MAUSAM, 54, 2 (April 2003), 511-520

551.521.1(620)

On the estimation of global and diffuse solar radiation over Egypt

S. M. ROBAA
Astronomy & Meteorology Department
Faculty of Science, Cairo University - Giza, Egypt
(Received 20 June 2001, Modified 23 July 2002)

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D/H vkSj /kwi dh lkisf{kd vof/k] vof/k n/N ds ijLij laca/k Hkh fu/kkZfjr fd, x, gSA buls izkIr fd, x,
laca/kksa dks ykxw djrs le; ekfir vkSj vkdfyr ekuksa ds e/; csgrj esy ik;k x;k gSA vr% felz ds fdlh Hkh
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lkSj fofdj.k ds fy, rqyukRed v/;;u fd, x,A
ABSTRACT. Measurements of global, H, diffuse, D, solar radiation on a horizontal surface and sunshine duration,
n, at nine meteorological stations have been used to examine the validity of some methods of the estimate global and
diffuse solar radiation. In order to improve the obtained results, for prediction purposes, the investigated area of Egypt
has been divided into five regions represented by the nine selected stations (in cold and hot seasons). An appropriate
regional parameter, K, of an empirical relation of Barbaro et al. has been determined for each region. The agreement
between measurement and estimated values is remarkable. The maximum possible error of estimated values does not
exceed 9.6%. It is seen that the modified formula gives precise estimations for global solar radiation at any Egyptian
locality. Relation between the diffuse fraction, D/H, and the relative duration of sunshine, n/N, are also determined for
each region. Good agreement between the measured and estimated values applying the obtained relations has been found.
Therefore, the relations are recommended for use at any location in Egypt. A comparative study for the global and diffuse
solar radiation over different sites in Egypt has been made.

Key words − Global radiation, Diffuse radiation, Egypt, Sunshine duration.

1. Introduction number of rainy days, sunshine hours and a factor which

depends on the latitude and geographical location of the
The design of any solar energy conversion system place relative to the sea, in calculating the daily total
requires the knowledge of solar radiation data, obtained radiation. Sayigh, 1977 derived his equation by using
over a long period of time. For many countries, these data sunshine duration, relative humidity and temperature.
are not available. Therefore, for locations where measured Sabbagh et al., 1977related daily total solar radiation to
data are not available, empirical relations developed by the sunshine duration, relative humidity, maximum
various investigators are used in estimating global and temperature, latitude, altitude and the location of the place
diffuse solar radiation values using easily obtainable relative to the sea. Hoyt, 1978 developed a more
meteorological parameters such as sunshine duration, complicated theoretical model to give the global
relative humidity, minimum and maximum temperature, irradiation falling on the earth’s surface. Climatological
cloud cover and geographical location. values of total precipitable water, turbidity and surface
albedo was required as the model inputs.
Swartman and Ogunlade, 1967 used the relative
humidity in addition to the sunshine hours in establishing In Egypt, El-Shahawy, 1984 proposed a semi-
their formula. Reddy, 1971 suggested the use of the empirical formula for estimating the global solar radiation.

(511)
512 MAUSAM, 54, 2 (April 2003)

This formula essentially requires: the latitude, sun’s H = 4.9 (n)1.31 + 10550 (sin h) 2.1 (1)
declination, clouds amount and type and back scattering.
He found good agreement between estimated and where, H and n are the monthly global solar radiation
measured values of global radiation on monthly and daily (in cal cm-2) and the monthly sunshine hours, respectively.
basis. El-Shazly, et al., 1998, studied the solar radiation h, is the noon altitude of the sun on the 15 of the month.
characteristics at Qena/ Upper Egypt. They used the
measurements of the hourly global and diffuse solar
radiation on a horizontal surface of Qena in the period Barbaro et al., 1978 modified this formula to fit 31
from June 1992 to May 1993. They discussed the seasonal Italian stations that they divided into three zones
and climatic effects on the fluctuation of the different according to their climatological characteristics. The
components of solar radiation. They found that these modified formula is ;
effects were particularly large during spring and winter
months owing to the high fluctuation of the atmospheric H = K(n)1.24(h)-0.19 + 10550(sin h)2.1 + 300(sin h)3 (2)
conditions with respect to cloud amounts, water content,
and concentration of aerosol dust particles. They also where, K = 8, 9.5, 11 for zone 1, zone 2 and zone 3
found that the relative reduction of global solar radiation respectively. The computation of H is based on the
by cloud over the whole period is around 4.5% due to the knowledge of the appropriate zone parameter and long-
low degree of cloudiness in the study region. term averages of sunshine hours and altitude of the sun.

Trabea and Shaltout, 2000 related the measurements Relation (2) which was proposed for high latitudes
of global solar radiation with five meteorological (35° - 65° N) was tested by Khogali, 1983 for low
parameters namely: maximum air temperature, relative latitudes (4° - 19° N) and has been found applicable with a
humidity, atmospheric pressure, vapor pressure and hours good degree of accuracy provided that the parameter K is
of bright sunshine at five selected locations over Egypt. appropriately adjusted.
They found that the values of correlation coefficients
between the global radiation and the mentioned five The diffuse solar radiation could be estimated by the
meteorological parameters vary from 89% to 99% and the widely used empirical formula, which was developed by
errors of estimation are between 0.01 and 0.04. Darwish Page, 1961
and Taha, 2000 used the induced empirical formulae to
estimate the diffuse radiation as a function of global solar D/H = 1−1.13KT (3)
radiation over the Eastern Arab Region. They found that
Where D is the monthly average of the daily diffuse
the used formulae are available for regular observation for
solar radiation, H is the monthly average of the daily
a long time at sufficient number of stations located in
global solar radiation and the ratio KT = H/H0 is the
different climatic regions.
clearness index. The extraterrestrial solar radiation H0 is
obtained from Duffie and Beckman, 1974;
Although Egypt is a vast country, the number of its
meteorological stations that measure the solar radiation 24 360n ′
components are only a few. Therefore, the main objective H0 = I s (1 + 0.033 cos )
of this paper is to establish simple model to estimate the π 365
(4)
2π
monthly mean daily global and diffuse solar radiation and (cos ϕ cos δ sin w + w sin ϕ sin δ )
hence direct solar radiation. An empirical relation of 360
Barbaro et al., 1978 is very suitable to estimate the
components of solar radiation at any time and locality in Where the solar constant Is = 1369 ± 7 Wm-2, n′ is
Egypt where there are no measured data of solar radiation the day number (starting 1 January), w is the sunrise hour
components or there are instrumental and other difficulties angle, ϕ is the latitude and δ is the sun declination.
encountered in measuring components of solar radiation.
Computations have been made to illustrate that the Another commonly used relation is due to Liu and
proposed relation gives precise estimations of solar Jordan, 1960 and developed by Klein, 1977 to take the
radiation components than other methods. form :

D/H = 1.93 − 4.027KT + 5.531(KT)2 − 3.108(KT)3 (5)

2. Methods of prediction
The direct beam component is estimated from the
Sivkov, 1964 proposed original empirical relation to relation;
estimate the monthly mean global solar radiation at the
latitudes from 35° to 65° N in the form : I sin h = H−D (6)
 ROBAA : GLOBAL & DIFFUSE SOLAR RADIATION 513

TABLE 1

Coordinates of the Egyptian radiation measurements network and the radiation

components measured together with the date of commencement of recording

Station Latitude Longitude Elevat Measurements Date of

°N °E (m) H D I S commencement
of records
Sidi-Barrani 31° 38′ 25° 24′ 27 X X - X 1984
Matruh 31° 20′ 27° 13′ 38 X X - X 1961 (1981)
El-Arich 31° 05′ 33° 49′ 32 X X - X 1980
Tahrir 30° 39′ 30° 42′ 16 X X - X 1960 (1981)
Bahtim 30° 08′ 31° 15′ 17 X - - X 1969
Cairo 30° 05′ 31° 17′ 36 X X X X 1969 (1974)
Asyut 52 X - - X 1979
27° 03′ 31° 01′
El-Kharga 78 X X - X 1964 (1981)
25° 27′ 30° 32′
Aswan 192 X X - X 1972 (1981)
23° 58′ 32° 47′

*The year in brackets indicates the data of commencement of diffuse and/or direct solar radiation
records. H is the global solar radiation; D is the diffuse solar radiation, I is the direct solar radiation,
and S is the sunshine duration.

Where the product, I sin h, is the average horizontal TABLE 2

beam component.
Regions of Egypt and their represented stations with the
values of the parameter, K
Although, there are many good formulae to estimate
global solar radiation in Egypt, as mentioned above, the Regional parameter, K
empirical relation (2) of Barbaro et al. 1978 has been Region Represented
stations Cold Hot All
chosen to estimate global solar radiation in Egypt for the season season year
following reasons : Region 1
Northern Egypt Sidi-Barrani
& Mediterranean Matruh 12.4 14.6 13.7
(i) This formula has been applied for different latitudes El-Arich
coast
(such as Italy, Yemen and Sudan) to estimate global solar
radiation. It has been found that it gives better estimates of Region 2
Lower Egypt & Tahrir
solar radiation compared to other methods. Delta Bahtim 12.3 15.1 13.9
Cairo
(ii) This formula is independent of meteorological Region 3
parameters such as the relative humidity, minimum and Middle Egypt Asyut 14.3 16.8 15.8
maximum temperature, cloud cover and other parameters. Region 4
Western desert El-Kharga 11.5 14.5 13.3
It requires only hours of sunshine and minimum optical
depth of the persisting air mass as input parameters. Region 5
Upper Egypt Aswan 13.5 16.5 15.3
Therefore, this formula is very suitable to be applicable at
All Egypt — 12.8 15.5 14.4
any locality especially in the absence meteorological
stations and lack of measured data of solar radiation
components. type of measured radiation at each station and it’s date of
commencement of records. In order to predict global and
3. Results and discussion diffuse radiation with greater accuracy, the year has been
divided into two seasons, cold season (October to
In this study, all stations in Egypt that measure solar February) and hot season (March to September). The
radiation have been used. Table 1 gives a list of the nine investigated area has been divided into five regions
selected stations and their coordinates in addition to the according to the distribution of network of radiation
514 MAUSAM, 54, 2 (April 2003)

TABLE 3

The regional values of the parameter K, sunshine hours n, the noon altitude of the sun h, in addition to one year (1995) measured Hm and
estimated Hc values of monthly mean global radiation (MJ/m2.day) and their percentage error, e, at the different stations

Region & J F M A M J J A S O N D
station
Region 1
K 12.4 12.4 14.6 14.6 14.6 14.6 14.6 14.6 14.6 12.4 12.4 12.4
n 7.0 7.1 8.4 9.0 9.6 11.7 12.4 11.7 10.0 9.4 7.4 6.5
Sidi-Barrani h 36.6 44.8 55.3 67.4 76.5 80.2 78.1 71.4 61.2 49.9 39.9 34.9
Hc 11.8 14.4 19.2 22.7 24.4 28.0 28.4 26.7 23.4 17.7 13.2 10.9
Hm 10.8 13.6 19.6 22.9 25.0 28.1 28.9 27.0 23.6 18.6 12.8 10.4
e -9.3 -5.9 2.0 0.9 2.4 0.4 1.7 1.1 0.8 4.8 -3.1 -4.8
K 12.4 12.4 14.6 14.6 14.6 14.6 14.6 14.6 14.6 12.4 12.4 12.4
El-Arich n 6.7 6.9 8.5 9.5 10.2 12.6 12.0 10.9 9.4 8.5 7.4 6.1
h 37.4 45.7 56.7 66.6 77.5 81.5 79.4 72.5 61.9 50.5 40.5 35.6
Hc 11.6 14.4 19.6 23.3 25.3 29.3 28.0 25.7 22.2 16.8 13.3 10.5
Hm 10.8 14.0 19.8 23.5 25.6 29.7 28.4 26.0 22.6 16.8 12.8 10.0
e -7.4 -2.9 1.0 0.9 1.2 1.4 1.4 1.2 1.8 0.0 -3.9 -5.0
K 12.4 12.4 14.6 14.6 14.6 14.6 14.6 14.6 14.6 12.4 12.4 12.4
Matruh n 6.7 7.6 8.1 9.0 11.0 12.7 12.9 11.7 10.2 9.4 7.5 6.0
h 36.1 44.0 54.4 66.4 74.9 77.9 75.7 69.9 60.5 49.7 39.9 34.7
Hc 11.4 14.8 18.6 22.6 26.2 29.2 28.9 26.5 23.1 17.7 13.3 10.2
Hm 10.4 14.0 19.5 23.1 26.9 29.7 29.7 26.8 23.3 17.8 13.0 9.8
e -9.6 -5.7 4.6 2.2 2.6 1.7 2.7 1.1 0.9 0.6 -2.3 -4.1
Region 2
K 12.3 12.3 15.1 15.1 15.1 15.1 15.1 15.1 15.1 12.3 12.3 12.3
Tahrir n 7.2 7.1 8.3 9.6 10.0 12.2 12.0 11.1 10.2 8.7 7.1 6.2
h 37.4 45.5 56.0 68.1 77.1 80.5 78.3 72.0 62.0 50.8 40.9 35.8
Hc 12.2 14.5 19.5 24.0 25.4 29.1 28.3 26.4 23.8 17.0 13.0 10.6
Hm 11.4 14.1 20.2 25.0 25.9 29.9 28.6 26.7 24.7 17.8 13.2 10.2
e -7.0 -2.8 3.5 4.0 1.9 2.7 1.0 1.1 3.6 4.5 1.5 -3.9
Bahtim K 12.3 12.3 15.1 15.1 15.1 15.1 15.1 15.1 15.1 12.3 12.3 12.3
n 7.1 7.4 8.3 9.8 10.2 11.9 11.9 11.1 10.1 8.7 7.9 6.0
h 38.0 46.1 56.7 68.8 77.7 81.1 79.0 72.6 62.6 51.4 41.4 36.4
Hc 12.2 15.0 19.7 24.4 25.7 28.8 28.2 26.5 23.7 17.2 14.1 10.5
Hm 11.2 13.9 19.9 24.6 26.0 29.4 28.4 26.9 24.7 17.0 13.7 10.1
Cairo e -8.9 -7.9 1.0 0.8 1.2 2.0 0.7 1.5 4.0 -1.2 -2.9 -4.0
K 12.3 12.3 15.1 15.1 15.1 15.1 15.1 15.1 15.1 12.3 12.3 12.3
n 6.1 6.7 7.4 8.2 9.0 11.0 11.8 10.1 9.0 8.1 6.7 5.5
h 38.1 46.2 66.7 68.8 77.8 81.2 79.0 72.7 62.6 51.4 41.5 36.4
Hc 11.0 14.3 20.4 22.2 24.1 27.5 28.1 25.1 22.2 16.5 12.7 10.0
Hm 10.2 13.3 19.3 22.9 24.0 27.9 27.3 25.0 21.8 16.2 12.4 9.7
e -7.8 -7.5 -5.7 3.1 -0.4 1.4 -2.9 -0.4 -1.8 -1.9 -2.4 -3.1
Region 3
K 14.3 14.3 16.8 16.8 16.8 16.8 16.8 16.8 16.8 14.3 14.3 14.3
n 9.4 9.6 9.6 10.8 10.9 12.2 11.8 11.8 10.8 9.9 9.6 8.3
h 38.1 46.2 56.7 68.8 77.8 81.2 79.0 72.7 62.6 51.4 41.5 36.4
El-Kharga Hc 16.6 19.2 22.8 27.2 28.1 30.8 29.6 29.1 26.2 20.2 17.7 14.7
Hm 15.8 18.4 23.0 27.9 28.5 30.9 30.2 29.2 27.1 20.4 16.9 13.8
e -5.1 -4.3 0.9 2.5 1.4 0.3 2.0 0.3 3.3 1.0 -4.7 -6.5
Region 4
K 11.5 11.5 14.5 14.5 14.5 14.5 14.5 14.5 14.5 11.5 11.5 11.5
n 8.9 9.5 9.8 10.8 11.5 12.7 12.7 12.1 10.9 9.9 8.9 7.7
Asyut h 41.0 49.1 59.6 71.6 80.3 83.0 80.9 75.2 65.5 54.4 44.5 39.4
Hc 14.5 17.7 22.0 25.8 27.2 29.4 28.9 27.6 24.9 18.7 15.4 12.7
Hm 14.4 18.0 21.9 26.4 27.4 30.1 28.8 26.8 24.1 19.3 15.3 12.6
e -0.7 1.7 -0.5 2.3 0.7 2.3 -0.3 -3.0 -3.3 3.1 -0.7 -0.8
Region 5
K 13.5 13.5 16.5 16.5 16.5 16.5 16.5 16.5 16.5 13.5 13.5 13.5
n 10.1 10.3 10.5 10.8 11.0 12.2 12.4 11.6 10.4 9.7 9.2 9.0
h 44.3 52.5 63.0 75.0 83.8 85.6 83.8 78.7 68.9 57.6 47.6 42.6
Aswan Hc 18.3 21.1 25.2 27.8 28.4 30.6 30.5 29.0 26.4 20.7 18.0 16.4
Hm 18.2 21.4 25.7 28.3 28.6 30.8 30.6 29.6 27.5 21.4 18.1 15.7
e -0.5 1.4 1.9 1.8 0.7 0.7 0.3 2.0 4.0 3.3 0.6 -4.5
 ROBAA : GLOBAL & DIFFUSE SOLAR RADIATION 515

stations. The divided regions and its represented stations At urban area of Cairo, the method overestimates the
are given in Table 2. Both region 1 and region 2 are global radiation all the year round except during two
represented by three stations while the other regions are months of April and June. This can readily be explained
represented by one station only. on the basis that pollutants and aerosols are high in
Cairo’s atmosphere during most months of the year
3.1. Computation of diffuse solar radiation causing a reduction of global radiation. This factor is also
not considered in the estimation procedure.
The monthly mean daily values of measured global
radiation, Hm, and sunshine hours, n, of the five years The southern region has minimum error of
(1985 to 1989) in addition to h values for nine stations estimation since this region is characterized by the stable
have been obtained from the Egyptian Meteorological weather and cloud free skies.
Authority. The data of each region, represented by the
concerned stations, have been studied and analyzed using 3.2. Comparison between the current modified
the advanced computer programs and applying an formula (2) and El-Shahawy’s formula (7)
empirical relation of Barbaro et al., 1978 to obtain the
regional values of the parameter K. The results are given El-Shahawy, 1984 proposed a semi-empirical
in Table 2. formula for estimating the global solar radiation, H, in
Egypt as follows;
Verification of the obtained regional values of the
parameter, K, was carried out by estimating global H = AQ[1+2αƒ)(1−sin(ϕ-δ)−ƒh] cal.cm−2day−1 (7)
radiation using measured data of n for the year 1995 at
Where Q is the mean daily values of cloudiness
each of the selected station. The calculated data of global
coefficient, A = Jo d/h, Jo, is the solar constant (Jo is taken
radiation, Hc, are presented in Table 3 where a comparison
with measurements, Hm, of the same year, 1995, is here as 1396 Wm−2), d = 8cos−1(- tan ϕ tan δ) minutes,
also given. The relative percentage errors defined as : h = (π/2+δ−α) radians, δ is the sun declination and α is
H − Hc the surface albedo, φ is the latitude and f = sin(0.2δ)+0.1.
e= m × 100, , are also given in the same table.
Hm
El-Shahawy used his formula to estimate the
monthly mean global solar radiation for the year 1978 at
The agreement between experimental and estimated four selected stations in Egypt namely Matruh, Tahrir,
values is remarkable especially for non-cloudy months Bahtim and El-Kharga. His results are given in Table 4
(May to August) at all stations whereas the possible error where he compared his results with the corresponding
of estimated values, e, does not exceed 3% (Table 3). measured values, Hm, at Matruh and El-Kharga. He found
Also, good agreement between measured and estimated good agreement between the estimated and measured
values has been found at both middle and southern regions values of global radiation.
whereas the maximum error of estimated values is found
3.3% and 4.5% for two regions respectively. The In the present study, the previous results of El-
maximum error is found 9.6%, 8.9 % and 6.5 % for the Shahawy formula (7) have been compared with the
northern, Lower Egypt and Delta and western desert corresponding estimated values applying the current
regions respectively. For different cloudy conditions the modified formula (2) to show the merits of the two
maximum error of the estimated values is typically 9.6%. formulae. Therefore, The corresponding values of global
It is concluded that the error of estimated value relatively solar radiation have been estimated for the same year 1978
increases with the increase of cloud cover and vise versa. at the two stations of Matruh and El-Kharga using their
This is due to the factor of cloud effects is not taken in the recorded data of sunshine hours, n, and the values of the
consideration. parameter K with applying the modified formula (2). The
records of n values have been obtained from the Egyptian
Meteorological Authority while K values for the both
It may be noted that the method underestimates the stations are taken from Table 2. Tahrir and Bahtim are
global radiation all the year round except during the excepted from this comparison because the data of
months from November to February. The overestimation sunshine hours, n, are not recorded at them for the study
takes its maximum value during January month at year, 1978. On the other hand, Matruh and El-Kharga are
northern region and decreases gradually towards southern found appropriate for the comparison purposes. Matruh is
region. This is due to the corresponding effects of clouds a coast city and characterized by highest cloud cover in a
and moisture, which are not considered in the estimation year while El-Kharga is a desert city and characterized by
procedure. clear atmosphere and stable weather conditions. In
516 MAUSAM, 54, 2 (April 2003)

TABLE 4

Measured, Hm, and estimated values, HcH, of the monthly mean global solar radiation for the year 1978 and their
percentage errors, eH, at Matruh and El-Kharga stations applying formula (7), cited from El-Shahawy (1998) in
addition to the corresponding estimated values, HcB, using the current formula (2) and their percentage errors, eB

Station
Month Matruh El-Kharga
Hm HcH HcB eH eB Hm HcH HcB eH eB
Jan 09.7 08.9 10.6 8.2 -9.3 17.5 16.6 18.3 5.1 -4.6
Feb 13.5 12.9 14.2 4.4 -5.2 21.5 20.7 22.3 3.7 -3.7
Mar 17.4 18.2 16.7 -4.6 4.0 24.8 25.0 24.6 -1.8 0.8
Apr 20.7 21.7 20.1 -4.8 2.9 27.9 29.0 27.6 -3.9 1.1
May 23.6 24.1 23.2 -2.1 1.7 30.6 31.1 30.2 -1.6 1.3
Jun 25.5 25.7 25.4 -0.8 0.4 31.8 31.9 31.7 -0.3 0.3
Jul 24.8 25.2 24.5 -1.6 1.2 30.3 30.8 29.7 -1.7 2.0
Aug 22.6 23.1 22.3 -2.2 1.3 29.9 30.0 29.7 -0.3 0.7
Sep 20.4 21.4 20.2 -4.9 0.6 27.1 28.2 26.1 -4.1 3.7
Oct\ 17.1 17.8 17.0 -4.1 1.0 21.7 21.8 21.4 -0.5 1.4
Nov 12.6 12.3 13.2 2.4 -4.8 19.2 17.6 20.0 8.3 -4.2
Dec 09.2 08.8 09.8 4.3 -6.5 * 14.1 — — —

* Hm is not recorded

addition, El-Shahawy’s formula concerned with cloud This is due to, as mentioned above, Matruh is coast city
amounts and types as mentioned above. The obtained and characterized by highest cloud cover during most of
results are also given in Table 4 with El-Shahawy’s the year especially in winter months while El-Kharga is
results. characterized by clear atmosphere and stable weather
conditions.
The following results could be clearly seen from
Table 4:
(iv) The possible error of the annual mean of estimated
(i) eB at Matruh is higher than eH during cold winter values at Matruh applying the current formula (2) is very
season (From November to February) while the opposite small if compared with its corresponding value of El-
occurs during remaining months. This is attributed to Shahawy’s formula, (eB = −0.055 while eH = −1.38). This
higher cloud cover and its effects during winter season means that the formula (2) gives better estimations for
than during remain year months. The cloud effects are not global radiation as the annual average than El-Shahawy
taken in the consideration with respect to the formula (2). formula.

(ii) At both selected stations, El-Shahawy’s formula (7)

is underestimating during cold winter season (From From the above discussion, it could be concluded
November to February) and overestimating during that the above both two formulae are valid to compute
remaining months and vise versa with respect to the global solar radiation with high accuracy at any locality in
formula (2). The accumulation of observation errors of Egypt during all year months. However, the current
cloud types and amounts partially explain the modified formula is characterized by simplicity and
underestimation of El-Shahawy’s formula during winter independence of meteorological parameters, which in turn
season. On the other hand, the overestimation of El- precisely estimates solar radiation at any locality in Egypt
Shahawy’s formula during remain months could be during all months despite relatively higher computation
attributed to the solar constant which has been taken as errors during winter cloudy months. On the contrary, the
1396 Wm−2 in his computations while ISO and WMO accumulation of observation errors of cloud types and
have accepted a value of 1369±7 Wm−2. amounts and other input data could lead to higher
computation errors of El-Shahawy’s formula (7) beside
(iii) eH at Matruh is higher than eB at El-Kharga during the obtaining these input data require establishing
most year months especially during cold winter season. meteorological stations which cost exorbitantly.
 ROBAA : GLOBAL & DIFFUSE SOLAR RADIATION 517

TABLE 5

Values of regression and correlation coefficients of equation (10) and the standard mean
error for the selected stations and the corresponding regions

Region a b R E
& station Local region Local region Local Region Local region
Region 1
Sidi-Barrani 0.7983 -0.5566 0.9687 0.0016
Matruh 0.7279 0.8033 -0.4586 -0.5383 0.9662 0.8961 0.0030 0.0322
El-Arich 0.8671 -0.6052 0.9716 0.0042
Region 2
Tahrir 0.8262 0.8037 -0.5951 -0.5778 0.9634 0.9389 0.0432 0.0143
Cairo 0.8076 -0.5963 0.9839 0.0017
Region 3
El-Kharga 0.5913 0.5913 -0.3556 -0.3556 0.9644 0.9644 0.0062 0.0062
Region 5
Aswan 0.4394 0.4394 -0.1794 -0.1794 0.9690 0.9690 0.0083 0.0083
All Egypt 0.8413 -0.6191 0.8751 0.0314

3.3. Computation of diffuse solar radiation using the corresponding measured values of Hm and n/N
for the same year and applying equation (10) with the
The above data of measured global radiation Hm, and regression coefficients, a and b, from Table 5 for each
sunshine hours n, in addition to the corresponding values station. The used data of Hm are given above in Table 3.
of measured diffuse radiation Dm, for the same period The values of n/N are presented in Table 6 with the
(1985 to 1989) have been used to relate the values of the obtained calculated values of diffuse solar radiation, Dc,
fraction of diffuse solar radiation (Dm /Hm) with the where the verification has been performed through a
corresponding values of n/N for the selected stations. comparison between the estimated and measured values.
Bahtim and Asyut are excepted from this study as
measurements of diffuse radiation are not available at The agreement between measured and estimated
these places (Table 1). values is remarkable. The method of estimation is
fluctuated between small overestimation and
The mean daily number of hours of daylight (N) underestimation at all stations during all the months. The
between sunrise and sunset are calculated using Cooper’s maximum error occurs during the hot months from March
formula 1969; to July at all stations. This is due to the occurrence of
Khamsin depressions in the north and the effect of Sudan
N = (2/15) cos−1 [(-tan ϕ) (tan δ)] (8) monsoon low in the south during the mentioned months.
This factor is not considered in the estimation procedure.
Where ϕ is the latitude (in degree) and δ is the solar The maximum error is 7.6% at Sidi-Barrani, 7.52% at
declination angle; El-Arich, 7.64% at Matruh, 6.34% at Tahrir, 6.99% at
Cairo, 5.93% at El-Kharga and 6.5% at Aswan.
δ = 23.45 sin [360(284 + n′)/365] (9)

The obtained relation is linear. It could be written as It is noticed, from Table 6, that the possible error of
follows; estimated values, e, at Sidi-Barrani is lower than those the
other two stations of regional 1, Matruh and El-Arich,
Dm/Hm = a + b(n/N) (10) during winter months despite the fact that their skies
become more cloudy due to invasion of extratropical
where a and b are the regression coefficients. Their system in winter from the north. This is due to relatively
values in addition to the correlation coefficients R, and the lower winter clouds cover over Sidi-Barrani than those at
standard mean errors E, are given in the following Matruh and El-Arich during the year of 1995. It is also
Table 5. noticed that, the values of Dm show gradual increase as we
go eastward from Matruh to El-Arich. This is attributed to
The monthly mean values of diffuse solar radiation the corresponding gradual increase in cloud cover from
have been estimated for the year 1995 at each station west to east.
518 MAUSAM, 54, 2 (April 2003)

TABLE 6

The values of n/N and the estimated diffuse radiation, Dc, compared with the measured
values, Dm, with their percentage error, e, at different stations

Region & J F M A M J J A S O N D
station
Region 1
n/N 0.65 0.66 0.71 0.71 0.71 0.83 0.89 0.89 0.85 0.84 0.71 0.65
Dc 4.71 5.86 7.90 9.23 10.1 9.45 8.75 8.18 7.67 6.15 5.16 4.54
Sidi-Barrani Dm 4.74 5.93 7.86 9.50 9.64 8.78 8.96 8.08 7.82 6.24 5.19 4.67
e 0.63 1.18 -0.5 2.84 -4.8 -7.6 2.34 -1.2 1.92 1.44 0.58 2.78

n/N 0.66 0.63 0.72 0.74 0.83 0.90 0.87 0.83 0.77 0.76 0.68 0.61
Dc 5.05 6.80 8.54 9.85 9.34 9.58 9.67 9.48 9.06 6.84 5.83 4.98
El-Arich Dm 4.79 6.64 8.87 9.70 10.1 9.92 9.43 8.99 9.22 6.95 6.06 4.72
e -5.4 -2.4 3.72 -1.5 7.52 3.43 -2.6 -5.5 1.74 1.58 3.8 -5.5

n/N 0.66 0.70 0.69 0.70 0.81 0.91 0.93 0.89 0.84 0.84 0.72 0.60
Matruh Dc 4.42 5.70 8.02 9.40 9.59 9.22 8.95 8.57 7.98 6.10 5.17 4.44
Dm 4.16 5.80 8.19 9.14 9.96 9.32 9.69 8.59 7.98 6.28 5.06 4.31
e -6.2 1.72 2.08 -2.8 3.71 1.07 7.64 0.23 0.00 2.87 -2.2 -3.0
Region 2
n/N 0.70 0.65 0.70 0.75 0.74 0.87 0.87 0.85 0.84 0.77 0.68 0.62
Tahrir Dc 4.67 6.20 8.27 9.50 9.99 9.22 8.82 8.55 8.06 6.55 5.56 4.66
Dm 4.79 6.06 8.83 9.70 9.69 9.02 8.60 8.35 8.13 6.47 5.31 4.55
e 2.51 -2.3 6.34 2.06 -3.1 -2.2 -2.6 -2.4 0.86 -1.2 -4.7 -2.4

n/N 0.65 0.64 0.73 0.77 0.75 0.85 0.86 0.77 0.76 0.76 0.64 0.55
Cairo Dc 4.28 5.67 7.19 7.98 8.65 8.39 8.05 8.71 7.73 5.74 5.28 4.65
Dm 4.50 5.9 7.60 8.3 9.3 9.0 8.5 8.4 8.1 6.1 5.6 4.6
e 4.89 3.9 5.39 3.86 6.99 6.78 5.29 -3.7 4.57 5.9 5.71 -1.1
Region 3
n/N 0.89 0.86 0.81 0.86 0.82 0.90 0.88 0.92 0.89 0.87 0.89 0.80
El-Kharga Dc 4.34 5.25 6.98 7.97 8.54 8.38 8.41 7.71 7.45 5.75 4.64 4.23
Dm 4.50 5.44 7.42 8.29 8.65 8.20 7.81 7.78 7.89 5.61 4.59 4.20
e 3.56 3.49 5.93 3.86 1.27 -2.2 -7.7 0.9 5.58 -2.5 -1.1 -0.7
Region 4
n/N 0.95 0.92 0.84 0.86 0.88 0.91 0.93 0.90 0.86 0.85 0.85 0.86
Aswan Dc 4.90 5.87 7.42 8.07 8.05 8.51 8.34 8.23 7.84 6.14 5.19 4.48
Dm 4.78 5.64 7.20 7.96 8.61 8.90 8.11 8.12 7.67 6.21 5.33 4.41
e -2.5 -4.1 -3.1 -1.4 6.5 4.38 -2.8 -1.4 -2.2 1.13 2.63 -1.6

3.4. Annual variation of radiation components over 3.4. (a). Global solar radiation
Egypt
It could be clearly seen that Cairo has the lowest
The characteristics of the annual variation of the value of Hm, of all stations over a year. This could be
monthly mean daily values of measured global, Hm, and attributed to the urbanization of the area characterized by
diffuse solar radiation, Dm for the year 1995 over the five highly polluted air, which leads to loss in the incident
regions have been examined. El-Arich and Cairo have energy of solar beam due to backscattering and
been chosen to represent region 1 and region 2 absorption.
respectively, while remaining regions represented by the
other three stations as in Table 2. The monthly mean Also, it is noticed that the values of Hm, at El-Arich
values of , Hm, and Dm, for the five stations, El-Arich, are marginally higher than Cairo's values but lower than
Cairo, El-Kharga, Asyut and Aswan are illustrated in the values of the other three stations over the year. This is
Fig. 1&2 respectively. Asyut has been excluded from Fig. because El-Arich is a coastal station and characterized by
2 because Dm is not measured there. high amount of cloud cover and water vapor content. The
 ROBAA : GLOBAL & DIFFUSE SOLAR RADIATION 519

Fig. 1. Annual variation of global solar radiation, Hm, at Fig. 2. Annual variation of diffuse solar radiation, Dm, at
different stations different stations

difference between the Hm, values of Cairo and El-Arich mentioned above, the effect of high amount of cloud cover
is high in summer season as compared with winter season. and water vapor content of El-Arich. On the other hand,
This may be attributed to neglected effect of cloud cover Cairo has higher values of Dm, compared to El-Kharga and
and moisture phenomena during hot summer season over Aswan. This indicates that Cairo is turbid atmosphere and
El-Arich due to the maximum atmospheric heating. The equivalent over the year. It is also noticed that El-Kharga
comparison between global radiation at Cairo and El- has the lowest values of Dm, during the period from June
Arich shows clearly that, the effect of polluted air and to December, except in September month. This indicates
aerosols on reduction of global solar radiation is domination of clear sky condition at El-Kharga. Although
approximately equivalent the effect of clouds and water Aswan is characterized by stable atmospheric conditions
vapor content. like El-Kharga, it has relatively higher values of Dm, than
those of El-Kharga during most months. This is due to
Aswan has the highest value of Hm, of all the stations Aswan’s geographical location beside the River Nile,
over the year. This is mainly due to Aswan’s clear which in turn cause relatively higher atmospheric
atmosphere and stable weather through most of the year. humidity and water vapor than those are over El-Kharga,
Also, the values of Hm, at both stations of El-Kharga and which lies in the western desert. It is interesting to note
Asyut are high when compared to the values of Cairo and that Dm, reaches maximum in May at all places except at
El-Arich. This is also due to clear atmosphere and stable Aswan where it is in June.
weather conditions at El-Kharga and Asyut as compared
to Cairo and El-Arich. 4. Conclusion

On the other hand, there is a strong latitudinal The investigated area of Egypt has been divided into
gradient for global solar radiation in winter compared to five regions represent most the country and represented by
that of summer. This is due to the invasion of extratropical the nine selected stations while the year has been divided
systems in winter from north passing over the into cold season (October to February) and hot season
Mediterranean Sea providing an increased cloud cover (March to September). The provided data of sunshine
over northern Egypt. The summer season is influenced by hours, n, global solar radiation, H, have been analyzed
a high-pressure cell, which is characterized by stable and using an advanced computer program to obtain an
clear sky weather adding to increased values of global appropriate regional parameter K, of an empirical relation,
radiation. All stations reach maximum in June and have (equation 2) of Barbaro et al. for each region. The
continued higher Hm, during July as well. obtained results are given in Table 2. The agreement
between measured and estimated values is remarkable.
3.4. (b). Diffuse solar radiation The maximum possible error of estimated values do not
exceed 9.6%. This points to the high potential of the
Since diffuse solar radiation is largely influenced proposed regional parameters K in equation (2) for
by cloud cover and atmospheric turbidity, it attains its practical applications. The current modified formula (2)
distinct highest values at El-Arich. This is attributed to, as gives better estimations for global solar radiation at any
520 MAUSAM, 54, 2 (April 2003)

locality in Egypt. Relation between the diffuse fraction El-Shahawy, M. A., 1984, “Estimation of daily global solar radiation”.
Bull., Faculty of Science, Cairo University, 52, 641-653.
D/H and the relative duration of sunshine (n/N) is also
determined for each region and its represented stations.
El-Shazly, M. S., Abdelmageed, A. M. and El-Noubi, M., 1998, “Solar
The Regression coefficients and the relative percentage radiation characteristics at Qena / Egypt”. Mausam, 49, 59-70.
error are given in Table 5. Diffuse irradiation, D, could be
estimated with maximum error 7.7%. A comparative study Hoyt, D. V., 1978, “A model for the calculation of solar global
for the global and diffuse solar radiation over different insolation”, Solar Energy, 21, 27-35.
sites has been investigated. The study shows clearly the
effect of urban air of Cairo on the reduction of global Khogali, A., 1983, “Solar radiation over Sudan-comparison of measured
and predicted data”, Solar Energy, 31, 45-53.
radiation and the effect of cloud and moisture
phenomenon on the increase of diffuse radiation at coastal Klein, S. A., 1977, “Calculation of monthly average insolation on tilted
area of El-Arich. surfaces”, Solar Energy, 19, p325.

The used data of the monthly mean daily values of n, Liu, B. Y. and Jordan, R. C., 1960 “The inter-relationship and
H and D of the five years (1985 to 1989) for the nine characteristic distribution of direct, diffuse and total radiation”,
stations that measure radiation in Egypt have been Solar Energy, 4, 1-19.
obtained from the Egyptian Meteorological Authority.
Page, J. K., 1961, “Estimation of monthly mean values of daily total
short-wave radiation on vertical and inclined surfaces from
In conclusion, this study provides methods for sunshine records for latitudes 40° N - 40° S”, Proc. UN New
estimating global and diffuse solar radiation as well as Sources of Energy.
direct solar radiation with high accuracy at any location in
Egypt. This is useful for the design of various systems Reddy, S. J., 1971, “An empirical method for the estimation of the total
solar radiation”, Solar Energy, 13, p289.
utilizing solar energy.
Sabbagh, J. A., Sayigh, A. M. and El Salam, E. M., 1977, “Estimation of
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