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MTERNATIONAL JOURNAL OF CLIMATOLOGY, VOL. 16, 229-242 (1996)
BROAD-BAND TURBIDITY PARAMETERS AND SPECTRAL BAND
RESOLUTION OF SOLAR RADIATION FOR THE PERIOD 1954-1991, IN
ATHENS, GREECE
C. I? JACOVIDES
L.abomtoty of Meteorology, Department of Applied Physics, University of Athens, 33 Ippokmtous Str Athens 10680, Greece
AND
J. D. KARALIS
Hellenic Air Forces Academy, Dekelia, Atiica, Greece
Received 6 June I994
Accepted 27 June 1995
ABSTRACT
In the present analysis broad-band turbidity parameters, which depend upon the attenuation over the entire solar spectrum and
which can be determined from unfiltered pyrheliometric measurements of direct beam solar irradiance, are presented.
Unsworth-Monteith attenuation coefficient Tm, Linke factor TL and h g s t r o m turbidity coefficient fl (in parameterized form),
were calculated from mid-day observations at the National Observatory of Athens, Greece for the period 1954-1991. Values of
h g s t r o m turbidity coefficient fl compare well with those obtained directly through the so-called pyrheliometric formula Po.
Summertime turbidity levels were found to be higher than winter values.
The long-term variation of the turbidity parameters in conjunction with their frequency distribution depicts the
deterioration of air quality in the Athens basin during the period under study. The dependence on the aerosol amount of the
fraction of the various spectral bands to direct total irradiance as well as the ratio of diffuse to total global irradiation, are
also discussed.
KEY WORDS: atmospheric turbidity; spectral distribution of solar irradiance; air quality; Athens basin; Greece
1. INTRODUCTION
It is well known that aerosols attenuate solar radiation considerably. Airborne particulate and gaseous pollutants
alter the solar radiation incident at the ground in two ways: by depleting the total radiation and by changing the
proportions of direct to diffuse radiation (Peterson and Flowers, 1977). At urban sites, high aerosol concentrations
reduce the total incident energy and alter the diffuse to direct ratio (Hainel et al., 1990; Jacovides et al., 1993ab).
At rural locations, the decrease in the direct solar beam will be compensated largely by an increase in the diffise
flux. Furthermore, photochemical pollutants, which depend on ultraviolet radiation for their formation, drastically
affect the amount of solar energy reaching the ground. The particles formed from photochemically induced gas
cause both absorption and scattering of the incident radiation (Peterson and Flowers, 1977).
In general, natural and anthropogenic aerosols have different effects, both on the intensity and on the spectral distribution of solar irradiance. This may have important consequences for processes that depend on light
quality, such as solar energy conversion systems (Bower, 1977; Abdelrahman et al., 1988; Bird, 1989), plant
growth and photosynthesis (Unsworth and McCartney, 1973; Mavi, 1986; Jacovides et al., 1993a,b).
Concern about possible changes in global climate has stimulated an increasing interest in the radiative effects of
aerosols. Investigations on the aerosol’s radiative effects using various turbidity parameters have been reported for
several sites; Peterson and Bryson (1968), Flowers et al. (1969), Bridgman (1978), King et al. (1980) and O’Neil
CCC 0899-841 8/96/020229-14
0 1996 by the Royal Meteorological Society
230
C. P. JACOVIDES AND J. D. KARALIS
et al. ( 1993) from USA; Unsworth and Monteith ( 1972), Unsworth and McCartney (1973), and McCartney ( 1978)
from England; Uboegbulam and Davies (1983) and Freud (1983) from Canada; Abdelrahman et al. (1988) from
Saudi Arabia; and Katz et al. (1982), Louche et al. (1987), Karalis (1976), and Jacovides et al. (1994) from
Mediterranean sites.
Furthermore, irrespective of geography, information about the aerosols radiative effects is needed for
atmospheric model building, for the interpretation of radiometric measurements from satellites, for estimating
regional differences of surface water loss by evaporation, and for ecological studies of spectral composition in
relation to the growth and development of plants. The study of atmospheric turbidity is important for
meteorology, and climatology as well as for monitoring atmospheric pollution. The atmospheric turbidity
parameters are also required in order to determine the amount of spectral global irradiance for the design of
photovoltaic cells and selective absorpers for spectral thermal collectors. With these diverse needs in mind a
series of measurements of direct solar beam irradiance between 1954 and 1991 are reported and analysed in
terms of the aerosol amount.
Owing to the aerosol optical depth being a function of wavelength, turbidity can be described by various
coefficients. Here only broad-band coefficients, which depend upon the attenuation over the entire solar spectrum
300-2800 nm and which can be determined from unfiltered direct solar irradiance, are considered. Thus, three
coefficients of turbidity are used the Linke (1922) turbidity factor, the Unsworth and Monteith attenuation
coefficient (1972), and the hgstrom turbidity coefficient (1929), in its parameterized form.
2. EVALUATION OF TURBIDITY PARAMETERS
2.1. Unsworth-Monteith attenuation coefficient
TUM
The Unsworth-Monteith (1972) aerosol attenuation coefficient is used to measure atmospheric turbidity in this
analysis. This parameter expresses the absorption of the solar rays by a dust-laden atmosphere relative to a dustfree one with a specified water vapour content. It can be derived from the spectral flux density of direct beam solar
radiation Z(1) after attenuation by the atmosphere.
Z(1) = Z*(1) exp[-z,(l)m]
(1)
with
I*(4 = Zo(4 exp-I[zR(4
+ zo(4 + zw(4lm)
(2)
where now I*@) is the flux density at wavelength 1,beneath an aerosol-free atmosphere; Zo(l) is the flux density
at wavelength 1received at the top of the atmosphere by a plane normal to the solar beam; rn is the air mass
number or the number of equivalent vertical paths traversed by the direct beam, and z~(1),z&), zw(1), and za(l)
are the spectral optical depths for Rayleigh scattering, ozone absorption, water vapour absorption, and aerosol
attenuation. The Unsworth-Monteith coefficient, TuM,is a weighted mean aerosol optical thickness that is defined
by7
This coefficient can be calculated through the following equation
T i = m-’ W*[email protected]
(4)
where I* = JZ*(rl)d1, is the normal incidence irradiance at the bottom of an aerosol-free atmosphere;
Z = JZ(A)dA, is the measured normal incidence irradiance at the Earth’s furace. S= (R/Ro)2 is the correction
factor for mean solar distance, R and Ro denote the mean Sun-Earth distances. The quantity I* is calculated
via Bird and Hulstrom’s (1981) formulation as described in section 3. Typically TuM values vary between 0
and 1.
TURBIDITY AND SOLAR RADIATION M ATHENS
23 1
2.2. Linke turbidity factor, TL
This coefficient is a relatively simple measure of the haze and water vapour content of the atmosphere. Linke
(1922) defined TL, as the equivalent number of clean dry atmospheres required to produce the observed
attenuation of solar radiation. Linke's turbidity factor can be defined as,
where Zo is the extraterrestrial solar radiation; 8, is the integral 'Rayleigh' scattering optical thickness of a clean,
dry atmosphere (Louche et af., 1987). Thus Linke's turbidity factor can be written as,
TL = (In I0 - In I - In S)/[&(m)m]
or
TL = P(m)(ln l o - In I - In 5')
where P(m) = (&(m)rn he)-'. & is expressed as a function of the air mass m, because the spectral distribution
of solar irradiance changes with increasing m. According to Louche et af. (1987) 8, is given as,
8,
= [6.5567
+ 1.7513 m - 0.1202 m2 + 0-0065 m3 - 0.00013 m4]-'
(7)
Furthermore, the major physical differences between what is measured by TL and TUMis that the former factor is
focused on the attenuation of the solar rays produced by a water-vapour-free atmosphere, whereas the latter one
refers to an atmosphere with a specified water vapour content. Values of Linke factor vary between 1 and 10, and
its ease of measurement in meteorological stations has made it quite popular.
2.3. hgstmm turbidity factor /3
The amount of aerosols present in the atmosphere in the vertical duection can also be represented by an index
called hgstrom's turbidity coefficient /3, proposed by hgstrom (1929, 1930). The value of /?varies typically
from 0.0 to 0.5. Angstrom's turbidity formula also gives an index of average aerosol size distribution represented
by wavelength exponent a. For most natural atmospheres a = 1-34~0.5. The two parameters, a and /3, enter into
hgstrom's turbidity formula for aerosol spectral attenuation coefficient as follows:
kai = BI-"
where kal is the monochromatic aerosol attenuation coefficient, also called aerosol optical depth in the vertical
direction, and I is the wavelength in micrometres. The exponent a is a measure of the particle size distribution and
varies between a=O for very large particles and a=4.0 for very small Rayleigh particles. Its value therefore
provides a good indication of the particle size distribution of the aerosols. There are a number of techniques to
measure a and 8. Dual wavelengths sunphotometer is used to determine kal at two wavelengths where molecular
absorption is either absent or is negligible. The wavelengths usually chosen are 380 and 500 nm. This method is
accurate and yields simultaneously the values of a and /3. However, /3 can be measured at I = 1 pm with a single
wavelength Volz instrument, and from equation (8) it is obvious that at this wavelength the effect of (I disappears.
In field measurements, it is common to determine /3 from pyrheliometric measurements using an RG630 filter
(formerly RG2).
Owing to the considerable selective absorption of radiation by water vapour within the infra-red region of the
spectrum, the determination of /? from pyrheliometric measurements of normal incidence irradiance is usually
restricted to the ultraviolet and visible wavebands. However, this leads to the so-called pyrheliometric formula.
Because the present study deals only with broad-band turbidity coefficients, the so-called parameterization method
is used (Iqbal, 1983; Louche et af., 1987).
232
C. I? JACOVIDES AND J. D. KARALIS
3. DATA BASE AND PROCEDURES
For the study of the broad-band turbidity parameters in Athens, long-term pyrheliometric measurements for the
period 195&1991 were used. The observations were made at the National Observatory of Athens (NOA: 37"58'N,
23"43'E, h = 107 m above m.s.l.), at 0820, 1120, 1420, and 1720 local standard time (LST is 2 h ahead of UT),
whenever clouds were not present in the sightpath. In the present analysis only measurements made at 1120 and
1420 LST are used, because measurements from the earlier and later times are scarce, especially during the winter
months. In addition, the corresponding air masses at these times are of the same order (m 5 2). This was done to
avoid the effects of different air masses on the turbidity coefficients.
Direct beam solar irradiance in several wavebands was measured using the Linke-Feussner pyrheliometer.
Separation of the spectral bands was achieved by inserting a quartz filter and OG530, RG630 (formerly RG2),
and RG695 (formerly RG8) Schott glass filters into the direct beam. The filters enable direct irradiance to be
determined in the following regions: 525-2800 nm, 630-2800 nm, 710-2800 nm, and 380-2800 nm.
Subtracting readings made with different pyrheliometer filters made it possible to evaluate the incident
energy in the wavebands 380-525 nm (blue), 525-630 nm (green-orange), 630-710 nm (red), and 380710 nm. The latter band corresponds to the so-called photosynthetically active radiation (PAR band). It must
be noted here that a quartz filter usually has a nominal cut-off wavelength of approximately 250 nm (Iqbal,
1983). However, this cut-off is taken as 380 nm as determined by NOA. Although the discrepancy in the
quartz cut-off wavelength is rather large, the energy in this waveband is small and introduces only minor
errors (Jacovides et al., 1993a,b).
The Linke-Feussner pyrheliometer was situated at NOA, on a small hill (about 30 m above the street level
of Athens) in the centre of Athens, a city known for its high pollution level. The instrument was calibrated
periodically, and compared approximately once a year with a 'standard' set kept inside the laboratory. The
absolute calibration of the 'standard' set was controlled by comparison with an Angstrom compensation
pyrheliometer. Total experimental error is of the order of 3% for an instantaneous measurement in a given
band. In the band energies the error may also be somewhat larger, about 8 per cent, because these energies
are obtained as differences between readings of several filter pyrheliometers. The measurements were
corrected for the attenuation of the light by filters following the instructions of the Radiation Commission
(CSAGI, 1957) and those of the manufacturer. In addition the measured irradiances were corrected for
variation in temperature of the thermopiles.
An Eppley PSP pyranometer was used for measuring total global irradiance. The diffuse irradiance was
calculated from the difference between the corresponding values of the global and direct beam component of solar
irradiance on a horizontal surface. Additionally, other necessary meteorological parameters, such as temperature,
relative humidity, pressure, and cloud amount are available on a daily routine basis.
Furthermore, the normal incidence irradiance at the Earth's surface through an aerosol-free atmosphere with a
specified water vapour content, i.e. I*, is calculated following the Bird and Hulstrom (1981) formulation:
I* = 0. ~ ~ ~ E I J Z R Z ~ Z W Z G
(9)
where Eo is the solar constant corrected for departure of the Sun-Earth distance from the mean value. For
completeness, the various transmittances and other related quantities are listed below.
The transmittance by Rayleigh scattering zR is given as (Iqbal, 1983),
ZR
+
= exp[-O. 0903 m0'84(l m - m""))]
where m is the air mass, duly modified by station pressure,
m = m,(P/Po)
where now m, the relative air mass given by Kasten (1966):
m, = [sin h
+ 0. 15(h + 3. 885)-1'253]-'
(10)
233
TURBIDITY AND SOLAR RADIATION IN ATHENS
and h is the solar altitude. The ozone transmittance is as follows:
TO
= 1 - [O. 1611U3(1
+ 139*48U3)-0.3035
- O.O02715U3(1 +
+ O*OO03U32)-1]
(13)
where U3= I m, and I is the thickness (in cm) of the total amount of ozone in the vertical direction, reduced to
standard pressure. The long-term spatial and temporal variations of I are given in Iqbal (1983). The transmittance
by water vapour is given as,
TW =
1 - 2. 4959U1[(I
+ 79-034Up 6828 + 6.385U11-l
(14)
where
U, = Wm,
(15)
and W is the sea-level water content, which is calculated through the equation (Louche et al, 1987)
W
= 0*492(4/T)exp(26.23 - 5416/T)
(16)
where T is ambient temperature in degrees Kelvin and q5 is relative humidity in fractions of one.
The transmittance by uniformly mixed gases, essentially O2 and C02 is defined as (Iqbal, 1983):
TG
= exp (-0.0127 mo’26)
(17)
Furthermore, for the calculation of the hgstrom turbidity factor fl, equation (9) is rewritten as,
I = 0- ~~~EOTRTOTWZGT~
where zA is the aerosol transmittance, which can be obtained from Iqbal (1983), and is given as,
= (0.12445~- 0.0162)
(18)
+ (1.003 - 0 . 1 2 5 ~ x) exp[-flm(l.O89a + 0.5123)]
(19)
Combining equations (18) and (19) by using the other transmittances defined above, an explicit expression for
fl can be obtained, assuming an average size distribution represented by the wavelength exponent a = 1-3.
Thus,
TA
1
fl=-h mD ( A C B )
B = 0 . 1 2 4 4 ~- 0.0162
(22)
C = 1.003-0.125~
(23)
+
D = 1 . 0 8 9 ~ 0.5123
(24)
It is because of the parameterization of aerosol transmittance, equation (1 9), that fl can be obtained explicitly from
direct total irradiance measurements. This is due to the fact that recently the transmittance of aerosols has been
parameterized in this manner (Iqbal, 1983; Machler, 1985). It must be noted that the spectral or filter
measurements of fl do not require water vapour or ozone content of the atmosphere.
4. RESULTS AND DISCUSSION
Before proceeding further with the results of the turbidity parameters it is instructive to examine the accuracy of
the parameterization scheme for the hgstrom coefficient. For the same pyrheliometric measurements the ‘true’
turbidity parameters a0 and j o have been calculated (Karalis, 1976). In the case that fl and flo coincide, it has been
found that the values of wavelength exponent a. ranged between 1.14 and 1.39. Figure l(a) shows the fl factor
versus the ‘true’ turbidity factor flo obtained directly through the pyrheliometric formula. The agreement between
the two is good (I? = 0.992), implying that the parameterization formula works adequately. In addition, the fl
234
C. P JACOVIDES AND J. D. KARALIS
0.6 Y = 0.00139 + 1.0108 X
a
R'=0.992
(0)
L
0
0
0.6 -
9
F
II
0
.w
u
2 0.4
x
._
V
.n
s0.4 -
I-
A
.-+
.-73
L
0
+
U
u
5 0.2
20.2
(u
2
-
!r
0.0
0
I
0.2
q.4
0.6
Angstrom Turbidity Factor
'"'8.0
0.2
0.4
0.6
Turbidity Factor a t a= 1.3
Figure 1. M i d i t y values j9 versus 'true' turbidity values PO(a); and turbidity Bll = I .O versus turbidity b.,=
I .3
(b)
turbidity values shown in Figure l(a) are based on a = 1.3. The p values were recomputed assuming a = 1.O. The
turbidity values are plotted in Figure l(b), showing very little influence of a with a = 1.O or 1.3. The turbidities are
related to each other by the regression line,
with a correlation coefficient R2= 0.998. An equation similar to (25) was reported by Louche et al. (1987), for
Ajaccio, a Mediterranean coastal site in France. Mean monthly values of TL, Tm, and p factors and their standard
deviations (SDs) are given in Table I. An annual cycle is evident for the three coefficients; summertime values are
higher than winter values. The annual variation of turbidity parameters in Athens is related to weather conditions
throughout the year. During winter frequent rains remove from the atmosphere a considerable amount of aerosols
by rainout and washout. The steady decrease of turbidity coefficients towards the end of the late summer period is
attributed to the diffusion mechanism, the effectiveness of which increases with velocity (Kallos et al., 1993).
During the late summer (August through to September) the prevailing winds, called Etesians, increase in
frequency and intensity (Karalis, 1976). The abrupt reduction of turbidity in September is due to the rains
observed at the end of this month after a long period of dryness. Generally, throughout the year TUMlevels in
Athens are higher than those reported by Rawlins and Armstrong (1985) for various locations in Britain.
Accordingly, the fi levels in Athens are higher than those reported by Louche et al. (1987) for Ajaccio (France) or
the rural site of Avignon (Katz et al., 1982). Finally, the TL levels are higher than those reported by Katz et al.
(1982) for Avignon, and of about the same order with the turbidity levels of Dhahran (Saudi Arabia)
(Abdelrhahman et al., 1988). Similar trends of TuM in various locations have been reported in the past (Flowers et
al., 1969; Peterson et al., 1981).
The mean turbidity data, such as in Table I, can be used in the design of solar energy utilization systems. The
entries in Table I indicate also that the values of SDs are relatively high in respect to the mean values. These high
deviations can be attributed not only to the influence of the local climatic conditions and other natural phenomena,
but also to the rapid development of the city of Athens. Earlier studies (Jacovides et al., 1993a,b), performed over
various spectral wavebands, have reported a pronounced decline in the period (1966-1990), which was attributed
to increasing levels of air pollution due to the continuous development of the city during this period, and to the
increasing number of the vehicles in circulation. This implies that TL, Tm, and p factors have increased during the
same period. Therefore, it becomes obvious that the determination of the long-term variation of TL,,,T and fl as
representative of the aerosol loading in the atmosphere is of particular interest. Figures 2-4 show the time
sequence of monthly mean values of TL, TuM,and 6, respectively, and their standard deviations, as estimated from
monthly data for the period under study, 1954-1 99 1. In addition, the data was smoothed by using a simple moving
average, and is shown in the figures.
235
TuRBIDlTY AND SOLAR RADIATION IN ATHENS
In general, the turbidity coefficientsincrease gradually from 1954, until approximately 1985; thereafter decrease
gradually. These long-term variations of the attenuation coefficients may be attributed to the increasing number of
circulating vehicles and industrial activity in this period in the city of Athens (it must be noted here that during the
beginning of the 1960s the number of circulating vehicles was about 60 000 whereas at the end of the 1980s the
number jumped up to one million and even more). From the individual points of the time sequences it is clear that
from mid-l980s, the turbidity coefficients tend to decrease slightly. This fact is due to particular preventative
actions, especially driving restrictions taken during the last decade. For instance, restrictions on the circulating
vehicles were imposed in the downtown of Athens area during working days. Additionally, a gas producing unit,
about 1.5 km from the centre of the city was removed in 1985. Another interesting feature is the long-term
variation of their SDs. It can be seen from the figures that the standard deviations follow closely the mean monthly
trend of the coefficients.
Following Unsworth and Monteith (1972) the turbidity coefficient TUM was correlated with
the Linke turbidity factor TL. Figure 5(a) shows the variation of Unsworth-Monteith’s attenuation coefficient
TuM versus Linke factor TL for all air masses encountered and for all data points. The regression line can be
written:
TUM= -0.185
+ 0.0839T~
or
TL = 2.24
+ 11.52Tu~
Equation (26) has a correlation coefficient R2= 0.989. Unsworth and Monteith (1972) produced a diagram (Figure
1 in their paper) with TL against T m for m = 1, 3, 5, from whlch the following equation can be derived (for
m = 1):
Comparing equations (27) and (28) it is seen that the slopes and the intercepts compare well. This is due to the fact
that the data used in the present analysis, i.e. mid-day observations, correspond to an air mass number <2, as can
be seen from Table I. Furthermore, when TuMtends to zero the value of TL is 2.24. The corresponding theoretical
value is 1.O. This disagreement is due to the great fluctuations of the daily values. If now monthly mean values are
assumed the results are very close to the theoretical ones. In Figure [email protected]), mean monthly values of TuM versus
Table I. Monthly statistics of Linke factor, TL, Unsworth-Monteith factor,
Month
TL
January
February
March
April
May
June
JdY
August
September
October
November
December
Annual
2.88
3.15
4.46
4.03
5.14
5.55
5.75
5.37
4.01
4.62
3.33
2.82
4.98
SD
TUM
0.822
0.841
1.206
1.092
1.214
1.221
1.317
1.206
1.025
1.145
0.772
0.541
1.251
0.154
0.166
0.2 10
0.207
0.228
0.245
0.248
0.252
0.204
0.224
0.173
0.145
0.22 1
TUM,
SD
B
SD
0.071
0.076
0.108
0-099
0.1 11
0.1 13
0.118
0.109
0.09 1
0.103
0.069
0.050
0.105
0.076
0.114
0.188
0.055
0.056
0.080
0.073
0.08 1
0.082
0.086
0.080
0.074
0.067
0.052
0.036
0.086
0.125
0.196
0.203
0.227
0.206
0.171
0.185
0.105
0.089
0.158
Angstrom factor 8, and air mass numbers
m
SD
(1120 LST)
2.079
1.729
1.355
1.174
1.090
1.066
1.109
1.139
1.259
1.482
1.859
2.162
1.458
m
SD
(1 420 LST)
0.087
0.107
0.079
0.039
0.015
0.009
0.045
0.075
0.08 1
0.092
0.105
0.087
0.077
2.265
1.817
1445
1.267
1.177
1.137
1.165
1.214
1.402
1.745
1.987
2.549
1.606
0.133
0.107
0.076
0.040
0.018
0.005
0.125
0.135
0.136
0.147
0.140
0.024
0,093
-
236
C. P. JACOVIDES AND J. D. KARALIS
8.0
&
-Linke Turbidity Factor TL
.-**-..
SD for T,
L
3 6.0
0
0
L
.-3 4 . 0
-0
.-
-2
22.0
a,
Y
C
2 0.0
1950195519601965197019751980198519901995
Year
Figure 2. Time series of monthly mean values of Linke turbidity factor TL(solid lines) and its standard deviation (dashed line), together with the
moving window average values (dot lines). The window extends 12 points leftward and rightward, for a total of 25 points. Values of SD have
been multiplied by 2
Unsworth-Monteith
*---.--.
SD for Tuu
_
c
.
I
0
-w
Factor Turr
Figure 3. As in Figure 2, but for Unsworth-Monteith attenuation coefficient TuM
‘0.3
I
0
t:
5
-
Angstrom Turbidit Factor
.--..---.
SD of Angstrom foptor
p
L
x0.2
+
.-0
.-
f3
I-
0.1
0
-w
I
v)
0
Figure 4. As in Figure 2, but for Angstrom turbidity factor /3
237
TURBIDlTY AND SOLAR RADIATION IN ATHENS
30.8
IL
0
Ty=-0.185 + 0.0839
R =0.989 (a)
30.4
k
TL
L
0
v
v
00.6
u 0.3
0
0
LL
LL
L
.,0.2
5
%0.4
+-
c
c
c
0
0
3
10.2
I
L
c
.+
10.1
Y
L
0
$0.0
c
3
o
2.b
6.0
8.0
inke Turbidity Factor TL
4.0
'
$0.0
10.0 c 0.0
3
O
2.0
I
4.0
6.0
Linke Turbidity Factor TL
8.0
Figure 5. Variation of Unsworth-Monteith coefficient Tm versus Linke factor TL.(a) Daily mean values; (b) monthly mean values
TL are shown, and the resulting regression line is:
TUM= -0.096
+ 0.0689T~
(29)
or
TL = 1 * 3 9 + 13.73Tu~
(30)
with a correlation coefficient of R2= 0.979.
Figures 6(a,b) show the variation of hgstrom turbidity coefficient fi versus TL and TUMfactors, respectively.
The resulting equations are:
p = -0.152
+ 0.0602T~
(31)
/? = 0.00738
+ 0.631 TUM
(32)
and
with correlation coefficients 0.996 and 0.976 respectively.
It is necessary to note that most values of turbidity factors lie in the regions: 4-0-6.5 for TL, 0 . 1 4 3
for Tm, and 0 . 0 5 4 0 2 for /?. These are demonstrated through the histograms of the relative frequency
distribution, plotted in Figures 7(a-c), for the respective turbidity factors, TL, TuM,and 8. Turbidity values that are
exactly on an interval ending point are counted in the interval to the right. These diagrams, in conjunction with the
long-term variation of the turbidity factors, indicate that the air quality of the atmosphere has deteriorated in the
period 1960-1985. Nevertheless, a slight tendency of improvement appears during the last 5 years. This might
have been the result of some preventative measures, as discussed above. However, of greatest interest is the fact
that turbidity levels decrease throughout the 1985-1991 period (see Figures 2 and 3). There is clearly a need to
examine this feature fiuther, especially to determine its areal extent and cause, which is a subject for future work.
It is instructive to examine some correlations between the attenuation coefficient of hgstrom and the spectral
composition of solar radiation. From Table 1 the air mass number in this series of measurements varies between
1.066 and 2.079 for 1120 (LST) and 1.137 and 2.265 for 1420 (LST). According to Unsworth and Monteith
(1 972) the fraction of radiation in the various wavebands is expected to depend on air mass number. For instance,
the fraction of radiation in the visible waveband 300-700 nm is 0-45 for unit air mass number and decreases to
0.42 for air mass 2. Keeping in mind the above, the various fractions of radiation in the different wavebands are
expected to vary little between m = 1.066 and 2, i.e. the range of air mass number concerned in the present
analysis. In addition, Jacovides et al. (1993a,b) reported some evidence on the dependence of the spectral
distribution on the atmospheric turbidity. Therefore, it is interesting to examine this dependency further. In the
following various radiation fractions versus atmospheric turbidity p are presented.
238
C.
I? JACOVIDES AND J. D. KARALIS
a
b0.5
Y
u
n
c0.4
Y = -0.152
R2=0.996 (a)
..
+
0.0602 X
,
“I
*L 0.5
0
-w
Y = 0.00738
R2=0.976 (b)
+
0.631 X
.
g0.4
LL
x
G0.3
.-
+?
z0.2
E
Fo.1
Z0.l
IT
C
4
0.0
0.0
40.0r
0.0
0.2
0.,4
0.6
Unswort h - Monte ith Factor
1
ity Factor TL
1.0
I
a
I
1
0.8
Figure 6. Variation of Angstrom turbidity coefficient versus (a) Linke factor, TL,and (b) Unswortl-Monteith factor, T m
“V
25n
-520
-
>r
I
(C)
-
i153
Figure 7. Histograms of the percentage frequency distribution of turbidity factors; (a) for Linke’s TL,(b) for Urnworth-Monteith TuM and (c) for
Angstrom turbidity factor B
TURBIDITY AND SOLAR RADIATION IN ATHENS
239
Figure 8 shows the dependence of the ratio (PARiDIR) on 8 derived from pyrheliometric readings. The best line
through the points is
PAR/DIR = 0.444- 0.08458
(33)
with a correlation coefficient of the order of R2= - 0.493.
It is clear that the increasing levels of atmospheric turbidity alter the ratio (PAR/DIR) slightly. An equation
similar to equation (33) was reported by Unsworth and Monteith (1972). Taking a value of p= 0.13 (which
corresponds to 0.2 for the T w factor) representing an average amount of aerosol in the air masses concerned (in
the present analysis an overall mean value of 8 = 0.158 was found), the corresponding value of the ratio (PAR/
DIR) is 0.43. This value was reported by Jacovides et al. (1993b). In addition, h a l i s (1989) reported an annual
mean value of the ratio (PAR/DIR) of about 0.45.
Figure 9 shows the dependence of the ratio (blue/DIR) on 8. The resulting regression line is,
blue/DIR = 0.230 - 0.1988
(34)
with R2= 0.68. As aerosol amount increases the energy incident in this waveband reduces. Assuming, as above, a
value of 8= 0.13, the corresponding value of the ratio is 0.205, which coincides with the mean value reported by
Jacovides et al. (1993b), i.e. 0.208. Figure 10 depicts the corresponding ratio (green-orange/DIR) versus 8. The
line fitted to the data points is,
green - orange/DIR = 0.109
+ 0.00778
(35)
with R2= 0.095. This waveband is not affected by the atmospheric turbidity. Figure 11 shows the ratio (red/DIR).
The data points resulted in the following regression line,
red/DIR = 0.104
+ 0.1078
(36)
with R2= 0.613. The dependence of this irradiation ratio on the turbidity is clear. Taking as above, 8 = 0.13,
the resulting value of the ratio is 0.110, whereas the reported value in Jacovides ef al. (1993b) is
0.093.
From the overall analysis it is clear that the spectral distribution of the direct beam irradiance is affected
directly by the aerosol amount in two ways: the shorter wavelengths, i.e. blue-band, decrease with increasing
levels of turbidity; whereas the longer wavelengths, i.e. red-band, increase with increasing levels of aerosol
amount. The above is consistent with the view that when a shift in spectral distribution takes place, the
energy taken away from the one side of the spectrum is approximately compensated by energy from the other
side (Robinson, 1966).
There is evidence that the ratio of diffuse to global irradiance in the total solar waveband
(DIF/GLOB) depends both on solar zenith angle and on atmospheric turbidity @ogniaux and Doyen, 1968;
Unsworth and Monteith, 1972). Dogniaux and Doyen showed that this ratio would be related linearly to Linke's
Y = 0.444-0.0845 X
42
u
. .
20.6
'
0.0
0.0
.... .
0.1
0.2
0.3
0.4
0.5
Angstrom Turbidity Factor P
Figure 8. Variation of the visible, 380-710 nm, fraction of direct total solar radiation (PAR/DIR) versus hgstrom turbidity factor
240
C. !F JACOVIDES AND J. D. KARALIS
R. = - 0 . ~ 8
4-4
g0.4
CK
-
e0.3
U
C
20.2
I
a,
3
mO.l
. , ... ..
a
.'
0.0
0.0
*
., .
a
) *
,
0.1
0.2
0.3
0.4
0.5
Angstrom Turbidity Factor P
Figure 9. As in Figure 8, but for the waveband 38&525 m (bluelDIR)
Y
+
Y = 0.109
R2=0.095
20.3
C
0.0077 X
..
-
0
n
I
g0.2
C
e
0
I 0.1
C
a,
Q)
*
-..
. . ..
., . ..
0.1
0.2
0.3
0.4
0.5
Angstrom Turbidity Factor P
Figure 10. As in Figure 8, but for the waveband 525630 nm (green-orangeDIR)
Y = 0.104
R2=0.61 3
rr 0.3
0.107 X
.. .
n
0.0
+
'
0.0
0.1
0.2
0.3
0.4
0.5
Angstrom Turbidity Factor P
Figure 11. As in Figure 8, but for the waveband 630-710 nm (redlDIR)
TURBIDITY AND SOLAR RADIATION IN ATHENS
1.0
0.8
r
I-
0.0
.
Y = 0.0604
.R2=0.856
+
24 1
0.874 X
0.1
0.2
0.3 0.4 0.5
Angstrom Turbidity Factor P
Figure 12. Variation of the diffuse fraction of global solar radiation @IF/GLOB) versus j?, on cloudless days
turbidity factor, TL, at fixed air-masses. Unsworth and Monteith showed that for zenith angles less than 60°, the
relationship between (DIF/GLOB) versus TuM,was well fitted by a straight line. Figure 12 shows the variation of
(DIF/GLOB) versus 8. The points were fitted by the regression line,
DIF/GLOB = 0.0604 + 0.8748
(37)
with a correlation coefficient R2= 0.856. The scatter of points may reveal differences in aerosol size distribution.
Equation (37) predicts that as the aerosol content tends to zero, the ratio @IF/GLOB) should tend to 0.0604. The
corresponding theoretical ratio is 0.072 for a model atmosphere containing 2 cm precipitable water.
5. CONCLUSIONS
There is a growing world-wide interest in atmospheric turbidity because this is related to air pollution studies and
because of its wider significance in tropospheric chemistry, climate studies and in technological utilization of solar
energy. From the overall analysis the principal conclusions are as follows:
(i) Broad-band turbidity coefficients, which depend upon the attenuation over the entire solar spectrum (3002800 nm) and which can be determined from unfiltered pyrheliometric measurements of direct beam solar
irradiance, are presented. Summertime turbidity levels are found to be larger than winter values. This is
attributed to the high synoptic winds and more frequent rains during winter time, which have a cleansing
effect on the atmosphere.
(ii) An interdependence between turbidity factors was found and is expressed as a mathematical h c t i o n . Values
of 8 turbidity coefficient compare well with those predicted from the so-called pyrheliometric formula 80.
(iii) From the long-term variation of atmospheric turbidity coefficients in conjunction with their frequency
distribution, some interesting information on the time evolution of air quality for a longer period in the past
can be drawn indirectly. Additionally, the reported results on the turbidity coefficients can be used in the
design of solar energy utilization systems.
(iv) The dependence of the various fractions of direct beam solar radiation in the various wavebands was
investigated further. The relation between these fractions and 8 was found to be linear. The results reported
here substantiate the findings of earlier works (Jacovides et al., 1993a,b). Finally, the variation of the ratio of
diffuse to total global radiation is investigated and the results agree with those reported in Unsworth and
Monteith (1972) and Dogniaux and Doyen (1968).
242
C. P. JACOVIDES AND J. D. KARALIS
ACKNOWLEDGEMENTS
The data used in this study were provided by NOA. The director of the Meteorological Institute of NOA, Professor
Dr D. N. Asimakopoulos is greatly acknowledged.
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