An analytical model for dispersion of pollutants from a continuous source in the atmospheric boundary layer

Abstract

For the dispersion of a pollutant released from a continuous source in the atmospheric boundary layer (ABL), a generalized analytical model describing the crosswind-integrated concentrations is presented. An analytical scheme is described to solve the resulting twodimensional steady-state advection-diffusion equation for horizontal wind speed as a generalized function of vertical height above the ground and eddy diffusivity as a function of both downwind distance from the source and vertical height. Special cases of this model are deduced and an extensive analysis is carried out to compare the model with the known analytical models by taking the particular forms of wind speed and vertical eddy diffusivity.The proposed model is evaluated with the observations obtained from Copenhagen diffusion experiments in unstable conditions and Hanford and Prairie Grass experiments in stable conditions. In evaluation of the model, a recently proposed formulation for the wind speed in the entire ABL is used. It is concluded that the present model is performing well with the observations and can be used to predict the short-range dispersion from a continuous release. Further, it is shown that the accurate parameterizations of wind speed and eddy diffusivity provide a significant improvement in the agreement between computed and observed concentrations.

Assessment of the unified analytical solution of the steady-state atmospheric diffusion equation for stable conditions

“…that the turbulence becomes very weak, sporadic, intermittent and no longer continuous in time and space [14]. For comparative purposes, we use the same digital version of the dataset used by Kumar & Sharan [3] as available at http://www2.dmu.dk/ atmosphericenvironment/Docs/PrairieGrass.xls, that gives the normalized crosswind-integrated concentrations and meteorological variables with a surface roughness length z 0 = 0.006 m.…”

“…Tables 1 and 2 summarize the micrometeorological parameters, emission data and the observed crosswind-integrated concentrations normalized by the source strength. The very stable cases (z 1 /L > 10) were not considered, based on the same argument given by Kumar & Sharan [3], i.e. that the turbulence becomes very weak, sporadic, intermittent and no longer continuous in time and space [14].…”

“…However, the solutions are mainly available over unstable and neutral conditions [2][3][4][5], whereas there is a lack of works considering the solution of the pollutant dispersion equations under stable conditions [3,6,7]. As argued by Salmond & McKendry [8], the strongly layered structure and intermittent characteristics of turbulence in the very stable nocturnal boundary layer present a particular challenge to meteorologists and air pollution modellers alike.…”

Exploration of the impact of nearby sources on urban atmospheric inversions using large eddy simulation

“…We can use x = Ut to transform (3) to an x-dependent form. If then the bracketed averages are taken over sufficiently large samples (as would be the case for long time averages at stationary sensors such as a tower), the velocity variances on the RHS of (3) approach the total velocity variance in each dimension, denoted by However, as noted in multiple studies (e.g., Seinfeld 1986;Arya 1995;Degrazia et al 2001;Moreira et al 2005;Kumar and Sharan 2010), Taylor (1921) found an alternate formula appropriate to short time/near-source plume behavior. For t << T L the mean squared displacement of particles is given by:…”

A Mathematical Model on Dispersion of Air Pollutants

“…Srivastava et al [10] have given a three dimensional atmospheric diffusion model with variable removal rate and variable wind velocity using power law profile. Kumar et al [7] have presented an analytical model for the dispersion of pollutant released from a continuous source in the atmospheric boundary layer describing the crosswindintegrated concentration. They have claimed that the model can also be used for the concentration distribution of a pollutant released from a line source perpendicular to the direction of the mean wind and to study the turbulent dispersion from a steady two dimensional horizontal source in a wide open channel for a generalized profile of wind flow and eddy diffusivity.…”