent structures are larger thanthe plume dimensions, as for example in convective conditions. Being based onspectral formulations in both Eulerian and Lagrangian parts, the model is consistent in all the turbulent parameterizations utilised. Comparisons with a standard Lagrangian particle model as well as with a classical convective experimental dataset show good performance of the proposed model.     

基于大涡模拟评估GRAPES模式对对流边界层的模拟性能

为检验GRAPES半拉格朗日动力框架在大涡尺度上的模拟性能,为未来发展千米及其以下高分辨尺度的数值模式奠定基础,并构造GRAPES大涡模式以检验和发展边界层湍流参数化提供科学工具。通过在GRAPES模式中加入Smagorinsky-Lilly小尺度湍涡参数化,并将模式分辨率提高至50 m,构建GRAPES大涡模式(GRAPES_LES),以便分析GRAPES模式在大涡尺度上的适用性。同时利用广泛应用的已有大涡模式UCLA_LES作为参考,通过对干对流边界层湍流的模拟分析及与UCLA_LES模拟结果的对比,得出如下主要结论:GRAPES半拉格朗日动力框架能够模拟出与已有的大涡模式相似的边界层湍流特征;同时,通过分析也证明GRAPES存在由于采用半拉格朗日平流计算而带来过度耗散的问题:当使用相同的滤波尺度(Smagorinsky 常数)时,GRAPES_LES模拟出的速度场更为平滑,小尺度湍流结构过于光滑,通过对湍流能量的能谱分析更清楚地表明了这一点。进一步,对不同的Smagorinsky常数(对应不同的滤波尺度)进行了敏感性试验,表明可以通过改变滤波尺度,有效地缓解半拉格朗日框架隐含的耗散问题,得到更接近UCLA_LES所模拟的湍流特征。     

一个对流边界层中的随机扩散模式

通过对对流边界层(CBL)湍流结构的分析,首次提出用两种不同尺度的湍流模拟CBL中的铅直扩散.在此基础上发展了一个随机扩散模式,并用它模拟了典型对流条件下两种高架连续点源的扩散.与Willis水槽模拟和Lamb等人数值模拟以及CONDORS计划外场试验的结果的比较表明,本模式能成功地模拟CBL中的横向积分浓度.与其它数值模式相比,还具有输入参数少、计算量极小和更加简单实用的优点.     

AN EVALUATION OF SEVERAL TURBULENCE SCHEMES FOR THE PREDICTION OF MEAN AND TURBULENT FIELDS IN COMPLEX TERRAIN

A prognostic three-dimensional mesoscale model has been developed andused in one- and two-dimensional modes to evaluate ten local turbulenceclosure schemes. The schemes ranged from first-order to the two-equationprognostic schemes. Predictions by the models were compared for aone-dimensional convective boundary layer using mixed layer scaling andmeasurements to interpret the results. Two-dimensional simulations were alsoperformed for a sea-breeze flow and for flow over a hill. The results showedthat for all of the models considered, minor differences were produced in themean meteorological fields and in the vertical scalar fluxes, but majordifferences were apparent in the velocity variances and dissipation rate.Predicted tracer concentrations were very sensitive to the turbulence modelformulation for dispersion from a point source in the convective boundarylayer, particularly for the prediction of maximum concentrations. Predictedtracer concentrations from a surface volume source for the two-dimensionalsimulations were similar for all models, although the degree of mixing in themorning growth period produced some differences. Generally, good results forthe mean meteorological fields can be obtained with first-order schemes, evenif they underpredict the magnitude of turbulence in the convective boundarylayer, and reasonable tracer concentrations can also be obtained with thesemodels provided near-source effects are not important. The two-equationprognostic models performed best for the prediction of turbulence in theconvective boundary layer.     

A Lagrangian Stochastic Model for Sea-Spray Evaporation in the Atmospheric Marine Boundary Layer

The dispersion of heavy particles subjected to a turbulent forcing is often simulated with Lagrangian stochastic models. Although these models have been employed successfully over land, the implementation of traditional LS models in the marine boundary layer is significantly more challenging. We present an adaptation of traditional Lagrangian stochastic models to the atmospheric marine boundary layer with a particular focus on the representation of the scalar turbulence for temperature and humidity. In this new model, the atmosphere can be stratified and the bottom boundary is represented by a realistic wavy surface that moves and deforms. Hence, the correlation function for the turbulent flow following a particle is extended to the inhomogenous, anisotropic case. The results reproduce behaviour for scalar Lagrangian turbulence in a stratified airflow that departs only slightly from the expected behaviour in isotropic turbulence. When solving for the surface temperature and the radius of evaporating heavy water droplets in the airflow, the modelled turbulent forcing on the particle also behaves remarkably well. We anticipate that this model will prove especially useful in the context of sea-spray dispersion and its associated sensible heat, latent heat, and gas fluxes between spray droplets and the atmosphere.     

A Homogeneous Langevin Equation Model, Part ii: Simulation of Dispersion in the Convective Boundary Layer

We present a Lagrangian stochastic model of vertical dispersion in the convective boundary layer (CBL). This model is based on a generalized Langevin equation that uses the simplifying assumption that the skewed vertical velocity probability distribution is spatially homogeneous. This approach has been shown to account for two key properties of CBL turbulence associated with large-scale coherent turbulent structures: skewed vertical velocity distributions and long velocity correlation time. A 'linear-skewed' form of the generalized Langevin equation is used, which has a linear (in velocity) deterministic acceleration and a skewed random acceleration. 'Reflection' boundary conditions for selecting a new velocity for a particle that encounters a boundary were investigated, including alternatives to the standard assumption that the magnitudes of the particle incident and reflected velocities are positively correlated. Model simulations were tested using cases for which exact, analytic statistical properties of particle velocity and position are known, i.e., well-mixed spatial and velocity distributions. Simulations of laboratory experiments of CBL dispersion show that (1) the homogeneous linear-skewed Langevin equation model (as well as an alternative 'nonlinear-Gaussian' Langevin equation model) can simulate the important aspects of dispersion in the CBL, and (2) a negatively-correlated-speed reflection boundary condition simulates the observed dispersion of material near the surface in the CBL significantly better than alternative reflection boundary conditions. The homogeneous linear-skewed Langevin equation model has the advantage that it is computationally more efficient than the homogeneous nonlinear-Gaussian Langevin equation model, and considerably more efficient than inhomogeneous Langevin equation models.     

Scaling of the Vertical Spreading of a Plume of a Passive Tracer in a Rough-Wall Neutral Boundary Layer

The influence of surface roughness on the dispersion of a passive scalar in a rough wall turbulent boundary layer has been studied using wind-tunnel experiments. The surface roughness was varied using different sizes of roughness elements, and different spacings between the elements. Vertical profiles of average concentration were measured at different distances downwind of the source, and the vertical spread of the plume was computed by fitting a double Gaussian profile to the data. An estimate of the integral length scale is derived from the turbulence characteristics of the boundary layer and is then used to scale the measured values of plume spread. This scaling reduces the variability in the data, confirming the validity of the model for the Lagrangian integral time scale, but does not remove it entirely. The scaled plume spreading shows significant differences from predictions of theoretical models both in the near and in the far field. In the region immediately downwind of the source this is due to the influence of the wake of the injector for which we have developed a simple model. In the far field we explain that the differences are mainly due to the absence of large-scale motions. Finally, further downwind of the source the scaled values of plume spread fall into two distinct groups. It is suggested that the difference between the two groups may be related to the lack of dynamical similarity between the boundary-layer flows for varying surface roughness or to biased estimates of the plume spread.