1. Introduction
Aerosols exhibit spatial and temporal variations in urban environments like Athens area. Scientific interest has focused on the evaluation of atmospheric turbidity, a
measure of the aerosol load in the atmosphere. Various turbidity definitions have been Ž
. proposed such as the Linke turbidity factor, T
Linke, 1922; 1929 , the Unsworth–
L
˚
Ž .
Monteith turbidity factor, T Unsworth and Monteith, 1972 , the Angstrom turbidity
¨
U
˚
Ž .
Ž .
parameters, a and b Angstrom, 1929 , the Schuepp coefficient B, Schuepp, 1949 ,
¨ ¨
¨
Ž .
and the horizontal visibility V McClatchey and Selby, 1972 . Many studies dealing Ž
with aerosol optical properties appear in the literature e.g. Louche et al., 1987; Kocifaj, 1994; Bokoye et al., 1997; Schmid et al., 1997; Tomasi et al., 1997; Devara, 1998;
. Kambezidis et al., 1998b; Jacobson, 1999 . Some of those appear as spectral narrowband
Ž studies e.g. McCartney and Unsworth, 1978; Cachorro et al., 1987; Lorente et al., 1994;
. Adeyefa et al., 1997; Kambezidis et al, 1997b; Marenco et al., 1997 . Furthermore, a
Ž .
variety of atmospheric aerosols absorbing solar radiation are known Jacobson, 1999 . The necessity in estimating the total atmospheric transmittance is discussed in the
Ž .
companion paper Kambezidis et al., 2000 . In addition, the effect of wind regime on the above quantity is studied. Here, an attempt is made to model the extinction of solar
irradiance, taking into account various attenuation processes and constituents. Ž
. Starting with Leckner 1978 , the total atmospheric transmittance was analyzed as a
product of partial transmittance functions due to various atmospheric constituents considering Rayleigh scattering, absorption by ozone, water vapor and mixed gases as
well as aerosol scattering. However, there was a special need to include nitrogen dioxide, the contribution of which to the extinction procedure is very significant in
Ž .
polluted areas. Therefore, Gueymard 1995
added one more term in his spectral radiative code SMARTS2, the transmittance function due to atmospheric NO .
2
2. Methodology
In this study, we use the spectral measurements of solar beam irradiance taken by Ž
PPS on the same selected days as described in the companion paper Kambezidis et al., .
Ž .
2000 . Based on SMARTS2 algorithm proposed by Gueymard 1995 , a new radiative Ž
. transfer model was first developed by Kambezidis et al 1997a . This calculates spectral
radiative properties such as atmospheric optical thickness and transmission and also Ž
estimates atmospheric constituents such as O and NO
Kambezidis et al., 1996,
3 2
. 1997a . Ground-based multispectral measurements of direct solar irradiance are required
as input values to the model. Such measurements were performed every 30 min in the spectral range 310–575 nm with a resolution of about 0.5 nm.
Ž . Ž
. The total spectral atmospheric transmittance, t l,u
in the sun-sensor direction ,
z
considering single scattering, can be written as follows: t l,u
s H l,u rH l S
1
Ž .
Ž .
Ž . Ž .
z z
o
Ž .
y2
Ž where H l,u
is the measured beam irradiance calibrated in W m a function of
z
. Ž .
wavelength, l, and zenith angle, u , H l the spectral extraterrestrial radiation after
z o
Ž .
Ž Gueymard 1995 , and S is the correction factor for the sun–earth distance Kambezidis
. et al., 1997a .
Ž .
X
Ž . The spectral optical thickness
towards zenith , d l , is determined from the equation:
X
d l,u
s 1rm ln 1rt l,u 2
Ž .
Ž .
Ž .
z z
where m stands for the atmospheric optical mass. Ž
.
X
The total spectral transmittance function towards zenith with m s 1 , t , is, there- fore, given by the following equation:
X X
t l,u
s exp yd l,u
. 3
Ž .
Ž .
Ž .
z z
To model the atmospheric transmittance in any spectral range, six individual atmo- spheric processes are considered here: Rayleigh scattering, absorption by ozone, nitro-
Ž .
gen dioxide, uniformly mixed gases such as CO , O , water vapor as well as aerosol
2 2
extinction. Their respective spectral transmittance functions are denoted t , t , t , t ,
r o
n g
t , and t . Within narrow spectral regions, these atmospheric processes can be consid-
w a
ered independent of each other, so that the total transmittance function can be derived as Ž
the product of these individual spectral transmittance functions Kambezidis et al., .
1997a,1998a; Gueymard, 1995 . Thus: t l,u
s t l,u t l,u t l,u t
l,u t l,u t l,u .
4
Ž .
Ž . Ž
. Ž . Ž
. Ž
. Ž .
Ž .
z r
z o
z n
z g
z w
z a
z
Ž .
For each ith atmospheric extinction process i s r, o, n, g, w, a mentioned above, the transmittance function t can be written in terms of optical thickness d , and the
i i
optical mass m , as follows:
i
t s exp ym d . 5
Ž .
Ž .
i i
i
Ž . According to Eq. 5 the atmospheric transmittance due to Rayleigh scattering is
retrieved as follows: t l,u
s exp ym u d l 6
Ž .
Ž . Ž . Ž .
r z
z r
Ž .
where the molecular optical thickness is calculated from Leckner 1978 : d l s 0.008735l
y4 .08
. 7
Ž . Ž .
r
The units of l in all the expressions are microns. The relative optical air mass, m
X
, for standard pressure P s 1013.25 hPa at sea level, is calculated from Gueymard
Ž .
1995 :
y1 y1 .697
X 0 .07
m u s cosu q 0.45665 u
96.4836 y u 8
Ž . Ž
. Ž .
z z
z z
where u is in degrees. The pressure corrected air mass, m, is calculated from:
z
m s m
X
PrP , where P is the measured surface pressure in hPa. Ž
. The water vapor transmittance and air mass are after Gueymard 1995 :
c 1 .05
n
t l,u
s exp yk m J
f B 9
Ž .
Ž .
Ž .
w z
w w
where the atmospheric mass due to water vapor is calculated from:
y1 y1 .3814
0 .1
m u
s cosu q 0.031141 u 92.471 y u
10
Ž . Ž
. Ž
.
w z
z z
z
where:
0 .75
J s 0.493 RH e rT PrP
P 273.15rT , in cm,
11
Ž . Ž
. Ž
.
s
Ž .
Ž .
RH is the relative humidity in , e is the saturation water vapor in hPa calculated
s
Ž .
from Gueymard 1994 : e s exp 22.329699 y 49.140396T
y1
y 10.921853T
y2
y 0.39015156T 12
Ž .
Ž .
s o
o o
Ž .
with T s Tr100, T being the absolute air temperature in K
o
f s A 0.394 y 0.26946l q 0.46478 q 0.23757l PrP
13
Ž . Ž
. Ž
.
is a pressure scaling factor that compensates for inhomogeneities in the water vapor path length according to the Curtis–Godson approximation, and:
A s 1 for l - 670 nm. In addition:
n s 0.88631 q 0.025274l y 3.5949exp y4.5445l 14
Ž .
Ž .
c s 0.53851 q 0.003262 l q 1.5244exp y4.2892 l . 15
Ž .
Ž .
The correction factor B takes into account the variation of the absorption with distance from the band center:
B s f
X
m J exp 0.1916 y 0.0785m q 4.706 = 10
y4
m
2
16
Ž .
Ž .
Ž .
w w
w
with: f
X
m J s 0.624 m J
0 .457
for k - 0.01 17a
Ž .
Ž .
w w
w 0 .45
X
f m , J s 0.525 q 0.246 m J
for k G 0.01 17b
Ž .
Ž .
Ž .
w w
w
k being the water vapor absorption coefficient, in cm
y1
.
w
Since mixed gases possess no absorption lines in the spectral range under considera- tion, the respective formulas are not taken into account here.
The transmittance function due to absorption by NO is:
2
t s exp yk l m ,
18
Ž .
Ž .
n n n
n
where l is the total column of NO in the atmosphere. The corresponding atmospheric
n 2
Ž .
mass is calculated from Gueymard 1995 :
y1 y3 .4536
0 .5
m u
s cosu q 602.3 u 117.96 y u
. 19
Ž . Ž
. Ž
.
n z
z z
z
Ž .
The corrected absorption coefficient is calculated from the data of k l, T via the
n n
Ž .
relationship Gueymard, 1995 :
5
i y1
k l,T s max 0,k
l,T 1 q T y T
f l , in cm
, 20
Ž .
Ž .
Ž .
Ž .
Ý
n n
r a
r i
½ 5
is0
Ž .
where k l,T is the absorption coefficient for the reference temperature of T s 243.2
n r
r
Ž K, T s a q a T,
a s 332.41 K, a s y0.34467 for summer and a s 142.68 K,
a l
l
. a s 0.28498 for winter . The coefficients f are: f s 0.69773, f s y8.1829, f s
l i
1 2
37.821, f s y86.136, f s 96.615, f s y42.635 for l - 625 nm.
3 4
5
The atmospheric transmittance due to O absorption is calculated from:
3
t l,u
s exp yk T , l l m
. 21
Ž .
Ž .
Ž .
o z
o o
o
Ž .
l is the total ozone column in atm-cm calculated as in Kambezidis et al. 1997a .
o
Ž .
The ozone air mass is calculated from Gueymard 1995 :
y1 y3 .2922
0 .5
m u
s cosu q 268.45 u 115.42 y u
. 22
Ž . Ž
. Ž
.
o z
z z
z
The temperature-dependent absorption coefficients, k , are calculated from:
o 2
y1
k l,T s max 0, k
l,T q C T y T q C T y T , in cm
23
Ž .
Ž .
Ž .
Ž .
Ž .
4
o o
r 1
e r
2 e
r
Ž where T s a q a T a s 332.41 K, a s y0.34467 for summer and a s 142.68 K,
e l
l
. Ž .
a s 0.28498 for winter , T K is the temperature at which the ozone absorption
l
coefficient is to be estimated. The constants C and C are:
1 2
C s 0.39626 y 2.3272 l q 3.4176l
2
for 310 - l - 344 nm 24a
Ž .
Ž .
1
C s 1.8268 = 10
y2
y 0.10928 l q 0.16338 l
2
for 310 - l - 344 nm. 24b
Ž .
Ž .
2
In the spectral range 344 - l - 560 nm, k is given by:
o
k T , l s max 0, k
T , l 1 q 0.0037083 T y T
Ž .
Ž .
Ž .
o o
r e
r
= exp 28.04 0.4474 y l
. 25
Ž .
Ž .
4
Ž .
If the calculations are made for optical masses, m s 1, the individual spectral
i
Ž
X
. transmission functions t
are derived in the direction towards zenith, and therefore, are
i
Ž . independent of the solar elevation angles at the times of the measurements. Thus, Eq. 4
can also be written as: t
X
l s t
X
l t
X
l t
X
l t
X
l t
X
l t
X
l . 26
Ž . Ž . Ž . Ž . Ž .
Ž . Ž . Ž
.
r o
n g
w a
Making the aerosol transmittance subject of the formula, we can estimate this parameter:
X X
X X
X X
X
t l s t
l r t l t
l t l t
l t l
. 27
Ž . Ž .
Ž . Ž . Ž . Ž . Ž .
Ž .
a r
o n
g w
3. Results and discussion
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