Rene.able Lheryv Vol. I, No. 2. pp. 269 276, 1991 0960-1481/91 $3.00+.00 Printed in Great Britain. Pergamon Press plc

D A T A B A N K

Prediction of ground-level solar radiation in Egypt

M. S. ABDEL-SALAM,* A . F . E L - D I B a n d M . A . EISSA

Mechanical Power Department , Faculty of Engineering, Cairo University, Giza, Egypt

(Received 28 February 1990 ; accepted 21 June 1990)

Abs t rae t - -A model has been developed to predict both beam normal and diffuse components of solar radiation in Egypt. The data used were measured by the Egyptian Renewable Energy Development Organization (EREDO) through a period of 9 months in 1980 at A1-Ahram region, Egypt. The present equations have also been applied to estimate the month ly mean daily global radiation for seven locations in Egypt: Cairo, Giza, Bahteem, Tahrir, Khargah , Mat ruh and Aswan. The measured data of these locations are published by the Egyptian Meteorological Authori ty (EMA). A correction factor related to cosine of latitude angle of the location has been introduced. Compar ison with previous predictions indicates that the present calculations are more accurate.

1. I N T R O D U C T I O N

Many articles are being published at the present time on the subject of solar energy. This reflects the growing interest in all aspects of alternative, renewable energy resources. However, solar energy conversion systems differ from other con- version systems in an important respect. It is that the amount of energy available to a solar energy system is not easily controlled. The usual system design problem of specifying a system adequate for the expected load is a far more com- plicated problem for solar systems than for other familiar energy systems. For solar systems, this design problem has another variable. It is the energy input. This shows that an understanding of solar radiation as a variable energy resource is essential for proper solar system design and analysis.

The best data for use in solar energy applications are the measured data. However, in many locations in Egypt there are no published measurements of solar radiation. Therefore, it is desirable to develop a model for solar radiation esti- mation, which is as accurate as possible, to be applicable for Egypt.

Solar radiation on the earth 's surface is affected by many factors. These factors include variation of the extraterrestrial solar radiation, the incident angle of radiation, and two more significant phenomena. The first one is the atmospheric scat- tering by air molecules, water vapour, and dust. The second phenomenon is the atmospheric absorption by oxygen, ozone, water vapour, and carbon dioxide. As a result the total solar radiation reaching the earth 's surface is divided into beam and diffuse components .

2. PREVIOUS M O D E L S FOR E S T IM AT ING SO L AR RADIATION

The models of estimating solar radiation may be divided into three categories. The first one includes the models which require many meteorological observations such as clouds type and amount , air mass above clouds, aerosol extinction

* ISES member.

coefficient, pressure, optical path length of water vapour, optical thickness of aerosol layer, etc. [1 3]. These meteoro- logical data may not be available in many locations. The second type uses meteorological data too, but only one of these data, such as the durat ion of sunshine or the cloud cover, to estimate the month ly mean daily global or diffuse radiation is essential [4-8]. The third category comprises the models which assume clear sky [9-14].

One of the most famous models, which is being referred to in this study, is the A S H R A E clear sky model explained by Powell [9]. Beam normal solar radiation estimated by the A S H R A E model is given as follows :

lb. = A exp (-- Bin) (W/m2). (1)

On the other hand, the diffuse radiation may be estimated from :

la - C(Ibn) (W/m2). (2)

Values of A, B and C for U.S.A. and Canada are presented in Table 1. Hanna [10] modified this model by introducing new values of the constant A to be suitable for Egypt. These values of A are also tabulated in Table 1.

3. PRESENT M O D E L

The first type of the previous models requires too many meteorological data, while the second type and some other models of the third type require only one sort of meteoro- logical observation [12 14]. However, it is more convenient to use a model which does not need these meteorological observations because of the lack of such published data for many locations in Egypt. On the other hand, the second type of models estimates the monthly mean solar radiation. It is, however, desired to have a model which may be useful in studying the dynamic behaviour of solar energy equipment.

Hanna ' s [10] modifications of the A S H R A E model [9] seem to be acceptable according to such requirements, taking into consideration that the clear sky condition is the situ- ation for most days in Egypt. However, this model considers hypothetical s tandard clear sky conditions instead of using actual atmospheric ones. Hanna [I0] assumed the same hypo-

269

270 Data Bank

Table 1. A S H R A E model constants for U.S.A. and for Egypt

A* At Month (W/m s ) (W/m 2 ) B:~ C~

Table 2. The constants of eq. (9)

Period from to W c

1 1230 1205 0.142 0.069 2 1214 1191 0.144 0.072 3 1185 1162 0.156 0.085 4 1135 1113 0.180 0.116 5 1103 1082 0.196 0.145 6 1088 1066 0.205 0.161 7 1085 1063 0.207 0.163 8 1107 1085 0.201 0.146 9 1151 1130 0.177 0.I10

10 1192 1168 0.160 0.088 11 1220 1197 0.149 0.076 12 1233 1208 0.142 0.068

1 60 - 3 5 5 . 0 167.8 61 172 - 3 7 3 . 0 173.4

173 311 350.0 172.4 312 354 375.0 181.8 355 365 - 3 5 5 . 0 167.8

* For USA [9]. t For Egypt [10].

Dimensionless.

thetical atmosphere, and calculated values of apparent solar radiation (A) to be applicable for Egypt. The present work assumes clear sky conditions too, but it considers actual atmospheric conditions of Egypt.

3.1. Beam normal solar radiation intensity Applying the Bouguer and Lambert law, which is

explained in [16], to the atmosphere, it is recommended to use the following form to estimate solar beam normal intensity :

Ib, = I0 exp ( - B m ) (W/m2). (3)

This model yields the fact that the beam normal radiation is the extraterrestrial solar radiation at an air mass equal to zero, which is not realized by the A S H R A E model.

Values of the beam normal solar radiation intensities were measured in AI-Ahram region (Egypt) by the Solar Energy Laboratory of the Egyptian Renewable Energy Development Organization (EREDO) [17]. The measured data considered extend through a period of 9 months from January to September 1980. Only the data of 204 days are presented, with 2453 observations. These considered days are the only days which satisfy clear sky conditions. The data were measured at a site about 26 km from Cairo on the desert road to Alexandria. The geographical location of this site is defined as follows : latitude = 30°N, longitude = 31.1 °E and altitude = 21 m above mean sea level. Equat ion (3) is used to calculate the actual atmospheric extinction coefficient using the above mentioned measured data. A computer pro- gram has been developed to calculate the atmospheric extinc- tion coefficient for each day. Extraterrestrial solar radiation is calculated as follows [18]:

10 = 1367/[l + e sin {360(N-95)/365}] (W/mZ). (4)

Powell [9] illustrated that the modified version of the A S H R A E model uses the following expressions to calculate the air mass at sea level :

m = 35/[1224 cos 2 (0z)+ I] 1:2. (5)

The adjustment of the air mass for local altitude is made in terms of the local atmospheric pressure as follows :

m = (e*/P)m*. (6)

The pressure ratio (P*/P) is calculated using the following equation recommended by Lunde [19]:

(P*/P) = exp ( - 0.0001184h). (7)

The zenith angle can be calculated as follows [4, 16]:

cos 0z = cos (~b) cos (6) cos (w)+ sin (q~) sin (6). (8)

The declination angle is calculated using the equation rec- ommended by Abdel-Salam et al. [20] :

6 = 23.45 cos [360 (N- c)/W] degrees. (9)

Values of W and c are presented in Table 2. The considered solar radiation data were measured at local

time, while the calculations are performed at solar time. The conversion between solar time and local time is based on three corrections. The following form is used :

LT = ST - (EqT/60) ___ Lc + DST. (10)

There are many equations which approximate the cal- culation of the equation of time (EqT) [4, 15, 21, 22]. A comparison between these equations and the values o f the equation o f time calculated from the Astronomical Almanac for the year 1987 [23] results in the following equation by Woolf which is recommended by Stine and Harrigan [15] and Boes [21] is accepted in the present work :

EqT = 0.258 cos ( X ) - 7 . 4 1 6 sin (X)

- 3 . 6 4 8 cos (2X) -9 .228 sin (2X) (11)

where

X = 3 6 0 ( N - 1)/365.242.

The variation of the actual atmospheric extinction coefficient in Al -Ahram region with the days of the year, according to the measurements of the Egyptian Renewable Energy Development Organization, is illustrated in Fig. 1. Moreover, the least squares procedure is applied to get a relationship between the atmospheric extinction coefficient and the day o f the year. Many types of regression lines were examined. It is found that a second degree polynomial gives a good representation of the data as shown in Fig. 1. The resulting relation of the regression line is as follows :

B = 0.34327 +0.668504Ny-0.75566Ny 2 (12)

where

Ny = N/365. (13)

3.2. Diffuse solar radiation intensity The global solar radiation intensity on the horizontal was

measured by the Solar Energy Laboratory of EREDO [17] in AI-Ahram region for the year 1980, in addition to the beam normal radiation for the same 9 mon th period, in 133

Data Bank 271

o

0 o E O

O E

×

" E

. E CL

E

1.0

0.75

0 . 5

0.25

• Measured data Regression line

D

." ° * ,

• • . . . * ; . . 1% • .-. . - . . . ' . - ' . . . , - - . . . " ...:..

- - . : . : ... -..-..- . . . ~ .

m

0 [ [ I I I [ t [ I I I 1 30 60 90 120 150 180 210 240 270 300 330 360

Day of the year

Fig. 1. Variation of extinction coefficient throughout the year.

days and 1332 observations. Utilizing these measurements of both global and beam normal radiation intensities, the diffuse component on a horizontal surface can be calculated from the following equation :

Ig = lb, COS (O:)+Io. (14)

The ratio between the diffuse radiation intensity and beam normal radiation intensity is referred to as the diffuse ratio factor C, and is calculated for each observation in the 9 month period of measurements . The results are plotted in Fig. 2 as related to the ratio between beam normal radiation intensity to extraterrestrial radiation intensity (atmospheric transmissivity for beam normal radiation). It is clear from Fig. 2 that the results are well represented through a linear relation. The least squares method is used to find the

regression line equation which is as follows :

C = 0.39987-0.31922(T~n). (15)

3.3. Monthly mean daily 9lobal radiation Measurements of global radiation on a horizontal surface

are available in the form of monthly mean daily values for many locations in Egypt. They are measured and published by the Egyptian Meteorological Authori ty [24~28]. The geo- graphical conditions of such locations are given in Table 3.

Within this present study, the monthly mean daily global radiation for each month in the year at these locations is calculated. The results of calculations using the present model show significant errors at many locations. To improve the present model, a correction factor for each month is

O

t l 0

c)

0.5

.,-o 0.4 ~ ~ ' " . . ;: Regression line

'~-'-" ...~i...4i ,., • *- | . " . . * * .

~.** * .

0.2 - - " ' " " "~'L "

0.1

J J I l I I J I J 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Beam normal transmissivity

Fig. 2. Variation of diffuse ratio factor with beam normal transmissivity.

272

Table 3. Geographical locations for measured monthly mean daily global radiation in Egypt [26, 27]

Altitude Latitude (N) Longitude (E) above MSL*

Location deg. min. deg. rain. (m)

Cairo 30 5 31 17 34.4 Giza 30 3 31 13 21.0 Bahteem 30 9 31 15 16.9 Tahrir 30 39 30 42 15.6 Khargah 25 27 30 32 77.8 Mat ruh 31 20 27 13 35.0 Aswan 23 58 32 47 200.0

* MSL : mean sea level.

calculated. Then the correction factors are averaged over the year in order to get a mean correction factor for each location. It is found that a good fit will result by a straight line equation relating the location correction factors and the cosines of the latitudes. The correction factor at any latitude L(q~) can, then, be estimated from the following relation:

L(~b) = 2.09132 cos (q5)--0.79091. (16)

4. RESULTS AND DISCUSSION

Values of the beam normal solar intensity have been cal- culated using the present equations. A sample of the results is plotted in Fig. 3 compared with calculations from the A S H R A E model modified by Hanna [10]. It is clear from Fig. 3 that the present model is more accurate than Hanna 's model [10]. Hanna ' s model assumes a s tandard clear sky and, thus, the beam normal solar intensity is overestimated. The present model also assumes clear sky conditions, but the actual conditions instead of the hypothetical ones. The results of Hanna ' s model and the present work are compared relative to the measured data using two types of statistical

Data Bank

error analysis ; the root mean square error (RMSE) [29] :

RMSE = [E(Dv)2/No]'¢2 (17)

and the mean bias error (MBE) [29] :

MBE = Z (Ov)/No. (18)

A computer program has been developed to calculate the root mean square error and the mean bias error for Hanna ' s model [10] and for the present work. The program calculates these errors for each month and as a total for all the period of the 9 months of measurements . The results, presented in Fig. 4, indicate that the present work gives more accurate results than Hanna ' s model in all months and, consequently, in all the period. The min imum value of the root mean square error of Hanna ' s model is 200.2 W/m 2, while the max imum error of the present work is 130.6 W/m 2. The root mean square error of the present work for all the period represents only about 45% of the corresponding value of Hanna ' s model. Hanna ' s model overestimates the intensity of the beam normal solar radiation as all values of the mean bias error are positive. These results are expected because, in the present study, actual atmospheric clear sky conditions are considered instead of using hypothetical ones.

The present model has been used to calculate the diffuse radiation for all observations in the period of measurements. A sample of the results is plotted in Fig. 5. The diffuse radiation estimated by Hanna 's model [10] is also plotted, for comparison. The root mean square error and the mean bias error are calculated for each month in the period of measure- ments. They are also calculated for all the 9 month period as a total. The results are presented in Fig. 6 which illustrates that the present calculations are more accurate than those from ref. [10]. The min imum root mean square error from Hanna ' s model is 23.24 W/m 2, while the max imum error in the present work is 15.63 W/m 2. The root mean square error for the whole period in the present work represents about 25.9 % of that of Hanna ' s model. Moreover, all values of the mean bias error for Hanna ' s model are negative. This is because the assumed atmosphere is more clear than the actual

1400

1300 - -

1200 - -

1100 - -

1 0 0 0 - -

900

800

a M e a s u r e d da ta P r e s e n t w o r k

- - - - - - H a n n a ' s m o d e l [10 ]

f f

,.- - - / / ~ \ \ 700 -

.c_ l/ / A A A N , 6 0 0 - -

oo-oo ,oo- IA oo_ , / X',

= : o o - / /- lOO -

o I A 1 4 / I I I I I I I I I ' ~ . " -..I 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Loca l t i m e (h)

Fig. 3. The beam normal radiation intensity on 27 January 1980.

Data Bank 273

A "E 500

[ ] Present work [ ] Hanna's model 400

, o oo-ii o 2oo -i!i!i~.; ~

_

~ lOO !2:):i:,

°° i!i N o 1 2

Fii ri 3 4 5 6 7 8 9

Months of the year

1-71 H RMSE

of whole period

Fig. 4. Comparison between present work and Hanna ' s model [10] for beam normal solar intensity estimation.

one. This assumption overestimates the normal radiation and, consequently, the diffuse radiation is underestimated.

The present model was used to calculate the monthly mean daily global radiation for the seven locations which are men- tioned in Table 3. As a sample of the results, only two of them are presented in Tables 4 and 5. In the same tables, the results of Hanna ' s model [10], Abd-EI-Salam model [30] and the measured data [24~28] are shown also for the sake of comparison. The percentage of error for each mon th for the present work, Hanna ' s model and Abd-EI-Salam results are also presented in these tables. The mean absolute values of the percentage of error (positive values) over the year for each location are plotted together in Fig. 7 for the sake of comparison.

As illustrated in the tables and figures, the present work presents the most accurate method for solar radiation estimation in different locations in Egypt. The comparison between the present work and Abd-EI-Salam [30] shows that the error using the present work represents only a value varying between 0.266 in Tahrir and 0.739 in Mat ruh from the corresponding errors of Abd-E1-Salam [30]. Moreover, the present work errors range between 0.314 and 0.753 in Mat ruh with respect to those of Hanna [10]. However, there are two exceptions where Hanna ' s model gives results better than those of the present work. The first one is in Khargah, where the difference between both errors is only about 0.23%. The second exception is in Aswan as shown in Fig. 7. The present work has an error ranging between 4% and

30O

275 A

¢M

E 250

225

._~ 200

175

.c_ 150 r -

-~ 125 .co

1 O0

7 5 -

5 0 ~

05

zx Measured data - - Present work

- - - - -- Hanna's model [10]

,¢

I L I L I I I I I I \ ~ 6 7 8 9 10 11 12 13 14 15 16 17

Local t ime (h)

Fig. 5. The diffuse solar radiation on 28 January 1980.

I 18 19

274 Data Bank

150

125

~ 100

~ 7 5 ¢-

E 5o

~ 25

0 I£

0

[ ] Present work [ ] Hanna's model

i~ii!i

lii' iili i!iI

lii I- 2 3 4 5 6 7 8 9 RMSE

Months of the year of whole period

Fig. 6. Compar ison between present work and Hanna ' s model [10] for diffuse solar intensity estimation.

6 % for the considered locations in Egypt with only an excep- tion in Mat ruh which has an error of about 10%.

These exceptions may be due to the substantial errors that may exist in measuring data in Ma t ruh and Aswan. Shaltout [14] explained that the global radiation is measured by 10- junct ion Epply pyranometers which are frequently calibrated in all considered locations. However, at Aswan and Matruh, the global radiation is measured with pyranographs which are not calibrated, and the Meteorological Authori ty applies correction factors for these two stations. Therefore, the mea- sured data at Aswan and Mat ruh mus t be considered with some caution.

5. S U M M A R Y AND C O N C L U S I O N S

In the present work, the actual measured data of the beam normal solar radiation at A1-Ahram region in Egypt are used to calculate the atmospheric extinction coefficient. Using numerical-analysis techniques, a second-degree equation

relating the extinction coefficient to the number of day in the year has been derived. This new equation, with the air mass and the extraterrestrial solar radiation, is used to calculate the beam normal solar radiation.

The actual measured data at A1-Ahram region are used, also, to estimate the diffuse radiation. Applying numerical- analysis procedures, a straight line equation relating the diffuse ratio factor to the beam normal atmospheric trans- missivity is derived for calculating the diffuse radiation.

In order to generalize these equations for other locations in Egypt, a location-correction factor, related to the cosine of the latitude, is introduced.

N O M E N C L A T U R E

a mathematical constant A apparent beam normal intensity at air mass = 0,

W/m 2 b mathematical constant

Table 4. Monthly mean daily global solar radiation in Cairo

Radiation (MJ/m z) Error (%) Month M H P H P

1 11.83 14.08 13.07 19.02 10.48 2 15.47 18.96 16.45 22.56 6.34 3 19.27 24.95 20.57 29.47 6.74 4 23.07 26.30 22.92 14.00 - 0 . 6 5 5 26.21 30.43 26.21 16.10 0.02 6 27.96 32.25 27.67 15.34 - 1.02 7 27.04 31.34 27.06 15.90 0.15 8 25.25 27.98 24.48 10.81 - 3 . 0 4 9 21.99 23.11 21.31 5.09 - 3 . 1 1

10 18.02 20.91 18.87 16.04 4.74 11 13.29 15.33 14.63 15.35 10.I1 12 11.12 12.78 13.32 14.93 19.76

M, measured ; H, Hanna ' s model ; P, present work. Mea- sured data are the average from 1969 to 1977 [8].

Table 5. Monthly mean daily global solar radiation in Giza

Radiation (MJ/m 2) Error (%) Month M H P H P

1 12.26 14.09 13.08 15.49 6.71 2 15.74 18.97 16.46 20.52 4.57 3 20.77 24.95 20.57 20.12 - 0 . 9 5 4 24.10 26.29 22.92 9.54 -4 .91 5 26.67 30.41 26.20 14.02 - 1.75 6 28.20 32.23 27.66 14.29 - 1.91 7 28.00 31.32 27.05 11.86 - 3 . 4 0 8 25.71 27.96 24.47 8.75 - 4 . 8 0 9 22.41 23.11 21.31 3.12 - 4 . 9 2

10 17.46 20.92 18.88 19.82 8.15 11 13.36 15.34 14.65 14.82 9.62 12 11.31 12.79 13.33 13.09 17.89

M, measured ; H, Hanna ' s model ; P, present work. Mea- sured data are the mean of the averages from 1956 to 1966 [24] and 1972 to 1976 [25].

Data Bank 275

$

<

2O I [ ] Present work [ ] Hanna's model [10]

• Abd-EI-Salam [30] 15

10

5

0 Cairo Giza Bahteem Tahrir Khargah Matruh Aswan Locations

Fig. 7. Errors in calculating monthly mean daily global solar radiation estimation in Egypt.

B atmospheric extinction coefficient c mathematical constant

C diffuse radiation coefficient DST day-light saving time parameter, h

Dv deviation between a s tandard value and an esti- mated one

e earth 's orbit eccentricity = 0.016733 EqT equation of time, rain

h local elevation above mean sea level, m /bn beam normal radiation intensity, W/m z 10 diffuse radiation intensity, W/m 2 Ig global radiation intensity, W/m 2 10 extraterrestrial solar radiation on a normal

surface, W / m 2 Lc longitude correction, h

LT local time, h L(qS) latitude correction factor

m optical air mass m* altitude corrected air mass

MBE mean bias error N day number in the year starting from 1 January

No number of observations N~ day ratio between day number and number of

days in the year P standard pressure at sea level, Pa

P* mean local atmospheric pressure, Pa RMSE root mean square error

ST solar time, h Tb atmospheric transmissivity for beam radiation

Tb,, atmospheric transmissivity for beam normal radi- ation

To atmospheric transmissivity for diffuse radiation w hour angle, degrees

W period of the cycle X mathematical variable

Greek letters 6 declination angle, degrees

0~ zenith angle, degrees q5 latitude, degrees.

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276 Data Bank

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