Mathematical Air Pollution Models: Eulerian Models
149
Mathematically, the situation is described by Gaussian models as a multiple refl ection
of pollutants between the terrain and the base of the inversion.
5.6.4 GROUND DEPOSITION
Ground deposition of the diffuse material is evaluated by means of various algorithms. Listed below are those most commonly utilized.
The decrease of material in the air is expressed by an exponential decrease
•
on the basis of a value of the average life of the pollutant.
The decrease of material in the air is expressed by a fi ctitious decrease of
•
the emission fl ux as a function of the distance from the source.
A lowering of the plume axis height is introduced as a function of the dis•
tance from the source to describe the fall due to the gravitational force of
the diffuse material.
The ground deposition fl ux is expressed as the concentration at the ground
•
for an assigned constant deposition rate.
Ground deposition due to meteoric precipitation is parameterized by an
•
exponential decrease linked to the precipitation intensity.
5.6.5 CHEMICAL REACTIONS
The mathematical description of the chemical transformation of the pollutants
dispersed in the atmosphere is a highly complex fi eld of study that remains far from
any satisfactory solutions. On the one hand, basic problems exist in the knowledge
and quantifi cation of the chemical reactions occurring in the atmosphere, while on the
other, there are considerable diffi culties in representing reactions higher than the fi rst
order (particularly, with constant fast reactions). Generally speaking, semiempirical
models empirically describe the impoverishment of a reactive pollutant by means
of an exponential decrease on the basis of an assigned value of average lifetime of
the pollutant. The K models prove to be theoretically most correct in representing the
diffusion of chemically reacting material. However, they are limited by the fact that
their characteristic time of transport and dispersion is not shorter than that of chemical reactions, which at times make description of dispersion with chemical reactions
problematic, even using numerical models (Seinfeld and Pandis, 1997).
5.7 NEW OPERATIVE MODELS
As mentioned above, most operative models for estimating gas and particle dispersion in the atmospheric boundary layer are based on the Gaussian approach. Such
models are founded on the hypothesis that the pollutant is dispersed in a homogeneous turbulence. However, due to the presence of terrain, turbulence is generally
not homogeneous along the vertical direction. In addition, the inputs of Gaussian
models often refer to simple turbulence schemes.
Over the past 20 years, following the works of Holtslag and van Ulden (1983),
Weil and Brower (1984), van Ulden and Holtslag (1985), Trombetti et al. (1986),
© 2010 by Taylor and Francis Group, LLC
149
Mathematically, the situation is described by Gaussian models as a multiple refl ection
of pollutants between the terrain and the base of the inversion.
5.6.4 GROUND DEPOSITION
Ground deposition of the diffuse material is evaluated by means of various algorithms. Listed below are those most commonly utilized.
The decrease of material in the air is expressed by an exponential decrease
•
on the basis of a value of the average life of the pollutant.
The decrease of material in the air is expressed by a fi ctitious decrease of
•
the emission fl ux as a function of the distance from the source.
A lowering of the plume axis height is introduced as a function of the dis•
tance from the source to describe the fall due to the gravitational force of
the diffuse material.
The ground deposition fl ux is expressed as the concentration at the ground
•
for an assigned constant deposition rate.
Ground deposition due to meteoric precipitation is parameterized by an
•
exponential decrease linked to the precipitation intensity.
5.6.5 CHEMICAL REACTIONS
The mathematical description of the chemical transformation of the pollutants
dispersed in the atmosphere is a highly complex fi eld of study that remains far from
any satisfactory solutions. On the one hand, basic problems exist in the knowledge
and quantifi cation of the chemical reactions occurring in the atmosphere, while on the
other, there are considerable diffi culties in representing reactions higher than the fi rst
order (particularly, with constant fast reactions). Generally speaking, semiempirical
models empirically describe the impoverishment of a reactive pollutant by means
of an exponential decrease on the basis of an assigned value of average lifetime of
the pollutant. The K models prove to be theoretically most correct in representing the
diffusion of chemically reacting material. However, they are limited by the fact that
their characteristic time of transport and dispersion is not shorter than that of chemical reactions, which at times make description of dispersion with chemical reactions
problematic, even using numerical models (Seinfeld and Pandis, 1997).
5.7 NEW OPERATIVE MODELS
As mentioned above, most operative models for estimating gas and particle dispersion in the atmospheric boundary layer are based on the Gaussian approach. Such
models are founded on the hypothesis that the pollutant is dispersed in a homogeneous turbulence. However, due to the presence of terrain, turbulence is generally
not homogeneous along the vertical direction. In addition, the inputs of Gaussian
models often refer to simple turbulence schemes.
Over the past 20 years, following the works of Holtslag and van Ulden (1983),
Weil and Brower (1984), van Ulden and Holtslag (1985), Trombetti et al. (1986),
© 2010 by Taylor and Francis Group, LLC