A turbulent energy model for diffusion in the convective boundary layer

A turbulent energy model developed by the authors to describe atmospheric flows is used to study diffusion in the convective boundary layer. The model is based on the turbulent energy transport equation coupled with eddy diffusivity expressions for momentum and heat transfer. The diffusion model assumes equality of the eddy diffusivity for heat and mass and Gaussian diffusion in the cross-stream direction. The model is shown to reproduce satisfactorily the main features of diffusion in convective flows, and its predictions compare well with the measurements of the laboratory experiments of Willis and Deardorff, as well as with field data.     

Air pollution in a convective boundary layer

Detailed profiles of the concentration and the concentration flux for pollutants released continuously from a point source near the ground are presented. Although there are no observational data of the concentration flux and the covariance of temperature and concentration, the distributions of concentration and eddy diffusivity derived from this study are in good agreement with those of laboratory experiments. This study also shows that the covariance of temperature and concentration is important in producing a countergradient concentration flux in a convective boundary layer.     

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.     

The relationship between the convective boundary layer and dispersion from tall stacks

This paper discusses the structure of the convective planetary boundary layer in relation to dispersion of pollutants. As tall stack plumes are brought down to the ground primarily during unstable conditions, we have investigated the conditions under which the PBL is convective. Our analysis indicates that the convective PBL occurs more often than is commonly thought. The second part of the paper describes some aspects of dispersion in the convective PBL. We propose a simple model capable of providing factor-of-two type estimates of ground-level concentrations. We also discuss some of the factors which complicate attempts to obtain more accurate results. In this context, we point out the problems associated with using model-predicted ensemble means to estimate observed concentrations.     

Fumigation of pollutants in and above the entrainment zone into a growing convective boundary layer: a large-eddy simulation

Fumigation of a passive plume located in or above the entrainment zone (EZ) into a growing convective boundary layer (CBL) has been simulated by large-eddy simulation (LES). Three non-dimensional parameters, α(=w_e0/w_*0), z₀/z_i0, and σ_z0/z_i0, are used to classify different cases, where w_*0 is the convective velocity scale, w_e0 the initial entrainment velocity, z_i0 the initial CBL height, z₀ the initial plume height, and σ_z0 is the initial plume half-depth. Forty cases have been run and analysed. The crosswind-integrated concentrations have been compared with existing laboratory data from a saline convection tank. The results show that LES is a promising tool to reproduce fumigation processes. With a relatively coarse grid mesh near the EZ, LES derives reliable results that are in a good agreement with the laboratory data. The first parameter, α, containing the effects due to inversion strength, plays an important role in determining C₀(T), the ground-level concentration (GLC) as a function of dimensionless time, T. For large α (say >0.03, corresponding to fast entrainment), variation of α gives significant change in C₀(T); whereas for a wide range of α between 0.01 and 0.02 (corresponding to slow entrainment), C₀(T) is almost independent of α. The starting time of fumigation does not vary significantly with the second parameter, z₀/z_i0 (relative height of plume), although C₀(T) is, in general, smaller for a higher plume. This confirms laboratory findings that the traditional notion of zero fumigation for a high plume (say above 1.10z_i) is not correct. The effect of the third parameter, σ_z0/z_i0, is on the magnitude of C₀(T); thinner initial plumes have higher GLCs.     

A simple and fast screening test to detect soils polluted by lead

Lead pollution is an environmental priority. The evaluation of contaminated soils was often based on the results of the toxicity characteristic leaching procedure (TCLP) or the synthetic precipitation leaching procedure (SPLP). This paper presents a simple and fast screening test to detect soil contaminated by lead. The test is based on the chemistry of the stomach (Cl- concentration, pH 2, T = 37 degrees C) and simulates the incidental oral ingestion of soil by young children. The gastric juice simulation test (GJST) and the TCLP were applied to six size fractions from five soils. The GJST solubilized more Pb (up to 169 mg/l) than the TCLP especially for the smallest size fraction. Particle size had less effect on the TCLP. The percentage of lead released with the GJST, was most significant for the <63 microm size fraction and varied from 18 to 74% of the total lead content. Lead leached during the TCLP as a function of the total lead content showed poor linear regression coefficient (R) values for soils <250 microm. R values were significant for all size fractions with the GJST. The pH of approximately 5 in the TCLP limits the solubilization of lead in the small size fractions. The five soils exceeded the toxicity threshold of 10 microgPb/dl of blood for a significant fraction of children between 0 and 36 months using the EPA's IEUBK model (Integrated Exposure Uptake Biokinetic). But the TCLP did not detect lead contamination in two of these five soils. The GJST proved to be a better estimator of lead bioaccessibility in the gastrointestinal tract.     

Further measurements in a simulated atmospheric boundary layer

Extensive power spectral and correlation measurements have been made in a simulated neutral atmospheric boundary layer in a wind tunnel.These measurements verify the existing data by showing that the flow in the simulated boundary layer is reasonably representative of real boundary layer flow. Comparison with the available full scale data shows good agreement provided that the height of the atmospheric boundary layer appropriate to rural terrain, which is the type represented here, is assumed to be of the order of 2000ft. Normally a height of 1000ft is adopted. It is also shown that measurement of the integral length scales of turbulence may provide a more accurate method of estimating the atmospheric boundary layer height.     

An analytical model for crosswind integrated concentrations released from a continuous source in a finite atmospheric boundary layer

An analytical model for the crosswind integrated concentrations released from a continuous source in a finite atmospheric boundary layer is formulated by considering the wind speed as a power law profile of vertical height above the ground and eddy diffusivity as an explicit function of downwind distance from the source and vertical height. A closed form analytical solution of the resulting advection–diffusion equation for these profiles of wind speed and eddy diffusivity with the physically relevant boundary conditions is derived using the separation of variables technique that leads to a Sturm–Liouville eigen value problem. Various particular cases of the model are deduced.The model is evaluated with the observations obtained from Prairie Grass experiment in various stability classes varying from very unstable to neutral and stable conditions and Hanford diffusion experiment in stable conditions. The agreement is found to be good between the computed and observed concentrations in both the diffusion experiments. For Prairie Grass experiment, the model is predicting 78% cases with in a factor of two and gives a value of NMSE as 0.075. On the other hand, for Hanford observations in stable conditions, it predicts 70% cases with in factor of two. An extensive analysis of statistical measures with the downwind distances from the source reveals that the model is performing well close to the source.     

Simple model for estimating dry deposition velocity of ozone and its destruction in a polluted nocturnal boundary layer

Determining the destructions of both ozone and odd oxygen, O_x, in the nocturnal boundary layer (NBL) is important to evaluate the regional ozone budget and overnight ozone accumulation. This work develops a simple method to determine the dry deposition velocity of ozone and its destruction at a polluted nocturnal boundary layer. The destruction of O_x can also be determined simultaneously. The method is based on O₃ and NO₂ profiles and their surface measurements. Linkages between the dry deposition velocities of O₃ and NO₂ and between the dry deposition loss of O_x and its chemical loss are constructed and used. Field measurements are made at an agricultural site to demonstrate the application of the model. The model estimated nocturnal O₃ dry deposition velocities from 0.13 to 0.19 cm s^?1, very close to those previously obtained for similar land types. Additionally, dry deposition and chemical reactions account for 60 and 40% of the overall nocturnal ozone loss, respectively; ozone dry deposition accounts for 50% of the overall nocturnal loss of O_x, dry deposition of NO₂ accounts for another 20%, and chemical reactions account for the remaining 30%. The proposed method enables the use of measurements made in typical ozone field studies to evaluate various nocturnal destructions of O₃ and O_x in a polluted environment.     

A comparison of the predictions of a simple gaussian plume dispersion model with measurements of pollutant concentration at ground-level and aloft

The NO_x pollution arising from a nitric acid works has been analysed. Measurements were taken at ground-level using continuous monitors over a 6 month period, and aloft at three heights within the plume using a specially constructed bag sampler. The measured concentrations and σ_z values have been compared with the predictions of a simple Gaussian plume dispersion model using the Turner (1970) values of σ_y and σ_z derived from Pasquill-Gifford stability categories. It was found that ground-level concentrations at 1–2 km distance from the source could be predicted reliably, but that close to the source predicted values of σ_z were greater than those measured experimentally.