ap-6-10.dvi


Acta Polytechnica Vol. 50 No. 6/2010

Color Portion of Solar Radiation in the Partial Annular Solar Eclipse,
October 3rd, 2005, at Helwan, Egypt

A. H. Hassan, U. A. Rahoma, M. Sabry, A. M. Fathy

Abstract

Measurements were made of various solar radiation components, global, direct and diffuse and their fractions during
the partial annular solar eclipse on October 3rd, 2005 at Helwan, Egypt (Lat. 29.866◦ N and Long. 31.20◦ E), and an
analysis has been made. The duration of the solar eclipse was 3 h 17 min, and the maximum magnitude of the eclipse
in this region was 0.65. The optical depth of the direct component and the relative humidity decreased, while both
the transparency and the air temperature increased towards the maximum eclipse. The general trends of the global
components are decreasing optical depth and increasing transparency between the first contact and the last contact. The
prevailing color during the eclipse duration was diffused infrared (77 % of the total diffuse radiation level).

Keywords: diffuse infrared solar radiation, partial solar eclipse, meteorological data, optical depth, transparency, linke
turbidity and Angstrom turbidity.

1 Introduction
The greatest eclipse is defined as the instant when
the axis of the Moon’s shadow passes closest to the
Earth’s center. For total eclipses, the instant of
greatest eclipse is virtually identical to the instants of
greatest magnitude and greatest duration. However,
for annular eclipses, the instant of greatest duration
may occur either at the time of greatest eclipse or
near the sunrise and sunset points of the eclipse path.
OnMondayOctober 3rd, 2005, apartial annular solar
eclipse of the Sun was visible from within a narrow
corridor which traversed half the Earth. The instant
of greatest eclipse occurred at 10:32 UT, when the
axis of the Moon’s shadow passed closest to the cen-
ter of the Earth. The maximum duration of totality
was 4 min 32 s; the Sun’s altitude was 71◦, and the
path width was 162 km. The maximum magnitude
was 0.95 at Lat. 12◦8′N and Long.E [1].
Extinction may be caused by a molecular ab-

sorption that is wavelength-dependent and follows
the Rayleigh formula. The molecular absorption ap-
pears in the form of absorption bands projected on
to the continuous background spectrum. In a clear
sky, at lower atmospheric layers in the wavelength
range 500–650 nm, extinction has three known com-
ponents. It consists ofmolecularabsorption following
Rayleigh scattering; absorption at a discrete wave-
length by water vapor; and weakening by the Chap-
puis band of ozone [2]. The absorbing components
of the atmosphere are O2, O3, H2O, CO2, N2, O,
N, NO, N2O, CO, CH4 and their isotopic modifi-
cations, though the contributions of the latter are
small. Spectra due to electronic transitions ofmolec-

ular and atomic of O, N, O3, lie chiefly in the ultra-
violet region, while those due to the vibration and
rotation of polyatomic molecules such as H2O, CO2
and O3, lie in the infrared region. There is a very
little absorption in the visible region. As the absorp-
tion coefficients associatedwith electronic transitions
are generally very large, much of the UV is absorbed
in the upper layers of the atmosphere. Some of the
Oxygen and Nitrogen molecules are dissociated into
atomic Oxygen and Nitrogen owing to absorption of
the solar radiation, while other molecules are ion-
ized. Dissociated atomic Oxygen and Nitrogen are
also able to absorb solar radiation of still shorter
wavelength, and some of these atoms become ionized
as a result. The ionized layers in the upper atmo-
sphere are formedmainly because of these processes.
Owing to the very strong absorption by O2, N2, O,
N andO3 in the spectral region up to about 300 nm,
the solar radiation in this region does not reach the
earth’s surface. In the visible region, there is some
absorption due to the weakChappuis bands of ozone
and due to the red bands ofmolecularOxygenwhich
occurat about690and760nm. IRabsorptionbywa-
ter vapor occurs at about 700, 800, 900, 1100, 1400,
1900, 2700, 3200and6300nmandbyCO2 at about
1600, 2000, 2700 and 4300 nm. These bands play a
part in the absorption in the lower atmosphere, be-
low 50 km, where water vapor and CO2 are largely
concentrated. No photochemical action is associated
with absorption in this region, and the absorbed en-
ergy is used entirely to heat the lower atmosphere [3].
Many studies of the variation of solar radiation

and transparency have been carried out in recent
years, dealing with solar eclipse totality and partial-

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Acta Polytechnica Vol. 50 No. 6/2010

ity in different countries. A study of atmospheric
responses due to the 11 August total solar eclipse in
Romania, conducted by Copaciu and Yousef (1999),
indicated that both global radiation and UVB ra-
diation dropped dramatically to a minimum around
totality. There was an opportunity to study the at-
tenuation of such radiation due to clouds. The net
radiation became negative for about 17 minutes at
Cãldãrusani. The temperature dropped to about
30◦Csoonafter totalityatbothAfumati andClarasi,
although at the beginning of the eclipse it was about
46.5◦C at Afumati and 34◦C at Cãalãarasi. At
Cãldãrusani, the surface temperature dropped from
34.1◦C to 29◦C. It seems likely that the air tem-
perature inside the umbra is between 29–30◦C. The
response time of minimum surface temperature was
about 18 minutes, which is comparable to the dura-
tion of the negative part of the net radiation when
the backward radiation became higher than the in-
cident radiation [4]. Studies of simultaneous mea-
surements of radiation; photolysis frequencies, O3,
CO, OH, PAN and NOx species were carried out in
the boundary layer, along with the relevant meteo-
rological parameters, under total solar eclipse con-
ditions [5]. This experiment, performed at about
34 solar zenith angles and under noontime condi-
tions, thus provided a case study of the interac-
tions between radiation and photochemistry under
fast “day-night” and “night-day” transitions, at high
solar elevation. The results revealed a close correla-
tion between photolysis frequencies and the UV ra-
diation flux. Due to the decreasing fraction of direct
radiation at shorter wavelengths, all three parame-
ters showed much weaker cloud shading effects than
global solar radiation. NO and OH concentrations
decreased to essentially zero during totality. Subse-
quently,NOandOHconcentrations increased almost
symmetrically with their decrease preceding totality.
The NO/NO2 ratio was proportional to NO2 over
±30 min before and after totality, indicating that
the partitioning of NOx species was determined by
JNO2. Simple box model simulations show the ef-
fect of reduced solar radiation on the photochemical
production of O3 and PAN. A study was made of
the depression of the different solar radiation com-
ponents during the solar eclipse, August 11th, 1999,
overEgypt (asapartial solar eclipse, 70%coveringof
the solar disk in Helwan, Egypt) [6]. The maximum
depressionvalues in the different components of solar
radiation was 54 % in red solar radiation (for global
and direct), while theminimumdepressionwas in in-
frared solar radiation (34 % for global and 41 % for
direct). The clearness index and the diffuse fraction
were 0.634 and 0.232, respectively. The atmospheric
red radiationwas 7.4%and the atmospheric infrared
radiation was 10.7 %. The percentage of ultraviolet
was 3 %. A study of the spectral composition of

global solar radiation by interference metallic filters
was carried out during the same previous eclipse in
August 11th, 1999 in Helwan, Egypt [7]. The con-
clusions indicated an increase in the whole interval
from350–450nmbutwithout risk to the human eye.
This interval lies at the end of ultraviolet solar ra-
diation, while the minimum variation lies between
500–700 nm. This interval represents the normal
maximum peak of the solar spectrum, and goes up
to the 700–900 nm band. The change in the mete-
orological parameters is related to the variability of
the solar spectrum shift from the short wave band to
the longwave band. The maximumdrop in the solar
spectrum lies in the interval that consists of the nor-
malpeak of the solar spectrum from500–600nm. An
investigationwasmade of the effects of pollutants on
the color portion,where the increase in pollutants re-
duces the violet-blue band by 11%, the green-yellow
bandby 14%, the red band by 13%and the infrared
band by 5 % of the average annual values [8].
Using ground-based spectral radiometric mea-

surements taken over the Athens atmosphere inMay
1995, an investigationwas carriedoutof the influence
of gaseous pollutants and aerosols on the spectral ra-
diant energydistribution. Itwas found that the spec-
tralmeasurements exhibited variationsbased onvar-
ious polluted urbanatmospheric conditions, as deter-
minedbygaseouspollutants recordanalysis. The rel-
ative attenuations caused by gaseous pollutants and
aerosols can exceed 27 %, 17 % and 16 % in the
global ultraviolet, visible and near infrared portions
of the solar spectrum, respectively, as compared to
“background” values. In contrast, an enhancement
of the near infrared diffuse component by 66 % was
observed, while in the visible and ultraviolet bands
the relative increases were 54 % and 21 %, respec-
tively [9].
The aim of the present work is to study and de-

termine the percentage of color portion variations for
the different solar radiation components during the
solar eclipse onOctober 3rd, 2005 at Helwan, Egypt.

Instruments and Measurements
Equipment was installed on the roof of the National
Research Institute of Astronomy and Geophysics
(NRIAG) building in Helwan, (29◦54′N 30◦20′E,
126 m elevation above sea level). The background
is taken as desert and pollution. Measurements were
conducted from sunrise to sunset. The time of mea-
surements was taken as the local mean time of Cairo
(GMT+2 hours).
The instruments used in this work were:
• A pyrheliometer for measuring the direct solar
radiation, in three different bands, direct
yellow (Y) (530–2800 nm), direct
red (R) (630–2800 nm), direct

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Acta Polytechnica Vol. 50 No. 6/2010

infrared (IR) (695–2800 nm), and also the total
direct band (I) (280–2800 nm).

• Four pyranometers for measuring the different
components of global solar radiation
(G, 280–2800 nm), global ultraviolet
(GUV , 285–385 nm), global infrared
(GIR, 695–2800 nm) and a black-and-white
type sensor to measure the diffuse
(D, 280–2800 nm) solar radiation.

• A meteorological station to measure the
different meteorological parameters.

Theoretical background

To calculate the extraterrestrial solar radiation at
any time during the partial solar eclipse, we carried
out the following:

Ei at eclipse = (Ei)(1 − M) (1)

where Ei is substituted by any radiation quantity,
e.g. Go, GIRo, GUVo, B1, B2, B3 and B4. Optical
depth (α) and transparency (τ) are calculated by the
formula:

Ibλ = Ioλ exp(−αm) (2)
where α and τ may be calculated as

α = − ln(Ibλ/Ioλ)(1/m) (3)
τ = 1/exp(α · m). (4)

The calculations of the extraterrestrial solar radia-
tion for the bands of various components bands are
based on [10].
The diffuse infrared (DIR) was calculated from

the equation:

DIR = GIR − IRCOS(Θ) (5)

The Linke turbidity factor, LT is given by:

LT =
1

δRmA
· ln ·

[
I0
I

]
(6)

where δR is given by:

δR =
1

9.4+0.9 · mA
(7)

where mA is given by:

mA=

[
P

1013.25
·

1
cosθ +0.15(93.885− θ)−1.253

]
(8)

The total amount of water vapor in the atmo-
sphere in the vertical direction is highly variable and
depends on the instantaneous local conditions. This
amount, expressedasprecipitablewater W (cm), and
can be readily computed through a number of stan-
dard routine atmospheric observations. The precip-
itablewater vapor can vary from0.0 to 5 cm [11, 12].

W =

[
0.493 · (Φr) · exp[26.23− (5416/tk)]

Tk

]
(9)

The Angstrom turbidity coefficient is a dimen-
sionless index that represents the amount of aerosol,
and the relation between the Linke turbidity (LT)
and the Angstrom turbidity (β) for Helwan is [13]:

β = −0.194933+0.0620059LT (10)

Results and discussion
Table 1 characterizes the phase and magnitude (the
fraction of the sun’s diameter covered atmid eclipse)
at different stages of the partial solar eclipse under
study at Helwan, Egypt. The duration of the solar
eclipse was 3 h 05 m, with maximum magnitude in
this region of 0.65 [1].

Table 1: Characterization of the partial solar eclipse,
3–10–2005 at Helwan

Eclipse Phase Magnitude hh:mm:ss a Az

S.P.E 0 10:27:14.4 51 149

M.E 0.65 11:59:11.2 56 187

E.P.E 0 13:31:41.3 47 222

Table 2 characterizes the environmental and me-
teorological conditions of the eclipse day in Helwan,
e.g. sunrise (S.R), upper transit of the sun (T.S),
sunset (S.S), dry-bulb temperature (Td), wet-bulb
temperature (Tw), airpressure (P), cloudcover (Cl.),
visibility (V is.), relative humidity (R.H) and dew
point (D.P).
Fig. 1 shows the temporal measurements of the

hourly variation of various global solar radiation
components, global horizontal (G), global infrared
horizontal (GIR) and total diffuse horizontal (D)
as well as the extraterrestrial solar radiation, Go in
(W/m2).

Table 2: Characterization and environmental conditions of the eclipse day

S.R T.S S.S Td Tw P Cl. V is. R.H D.P

hh:mm hh:mm hh:mm ◦C ◦C hPa Okta Km % ◦C

05:48 11:43 17:38 29.1 21.88 999.62 0 5.0 54.6 18.62

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Acta Polytechnica Vol. 50 No. 6/2010

Fig. 1: Hourly variation of G, GIR, D and Go

Fig. 2: Hourly variation of GU V , and GU Vo

This figure clearly shows the depression of the ir-
radiance of all components due to the eclipse, while
the depression of the diffuse radiation is lower, be-
cause of the percentage of direct change to diffuse
through the layer of atmosphere. Fig. 2 shows the
hourly variation measurements of global ultravio-
let solar radiation (GUV ) along with the extrater-
restrial global ultraviolet solar radiation (GUV o).
Fig. 3 shows the hourly variation measurements of
various direct solar radiation components: total di-
rect (I), direct yellow (Y), direct red (R) and di-
rect infrared (IR), in (W/m2). The depression gradi-
ent starting from the total to infrared bands passing
through the yellow and red bands before and after
the eclipse is clearly shown in the graph, but the

difference between the bands is narrow during the
maximum eclipse.

Fig. 3: Hourly variation of I, Y , R and IR

Fig. 4: Hourly variation of Kt, Kd and GU V

Fig. 4 shows the hourly variation of various clear-
ness indices, e.g. Kt, KUV and diffuse fraction Kd.
The clearness indices have higher values during the
eclipse, while the Kd value suffers no variation be-
cause the percentage decrease of diffuse is equal to
the percentage decrease of the global value. Fig. 5
shows information on the meteorological conditions
before, during and after the partial solar eclipse at
Helwan site, i.e. dry-bulb temperature (Td) and rel-
ative humidity (RH %). The decrease in ambient
temperature and the increase in relativehumidity are

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Acta Polytechnica Vol. 50 No. 6/2010

recorded as 1.8◦C and 2 %, respectively, as the dif-
ference between the first contact and the maximum
eclipse. Fig. 6 shows the hourly variation of the color
portion of the direct bands B1, B2, B3 and B4 over
the whole day from sunrise to sunset. The highest
short wavelength values (B1 and B2) over the day
are at low air mass (around true noon), while the
top long wavelength value (B4) is at higher air mass
near sunrise and sunset.

Fig. 5: Hourly variation of ambient temperature and rel-
ative humidity

Fig. 6: Hourly variation of B1, B2, B3 and B4

Fig. 7 shows thehourlyvariationof the horizontal
global infrared GIR and the direct infrared IR over
the whole day. The IR component is predominant
outside the eclipse period, but this changes during

an eclipse. The difference between GIR and IR is the
diffuse infrared (DIR) that appears in Equation 5.
It is clear from this figure that the direct infrared
is dominant before and after the eclipse, but during
the eclipse, the global infrared is dominant. Fig. 8
shows the hourly variation of the irradiance of the
total diffuse D and the diffuse infrared DIR, where
it is clear that the total diffuse radiation values were
higher than the diffuse infrared radiation values be-
fore, after and during the eclipse. Fig. 9 shows the
ratio (RD) of diffuse infrared (DIR) to the total dif-
fuse, where the maximum ratio RD conjugates with
themaximumeclipse, and the duration of RD conju-
gates with the duration of the eclipse.

Fig. 7: Hourly variation of IR and GIR

Fig. 8: Hourly variation of D and DIR

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Acta Polytechnica Vol. 50 No. 6/2010

Fig. 9: Hourly variation of DIR/D alongwith theEclipse
magnitude

Fig. 10: Hourly variation of Kd and KdIR

Fig. 10 compares the total diffuse fraction Kd
with the infrared diffuse fraction KdIR.. The top
value of KdIR wasverynear sunrise and sunset (high
airmass) andnear themaximumof the eclipse, while
the top Kd value was very near sunrise and sunset
only, while the minimum value was in the middle of
the day (low air mass). Fig. 11 shows the different
percentage of the color portion (C–P) through the
day from 0800 to 1600, passing through the different
intervals of the eclipse for the different bands. This
figure shows that theprevailing color in the clear case
is IB4 > IB1 > IB2 > IB3. These results agreewith

Figs. 7 and 9, where the prevalent color during the
eclipse is diffuse infrared. Thepercentage of the color
portion at the true eclipse interval shows the same
trend. However, the C–P in the direct infrared IB4
during the eclipse is low, while the high values are
very near to sunrise and sunset, where there are high
air masses, which are the major causation of the ab-
sorption and scattering of the infrared wavelengths.
Generally, the results for the color portion agreewith
previous work in this location [8].

Fig. 11: Variation of color portion of the different bands
over the day of eclipse

Table 3 presents the hourly variation of the opti-
cal depth (α) and transparency (τ) from0800 to 1600
through the duration of the eclipse of the global (G),
global infrared (GIR), global ultraviolet (GUV ), total
direct (I) aswell as direct color bands IB1, IB2, IB3
and IB4. This table demonstrates that the top op-
tical depth (α) and low transparency (τ) are for the
GUV , where the low transparency for GUV has two
causes. Firstly, the intensity of the scattered light is
proportional to 1/λ4 and to the square of the volume
of the particle [10, 11]. This means that the inten-
sity of the scattering of UV light is eleven times the
scattering of red light. This region is characterized
by the high pollutant limit and the large size of the
pollutants (mainly Ca and Fe) [8, 14]. Secondly, the
ozonosphere absorbs a large amount of this band.
Generally, the transparency increases gradually

from the short wavelength to the long wavelength.
The general trend of the global components in G
and GIR is the low optical depth (α) and high trans-
parency (τ). The coefficient of the atmospheric at-
tenuation is directly proportional to the wavelength,
showing a general reddening. At maximum eclipse,
the optical depth (α) is less and the transparency (τ)

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Acta Polytechnica Vol. 50 No. 6/2010

is higher in all bands. This is because the air tem-
perature decreased by 1.8◦C and the R.H increased
by 2 %, as shown in Fig. 5, due to the low thick-
ness of the atmospheric layers and, accordingly, lower
optical thickness and higher transparency where the
relationbetween transparencyand temperature is in-
verted [7].
Table 4 presents the different values of Linke tur-

bidity (LT),Angstromturbidity (β), precipitablewa-
ter (W , cm), total diffuse fraction Kd and infrared
diffuse fraction KdIR during the daypassing through
the eclipse period.

Both Linke and Angstrom turbidity values are
higher in the afternoon than in the morning. This
is because of the high temperature in the afternoon,
which expands and excites the gases and the dust in
the atmosphere. The distribution of precipitable wa-
ter (W), diffuse fraction Kd and the diffuse infrared
fraction KdIR give the concept of the atmospheric
character through the eclipse. The high values of LT
and β and W give an idea of the high turbidity of the
day of observation. The prevailing color throughout
the duration of the eclipse was diffuse infrared (77%
of the total diffuse).

Table 3: Various optical depth values (α) and transparency values (τ) during the day, including the phases of the eclipse
(from the FC to the ME to LC) of G, GIR, Guv, I, B1, B2, B3 and B4

8:00 9:00 10:00 10:31 11:00 11:59 13:00 13:31 14:00 15:00 16:00
F.C M.E L.C

G τ 0.696 0.829 0.818 0.784 0.796 0.945 0.796 0.732 0.697 0.653 0.492

α 0.125 0.100 0.136 0.190 0.202 0.047 0.182 0.237 0.257 0.245 0.282

GIR τ 0.657 0.783 0.759 0.727 0.781 0.798 0.789 0.707 0.672 0.565 0.459

α 0.148 0.132 0.191 0.254 0.201 0.190 0.192 0.269 0.288 0.334 0.315

GUV τ 0.164 0.207 0.233 0.216 0.196 0.243 0.215 0.190 0.173 0.154 0.104

α 0.622 0.838 0.991 1.200 1.300 1.172 1.226 1.265 1.249 1.078 0.901

I τ 0.432 0.535 0.615 0.574 0.494 0.654 0.558 0.508 0.466 0.388 0.198

α 0.289 0.333 0.331 0.434 0.563 0.352 0.465 0.516 0.544 0.674 0.645

B1 τ 0.360 0.473 0.594 0.509 0.449 0.613 0.521 0.474 0.433 0.329 0.112

α 0.352 0.398 0.354 0.528 0.639 0.405 0.520 0.568 0.596 0.641 0.870

B2 τ 0.422 0.595 0.692 0.696 0.539 0.712 0.676 0.575 0.498 0.436 0.173

α 0.297 0.276 0.250 0.285 0.493 0.281 0.312 0.421 0.476 0.478 0.698

B3 τ 0.563 0.689 0.764 0.615 0.664 0.585 0.476 0.673 0.601 0.531 0.263

α 0.198 0.198 0.183 0.383 0.327 0.444 0.592 0.301 0.362 0.365 0.532

B4 τ 0.451 0.530 0.586 0.569 0.486 0.632 0.530 0.485 0.456 0.387 0.237

α 0.274 0.338 0.363 0.444 0.576 0.380 0.506 0.551 0.559 0.547 0.573

Table 4: The different values of Linke turbidity (LT), Angstrom turbidity (β), precipitable water (W), total diffuse
fraction Kd and infrared diffuse fraction KdIR during the day passing through the eclipse period

8:00 9:00 10:00 10:31 11:00 11:59 13:00 13:31 14:00 15:00 16:00

F.C M.E L.C

LT 3.541 3.754 3.608 4.657 3.608 3.749 3.749 5.578 5.888 6.071 7.630

β 0.024 0.038 0.028 0.094 0.028 0.037 0.037 0.151 0.170 0.181 0.278

W 3.296 3.128 2.922 3.402 3.440 3.365 3.470 3.575 3.918 3.756 3.710

Kd 0.194 0.193 0.188 0.172 0.192 0.167 0.175 0.184 0.199 0.244 0.401

KdIR 0.380 0.347 0.228 0.198 0.358 0.295 0.278 0.253 0.250 0.216 0.366

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Acta Polytechnica Vol. 50 No. 6/2010

2 Conclusion
The results obtained from this analysis of the spec-
tral composition of global and direct irradiance show
that various atmospheric parameters cause consid-
erable changes to the spectral distribution of radi-
ant energy reaching the ground. Our conclusions are
summarized as follows:
1 – The percentage of prevalent color during the

day is B4 > B1 > B2 > B3. The predominant colors
during the eclipse were infrared, blue, green and yel-
low, respectively. The variation of the color portion
is clearly obvious in B2 and B3, where thepercentage
was higher in B2 and lower in B3 during the eclipse
period. The C–P of B1 and B4 underwent almost no
change. The lowest percent of color portion was in
the red.
2 – At maximum eclipse (ME), optical depth (α)

is lower and transparency (τ) is higher. The air tem-
perature decreased by 1.8◦C and a 2 % increase in
RH was recorded; this was due to the low thick-
ness of the atmospheric layers. The optical thick-
ness was therefore lower and, accordingly, this raised
the transparency values. The general trend of the
global components in G, GIR and GUV are low opti-
cal depth (α) and high transparency (τ) in the first
contact in comparison with the last contact. There
was high optical depth (α) and low transparency (τ)
in GUV , where theozonosphereandtheairpollutants
absorbed a large amount of this band. The top per-
centage of short wave length (IB1 and IB2) over the
day was at low air mass (around true noon), while
the top percentage of the longwavelength (IB4) was
at higher air mass.
The prevalent color throughout the eclipse was

diffuse infrared (77 % of the total diffuse).

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A. H. Hassan, U. A. Rahoma,
M. Sabry, A. M. Fathy
Phone: +20 227 044 422
E-mail: mohamed.ma.sabry@gmail.com
National Research Institute of Astronomy
and Geophysics
Helwan, Egypt

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Acta Polytechnica Vol. 50 No. 6/2010

Nomenclature
a Altitude of the sun above the horizon
Az Azimuth of the sun
D.P. Dew point (Co)
D Measured horizontal diffuse solar radiation
DIR Infrared diffuse solar radiation
F.C First contact of eclipse
G Global solar radiation, 280–2800 nm
GIR Horizontal infrared global solar radiation, 695–2800 nm
Go Extraterrestrial global solar radiation, 250–2800 nm
GUV Horizontal UV global solar radiation, 280–385 nm
GUV O Extraterrestrial UV global solar radiation, 250–385 nm
I Direct solar radiation, 280–2800 nm
B1 Value of band I − Y =280–530 nm
B2 Value of band Y − R =530–630 nm
B3 Value of band, 630–695 nm
B4 Value of band, 695–2800 nm
IB1 Color portion of B1 as a percentage
IB2 Color portion of B2 as a percentage
IB3 Color portion of B3 as a percentage
IB4 Color portion of B4 as a percentage
Ibλ Measured spectral irradiance at wavelength λ
Ioλ Extraterrestrial spectral irradiance corrected for the actual sun – earth distance
IR Direct infrared solar radiation, 695–2800 nm
Kd Diffuse fraction (D/G)
KdIR IR Diffuse fraction (diffuse infrared/global infrared=DIR/GIR)
Kt Clearness index (G/Go)
KUV Clearness index of U V (GUV /GUV o)
L.C Last contact of eclipse
LT Linke turbidity factor
M.E Maximum eclipse or mid eclipse
m Air mass, m = secΘ
M Magnitude of the solar eclipse, defined as the fraction of the solar diameter that is obscured
mA Relative optical air mass
P Air pressure (hPa)
R.H Relative humidity (R.H)
R Direct red solar radiation, 630–2800 nm
RD Ratio of diffuse infrared to the total diffuse= DIR/D
SP E Start of partial eclipse in local time (First contact)
SR Sunrise
SS Sunset
S Measurements of sunshine duration (hour)
So Calculation of sunshine duration (hour)
T.S Upper transit of the sun
Td Dry-bulb temperature (

◦C)
Tw Wet-bulb temperature (

◦C)
Tk Ambient temperature in kelvins
Y Direct yellow solar radiation, 530–2800 nm
α Optical depth for any bands
β Angstrom turbidity coefficient
Θ Zenith angle
τ Transparency for any bands
δR Spectrally integrated optical depth of the clean dry atmosphere
Φr Relative humidity in fraction of one (Φr = R · H/100)

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