On the Formulation of Lagrangian Stochastic Models of Scalar Dispersion Within Plant Canopies

Lagrangian stochastic models, quadratic in velocity and satisfying the well-mixed condition for two-dimensional Gaussian turbulence, are used to make predictions of scalar dispersion within a model plant canopy. The non-uniqueness associated with satisfaction of the well-mixed condition is shown to be non-trivial (i.e. different models produce different predictions for scalar dispersion). The best agreement between measured and predicted mean concentrations of scalars is shown to be obtained with a small sub-class of optimal models. This sub-class of optimal models includes Thomson's model (J. Fluid Mech. 180, 529–556, 1987), the simplest model that satisfies the well-mixed condition for Gaussian turbulence, but does not include two other models identified recently as being in optimal agreement with the measured spread of tracers in a neutral boundary layer. It is therefore demonstrated that such models are not universal, i.e. applicable to a wide range of flows without readjustment of model parameters. Predictions for scalar dispersion in the model plant canopy are also obtained using the model of Flesch and Wilson (Boundary-Layer Meteorol. 61, 349–374, 1992). It is shown that, when used with a Gaussian velocity distribution or a maximum-missing-information velocity distribution, which accounts for the measured skewness and kurtosis of velocity statistics, the agreement between predictions obtained using the model of Flesch and Wilson and measurements is as good as that obtained using Thomson's model.     

The Turbulent Lagrangian Time Scale in Forest Canopies Constrained by Fluxes,Concentrations and Source Distributions

One-dimensional Lagrangian dispersion models, frequently used to relate in-canopy source/sink distributions of energy, water and trace gases to vertical concentration profiles, require estimates of the standard deviation of the vertical wind speed, which can be measured, and the Lagrangian time scale, T _L , which cannot. In this work we use non-linear parameter estimation to determine the vertical profile of the Lagrangian time scale that simultaneously optimises agreement between modelled and measured vertical profiles of temperature, water vapour and carbon dioxide concentrations within a 40-m tall temperate Eucalyptus forest in south-eastern Australia. Modelled temperature and concentration profiles are generated using Lagrangian dispersion theory combined with source/sink distributions of sensible heat, water vapour and CO₂. These distributions are derived from a multilayer Soil-Vegetation-Atmospheric-Transfer model subject to multiple constraints: (1) daytime eddy flux measurements of sensible heat, latent heat, and CO₂ above the canopy, (2) in-canopy lidar measurements of leaf area density distribution, and (3) chamber measurements of CO₂ ground fluxes. The resulting estimate of Lagrangian time scale within the canopy under near-neutral conditions is about 1.7 times higher than previous estimates and decreases towards zero at the ground. It represents an advance over previous estimates of T _L , which are largely unconstrained by measurements.     

Simulation and Regionalization of Daily Global Solar Radiation: A Case Study in Quebec,Canada

Global solar radiation (GSR) is essential for agricultural and plant growth modelling, air and water heating analyses, and solar electric power systems. However, GSR gauging stations are scarce compared with stations for monitoring common meteorological variables such as air temperature and relative humidity. In this study, one power function, three linear regression, and three non-linear models based on an artificial neural network (ANN) are developed to extend short records of daily GSR for meteorological stations where predictors (i.e., temperature and/or relative humidity) are available. The seven models are then applied to 19 meteorological stations located across the province of Quebec (Canada). On average, the root-mean-square errors (RMSEs) for ANN-based models are 0.33–0.54?MJ?m^?2?d^?1 smaller than those for the power function and linear regression models for the same input variables, indicating that the non-linear ANN-based models are more efficient in simulating daily GSR. Regionalization potential of the seven models is also evaluated for ungauged stations where predictors are available. The power function and the three linear regression models are tested by interpolating spatially correlated at-site coefficients using universal kriging or by applying a leave-one-out calibration procedure for spatially uncorrelated at-site coefficients. Regional ANN-based models are also developed by training the model based on the leave-one-out procedure. The RMSEs for regional ANN models are 0.08–0.46?MJ?m^?2?d^?1 smaller than for other models using the same input conditions. However, the regional ANN-based models are more sensitive to new station input values compared with the other models. Maps of interpolated coefficients and regional equations of the power function and the linear regression models are provided for direct application to the study area.     

Passive scalar diffusion from surface sources in the convective boundary layer

We examine vertical and horizontal diffusion of a passive scalar puff from a surface point source in a convective boundary layer (CBL). Numerical results are presented from a large-eddy simulation (LES) with embedded subgrid Lagrangian particle simulation (LPS). There is good agreement in most respects with previous laboratory and numerical studies. Analytical approximations for the concentration, horizontal flux and vertical flux are found to work reasonably well; they are based on the assumption that the concentration follows a Gaussian function in the horizontal and vertical, and that the dimensionless width and height scales of the puff follow simple functions of time. Fluxes and concentration gradients are related through a continuity relationship, without the need for an eddy diffusivity assumption. The instantaneous, point-source fields can be integrated for any source geometry. We compare predictions from the LES/LPS model for a sinusoidal surface flux with previous results from an LES with sinusoidal buoyancy flux and confirm that the buoyancy perturbations diffuse like a passive scalar. We also consider a continuous point source and derive footprint functions for vertical flux measurements above the surface layer.     

A 3-dimensional nonhydrostatic dispersion modeling system for modeling of atmospheric transport and diffusion over coastal complex terrain in the Hongkong-Shenzhen area

Summary A dispersion modeling system consisting of a three-dimensional PBL model NHECM (non-hydrostaticE- closure model) and SLPTDM (seven-level puff transport and diffusion model) is developed to simulate the transport and dispersion of pollutant over coastal complex terrain. As an application of the system, the transport and dispersion of SO₂ released from an elevated point source are simulated during typical sea-land breeze circulation in the Hongkong-Shenzhen area of China. The NHECM provides time-varying, three-dimensional distributions of wind and turbulence fields to the SLPTDM. The NHECM predictions compare well with observational data. Reflection of both the ground and the mixing layer top and penetration of the mixing layer top are improved in the SLPTDM. Results obtained from the system indicate that temporal variation and nonuniformity of airflow and turbulence obviously affect the concentration distributions, especially during the sea-land breeze transition period. A diurnal cycle of the GLC (ground-level concentration) is discussed. The results are compared with those estimated using a Gaussian model. The study's results illustrate the complexity of the dispersion patterns due to diurnal effects and mesoscale circulations, and demonstrate the potential of the mesoscale atmospheric dispersion modeling system for studies of air quality in complex terrain.With 8 Figures     

Urban Dispersion Modelling and Experiments in the Daytime and Nighttime Atmosphere

An analytical model of atmospheric dispersion in urban areas in both daytime and nighttime conditions is presented. The model is based on a Gaussian formulation where the horizontal and vertical diffusion coefficients are determined according to analytical theories. The model is validated with dispersion measurements from field experiments conducted in Oklahoma City, Salt Lake City, St. Louis and London, U.K. The theory is in good agreement with the data for both daytime and nighttime conditions. The data support the conclusion that the magnitude of the nighttime stratification in the urban atmosphere is weak; however, its effects on dispersion are not negligible. The predicted existence of two distinct dispersion regimes, in the near and in the far field, is also confirmed by the data. The good collapse of the data suggests that urban dispersion is governed by the characteristic length scales of atmospheric boundary-layer turbulence, rather than urban canopy length scales that are more likely to affect dispersion only in the vicinity of the source.     

Tracer Flux Balance at an Urban Canyon Intersection

Despite their importance for pollutant dispersion in urban areas, the special features of dispersion at street intersections are rarely taken into account by operational air quality models. Several previous studies have demonstrated the complex flow patterns that occur at street intersections, even with simple geometry. This study presents results from wind-tunnel experiments on a reduced scale model of a complex but realistic urban intersection, located in central London. Tracer concentration measurements were used to derive three-dimensional maps of the concentration field within the intersection. In combination with a previous study (Carpentieri et al., Boundary-Layer Meteorol 133:277–296, 2009) where the velocity field was measured in the same model, a methodology for the calculation of the mean tracer flux balance at the intersection was developed and applied. The calculation highlighted several limitations of current state-of-the-art canyon dispersion models, arising mainly from the complex geometry of the intersection. Despite its limitations, the proposed methodology could be further developed in order to derive, assess and implement street intersection dispersion models for complex urban areas.     

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.     

A study of vertical velocity distributions in the planetary boundary layer

Until recently, pollution dispersion models have made predictions on the basis that the pollutant concentration is Gaussian. Such is not the case for convective conditions where the observed vertical velocity distribution is skewed towards the updraught portion of the distribution. One recent dispersion model assumes that the observed distribution can be synthesized by superimposing two Gaussians of appropriate means, variances and amplitudes.In the current paper, two techniques for deriving the constituent distributions are investigated. The first technique is based on conditionally sampling the vertical velocity time series and partitioning the vertical velocity samples into two sets — one set recorded when the sensor was experiencing an updraught and the other when the sensor was experiencing a downdraught. The second method consists of fitting two Gaussian distributions to the observed data and adjusting these using an iterative procedure until a specified tolerance is achieved.Both techniques give similar results which compare favourably with results obtained by other researchers. Assumptions, as well as advantages and disadvantages of each technique are also discussed.     

Proper Orthogonal Decomposition of Mesoscale Vertical Velocity in the Convective Boundary Layer

The proper orthogonal decomposition technique is used to analyze wind-profiler observations from the surface to the top of the convective boundary layer. The mesoscale thermal structures are identified by decomposing the vertical velocity measurements into a sequence of characteristic modes with random coefficients. Results show that the first two dominant modes contribute over 85 % to the average kinetic energy. These most energetic modes also show mixed-layer similarity, which indicates that the non-local static instability plays a major role in determining the structure of the most energetic modes. Reconstruction of the vertical wind profiles by the first two dominant modes shows that they represent the most significant thermal structures. The probability distributions of the random coefficients related to these first two dominant modes are also analyzed and found to be Gaussian.     

Simulation of Time Series of Concentration Fluctuations in Atmospheric Dispersion Using a Correlation-distortion Technique

Short-duration fluctuations in the concentration of airborne substances can be important in a variety of atmospheric dispersion problems, especially when assessing the risks posed by harmful materials. This paper discusses a simulation technique for generating individual realisations of fluctuating concentration time series in dispersing plumes based on target probability distributions and spectral functions. The scheme uses a correlation-distortion approach to simulate these time series. Gaussian processes with modified spectral characteristics are generated and then transformed to yield non-Gaussian processes with the desired spectral characteristics. The simulation scheme is initially developed for a single receptor, and is then extended to model pairs of correlated time series at two receptors. In fact, the modelling technique can be generalised to an arbitrary number of receptors and this provides, in principal, an approach that is applicable to a wide class of similar problems (such as the modelling of instantaneous puff releases or the response of line-of-sight detection systems). The simulation technique is illustrated using observations made during recent field experiments, conducted both in the United Kingdom and in the U.S.A., investigating the short-range dispersion of a passive tracer.     

Using the OSPM Model on Pollutant Dispersion in an Urban Street Canyon

An observational campaign was conducted in the street canyon of Zhujiang Road in Nanjing city in 2007.Hourly mean concentrations of PM10 were measured at street and roof levels.The Operational Street Pollution Model(OSPM)street canyon dispersion model was used to calculate the street concentrations and the results were compared with the measurements.The results show that there is good agreement between measured and predicted concentrations.The correlation coecient R2 values(R2 is a measure of the correlation of the predicted and measured time series of concentrations)are 0.5319,0.8044,and 0.6630 for the scatter plots of PM10 corresponding to light wind speed conditions,higher wind speed conditions,and all wind speed conditions,respectively.PM10 concentrations tend to be smaller for the higher wind speed cases and decrease rapidly with increasing wind speed.The presentations of measured and modelled concentration dependence on wind direction show fairly good agreement.PM10 concentrations measured on the windward side are relatively smaller,compared with the corresponding results for the leeward side.This study demonstrates that it is possible to use the OSPM to model PM10 dispersion rules for an urban street canyon.     

ModellingNO conversion by using probability density functions

An expression for concentration fluctuations in a smoke plume is derived from airborne measurements ofNO _X. A linear relation between the standard deviation of the fluctuations around a Gaussian concentration profile and the average gradient in the concentrations is assumed. With this relation the probability density function of expectedNO ₂ concentrations at 3 km from a source ofNO _X is modelled under the assumption of photostatic equilibrium, and is compared with measurements. A parametrisation for the concentration fluctuations of std(C)= 26(+/–7)*dc/dr is proposed (r in metres). CalculatedNO ₂ distributions are in reasonable agreement with the measurements and the averageNO ₂ concentration appeared not to be affected by the concentration fluctuations in theNO _X concentration. The spatial resolution of all measurements was 40 m.     

Along-wind dispersion of puffs released in a built-up urban area

The SF₆ gas tracer observations for puffs released near the ground during the Joint Urban 2003 (JU2003) urban dispersion experiment in Oklahoma City have been analysed. The JU2003 observations, at distances of about 100–1,100 m from the source, show that, at small times, when the puff is still within the built-up downtown domain, the standard deviation of the concentration time series, σ_t, is influenced by the initial puff spread due to buildings near the source and by hold-up in the wakes of large buildings at the sampler locations. This effect is parameterised by assuming an initial σ_to of about 42 s, leading to a comprehensive similarity formula: σ_t = 42 + 0.1t. The second term, 0.1t, is consistent with an earlier similarity relation, σ_t = 0.1t, derived from puff observations in many experiments over rural terrain. The along-wind dispersion coefficient, σ_x, is assumed to equal σ_t u, in which u is the puff speed calculated as the distance from the source to the sampler, x, divided by the time after the release that the maximum concentration is observed at the sampler. σ_x can be expressed as σ_x = σ_xo + 0.14x, with the initial σ_xo of 45 m. This initial σ_xo agrees with the suggestion of an initial plume spread of about 40 m, made by McElroy and Pooler from analysis of the 1960s’ St. Louis urban dispersion experiment. The puff speeds, u, are initially only about 20% of the observed wind speed, averaged over about 80 street-level and rooftop anemometers in the city, but approach the mean observed wind speed as the puffs grow vertically. The scatter in the σ_t data is about ± a factor of two or three at any given travel time. The maximum σ_t is about 250 s, and the maximum duration of the puff over the sampler, Dt, sometimes called the retention time, is about 1,100 s or 18 min for these puffs and distances.     

Wind-tunnel Modelling of Dispersion from a Scalar Area Source in Urban-Like Roughness

A wind-tunnel study was conducted to investigate ventilation of scalars from urban-like geometries at neighbourhood scale by exploring two different geometries a uniform height roughness and a non-uniform height roughness, both with an equal plan and frontal density of λ _p = λ _f = 25%. In both configurations a sub-unit of the idealized urban surface was coated with a thin layer of naphthalene to represent area sources. The naphthalene sublimation method was used to measure directly total area-averaged transport of scalars out of the complex geometries. At the same time, naphthalene vapour concentrations controlled by the turbulent fluxes were detected using a fast Flame Ionisation Detection (FID) technique. This paper describes the novel use of a naphthalene coated surface as an area source in dispersion studies. Particular emphasis was also given to testing whether the concentration measurements were independent of Reynolds number. For low wind speeds, transfer from the naphthalene surface is determined by a combination of forced and natural convection. Compared with a propane point source release, a 25% higher free stream velocity was needed for the naphthalene area source to yield Reynolds-number-independent concentration fields. Ventilation transfer coefficients w _T /U derived from the naphthalene sublimation method showed that, whilst there was enhanced vertical momentum exchange due to obstacle height variability, advection was reduced and dispersion from the source area was not enhanced. Thus, the height variability of a canopy is an important parameter when generalising urban dispersion. Fine resolution concentration measurements in the canopy showed the effect of height variability on dispersion at street scale. Rapid vertical transport in the wake of individual high-rise obstacles was found to generate elevated point-like sources. A Gaussian plume model was used to analyse differences in the downstream plumes. Intensified lateral and vertical plume spread and plume dilution with height was found for the non-uniform height roughness.     

Long-Term Mean Wind Profiles Based on Similarity Theory

We provide general forms for long-term mean wind profiles from similarity-based wind profiles, beginning with a probabilistic adaptation of Monin–Obukhov similarity theory. We develop an analytical formulation for the stability distributions prevailing in the atmospheric surface layer, which in turn facilitates the derivation of a long-term mean wind profile based on Monin–Obukhov similarity theory. The modelled stability distributions exhibit good agreement with measurements from sites having different local conditions. The long-term wind profile formulation is further extended to include the influence of the depth of the atmospheric boundary layer (h), which becomes relevant for heights above h/3, and the resultant long-term ‘tall’ profile form also matches observations.     

热浮升烟流扩散的拉格朗日粒子模拟

本文建立了一个处理对流边界层热浮升烟流扩散的拉格朗日粒子模式。模式既考虑了对流边界层的特殊气流结构，并作了均匀湍流参数化的简化；同时提出了在拉格朗日模式中合理计入热浮升烟流抬升影响的近似方法。模拟计算结果表明:烟流热浮力的影响使得地面最大浓度值远比被动烟流的低，而且出现位置离源更远。模式计算与外场试验结果合理地一致。模式物理概念明确合理，输入参数少，计算量小，具有简单实用的优点，适合日常环境应用需要。