138
Air Pollution and Turbulence: Modeling and Applications
where K 0 is a constant and a and b can be
a ≥ 0 and b = 0
a = 0 and b > 0 for 0 ≤ z ≤ H
a = 1 and b > 0 for 0 ≤ z ≤ H
a = 1 and b = 0 for 0 ≤ z ≤ H/2; a = 0 and b = 1 for H/2 ≤ z ≤ H
where H is the height of the atmospheric boundary layer.
Scriven and Fisher (1975) proposed a solution with constant u and K z as
for 0
z
s
K z
z z
≡
≤ ≤
(5.9a)
1
( ) for
z
z
s
K K z
z z H
=
< ≤
(5.9b)
where z s is a predetermined height (generally, the height of the surface layer). This
solution allows (as boundary conditions) a net fl ow of material toward the ground:
z
g
C
K
VC
z
∂ =
∂
(5.10)
where V g is the deposition velocity. The Scriven and Fisher solution has been used
in the United Kingdom for long-range transport of pollutant. In Fisher (1975), the
deposition of sulfur over the United Kingdom, Sweden, and the rest of Europe was
compared, and it was found that the British contribution to deposition over rural
Sweden was about one half of the Swedish contribution.
Yeh and Huang (1975) and Berlyand (1975) published bidimensional solutions for
elevated sources with u and K z following power profi les, but for an unbound atmosphere, that is,
0 at =
z
C
K
z
z
∂ =
∞
∂
(5.11)
Demuth (1978) put forward a solution with the same conditions, but for a vertically
limited boundary layer, that is,
0 at
z
C
K
z H
z
∂ =
=
∂
(5.12)
The solutions of Yeh and Huang, Berlyand, and Demuth are used in KAPPAG air
pollution model (Tagliazucca et al., 1985; Tirabassi et al., 1986; Tirabassi 1989).
By applying the Monin–Obukhov similarity theory to diffusion, van Ulden (1978)
derived a solution for vertical diffusion from continuous sources near the ground
only with the assumption that u and K z follow power profi les. His results are similar
to that of Roberts’, but he provided a model for non–ground-level sources, but applicable to sources within the surface layer. SPM (Tirabassi and Rizza, 1995) is a model
that utilizes the solution proposed by van Ulden.
© 2010 by Taylor and Francis Group, LLC
Air Pollution and Turbulence: Modeling and Applications
where K 0 is a constant and a and b can be
a ≥ 0 and b = 0
a = 0 and b > 0 for 0 ≤ z ≤ H
a = 1 and b > 0 for 0 ≤ z ≤ H
a = 1 and b = 0 for 0 ≤ z ≤ H/2; a = 0 and b = 1 for H/2 ≤ z ≤ H
where H is the height of the atmospheric boundary layer.
Scriven and Fisher (1975) proposed a solution with constant u and K z as
for 0
z
s
K z
z z
≡
≤ ≤
(5.9a)
1
( ) for
z
z
s
K K z
z z H
=
< ≤
(5.9b)
where z s is a predetermined height (generally, the height of the surface layer). This
solution allows (as boundary conditions) a net fl ow of material toward the ground:
z
g
C
K
VC
z
∂ =
∂
(5.10)
where V g is the deposition velocity. The Scriven and Fisher solution has been used
in the United Kingdom for long-range transport of pollutant. In Fisher (1975), the
deposition of sulfur over the United Kingdom, Sweden, and the rest of Europe was
compared, and it was found that the British contribution to deposition over rural
Sweden was about one half of the Swedish contribution.
Yeh and Huang (1975) and Berlyand (1975) published bidimensional solutions for
elevated sources with u and K z following power profi les, but for an unbound atmosphere, that is,
0 at =
z
C
K
z
z
∂ =
∞
∂
(5.11)
Demuth (1978) put forward a solution with the same conditions, but for a vertically
limited boundary layer, that is,
0 at
z
C
K
z H
z
∂ =
=
∂
(5.12)
The solutions of Yeh and Huang, Berlyand, and Demuth are used in KAPPAG air
pollution model (Tagliazucca et al., 1985; Tirabassi et al., 1986; Tirabassi 1989).
By applying the Monin–Obukhov similarity theory to diffusion, van Ulden (1978)
derived a solution for vertical diffusion from continuous sources near the ground
only with the assumption that u and K z follow power profi les. His results are similar
to that of Roberts’, but he provided a model for non–ground-level sources, but applicable to sources within the surface layer. SPM (Tirabassi and Rizza, 1995) is a model
that utilizes the solution proposed by van Ulden.
© 2010 by Taylor and Francis Group, LLC