Analytical Models for the Dispersion of Pollutants in Low Wind Conditions 165
From both these aspects, attempts have been made (Yadav et al., 1996; Sharan
and Gopalakrishnan, 2003; Sharan et al., 2003) to deal with the problem of atmospheric dispersion in low wind conditions. Here, we briefl y describe the analytical
models for the dispersion of air pollutants in low wind conditions.
6.4 ANALYTICAL MODELS IN LOW WIND CONDITIONS
6.4.1 CONSTANT K-MODELS
First, we briefl y describe the models derived by considering the downwind diffusion
and assuming U and K i ’s as constant.
6.4.1.1 Unsteady-State Models
6.4.1.1.1 Puff Model
The Gaussian puff model (Equation 6.14) accounts for the advection and the downwind diffusion term. In this model, the concentration of the material inside puff is
assumed to be distributed according to the Gaussian distribution. One of the advantages of the puff approaches is that it can handle very low or even zero wind speeds
because of the disappearances of U from the denominator. In other words, in puff
models, the wind speed affects the concentration computation only by controlling
the density of puffs in the region (i.e., the lower the wind speed, the closer a puff is
to the next one generated by the same source). Therefore, the puff approach allows,
at least theoretically, the treatment of calm or low wind conditions (Zannetti, 1990).
Inclusion of downwind diffusion is another of its advantage over the Gaussian plume
equation (Cirillo and Poli, 1992). However, as pointed out in Section 6.3.4, the problem may be encountered with the availability of dispersion parameters in low wind
conditions.
6.4.1.1.2 Segment–Puff Model
During weak and variable wind conditions, the dispersion process is generally
nonhomogeneous and nonstationary because of the complex meteorological and/
or terrain situations. Sharan et al. (1996c) described a time-dependent mathematical model to treat the nonstationary and nonhomogeneous dispersion from a point
source release. This approach involves coupling of plume segment and Gaussian
puff methods (Equation 6.14). In this approach, a continuous plume is approximated
by a fi nite number of segments, and each segment is represented by a series of contiguous puffs. The Gaussian puff model allows for the diffusion of pollutants in all
three directions (including along wind) and described the pollutant dynamics by
the temporal evolution of plume segments, while the plume segment approach helps
in tracking the trajectory of the plume. The characteristics of plume segments are
updated at each dispersion time interval. Zannetti (1986) also presented a mixed segment approach, which considered the plume to be divided into a series of elements
that are either segments or puffs.
The segment–puff model used to simulate the tracer tests (Sagendorf and Dickson,
1974) over a short range (up to 400 m) in the fl at area during low wind stable conditions. The overall agreement between the observed and the simulated curves found
© 2010 by Taylor and Francis Group, LLC
From both these aspects, attempts have been made (Yadav et al., 1996; Sharan
and Gopalakrishnan, 2003; Sharan et al., 2003) to deal with the problem of atmospheric dispersion in low wind conditions. Here, we briefl y describe the analytical
models for the dispersion of air pollutants in low wind conditions.
6.4 ANALYTICAL MODELS IN LOW WIND CONDITIONS
6.4.1 CONSTANT K-MODELS
First, we briefl y describe the models derived by considering the downwind diffusion
and assuming U and K i ’s as constant.
6.4.1.1 Unsteady-State Models
6.4.1.1.1 Puff Model
The Gaussian puff model (Equation 6.14) accounts for the advection and the downwind diffusion term. In this model, the concentration of the material inside puff is
assumed to be distributed according to the Gaussian distribution. One of the advantages of the puff approaches is that it can handle very low or even zero wind speeds
because of the disappearances of U from the denominator. In other words, in puff
models, the wind speed affects the concentration computation only by controlling
the density of puffs in the region (i.e., the lower the wind speed, the closer a puff is
to the next one generated by the same source). Therefore, the puff approach allows,
at least theoretically, the treatment of calm or low wind conditions (Zannetti, 1990).
Inclusion of downwind diffusion is another of its advantage over the Gaussian plume
equation (Cirillo and Poli, 1992). However, as pointed out in Section 6.3.4, the problem may be encountered with the availability of dispersion parameters in low wind
conditions.
6.4.1.1.2 Segment–Puff Model
During weak and variable wind conditions, the dispersion process is generally
nonhomogeneous and nonstationary because of the complex meteorological and/
or terrain situations. Sharan et al. (1996c) described a time-dependent mathematical model to treat the nonstationary and nonhomogeneous dispersion from a point
source release. This approach involves coupling of plume segment and Gaussian
puff methods (Equation 6.14). In this approach, a continuous plume is approximated
by a fi nite number of segments, and each segment is represented by a series of contiguous puffs. The Gaussian puff model allows for the diffusion of pollutants in all
three directions (including along wind) and described the pollutant dynamics by
the temporal evolution of plume segments, while the plume segment approach helps
in tracking the trajectory of the plume. The characteristics of plume segments are
updated at each dispersion time interval. Zannetti (1986) also presented a mixed segment approach, which considered the plume to be divided into a series of elements
that are either segments or puffs.
The segment–puff model used to simulate the tracer tests (Sagendorf and Dickson,
1974) over a short range (up to 400 m) in the fl at area during low wind stable conditions. The overall agreement between the observed and the simulated curves found
© 2010 by Taylor and Francis Group, LLC