Study of global daily solar radiation and its relation to sunshine duration in Bahrain

Solar Energy Vol. 47, No. 2, pp. 115-119, 1991

0038-O92X/91 $3.00 + .00 Copyright © 1991 Pergamon Press pie

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STUDY OF GLOBAL DAILY SOLAR RADIATION A N D ITS RELATION TO SUNSHINE DURATION IN BAHRAIN FAYEZ H. AL-SADAHand FAROUKM. RAGAB* Department of Mechanical & Chemical Engineering,College of Engineering,*Department of Physics, College of Arts and Sciences, University of Bahrain, Bahrain Abstract--The regression coefficientsa and b of Angstrom type correlation for the monthly daily average global solar radiation have been determined. The two constants a and b have been derived for different months during the period 1983-1987. The clearnessindex (H/Ho) based on predicted and measured values of global daily solar radiation is presented for different seasons of the year. The study depicts the various astronomical and meteorologicalparameters affectingthe global radiation in Bahrain.

1. INTRODUCTION In any solar energy conversion system, the knowledge of global solar radiation is extremely important for the optimal design and the prediction of the system performance. The usual practice is to correlate the global solar radiation with the sunshine duration at the place where the data are collected. The resultant regression may then be used for localities of similar meteorological and geographical characteristics at which solar data are not readily available. Bahrain with a relatively low average rainfall of about 90 mm and a semi-arid climate enjoys a substantial amount of insolation. Long term measurements of solar radiation on a horizontal surface exist for a small number of recording stations. In this study it is attempted to provide a model to predict global solar radiation in terms of sunshine duration for places where measurements are lacking. AngstrOm[ 1] was the first to propose a correlation for estimating the monthly average global radiation on a horizontal surface as

sented in [2]. This means that 12 equations, one for each month, are required for a specific location. These are linear equations in the form

Y = a + bX

(2)

where Y = (H/Ho) and X = ( s / N ) . Although a number of correlations that include more parameters than sunshine duration have been developed[ 3, 4], yet ~ngstrrm regression has been found to be widely applicable in determining global solar radiation for a large number of locations [ 5-9 ]. Nonetheless, some spatial and temporal scatter in the constants a and b of eqn (1) have been reported by several investigators [ 10-14 ]. Hay [ 15 ] attributed the scatter to (i) the effect of multiple reflections between the earth's surface and the atmosphere, (ii) inaccuracies involved in the measuring devices of sunshine hours when the sun elevation is less than 5 degrees. Rietveld [11] reported that the constants a and b are themselves functions of the parameter (s/N) as a = 0.1 + 0 . 2 4 ( s / N ) (3)

b = 0.38 + 0.08 ( s / N ) Prescott [ 2 ] has substituted Ho instead of Hc in eqn ( 1) which has been used on a wide scale for different locations around the world. The duration of sunshine (s) that is routinely recorded with a heliograph may be used as an indication of cloud cover or turbidity. The time between sunrise and sunset gives the maximum possible duration of sunshine (N). The daily absolute duration of sunshine is a function of latitude, declination angle and cloudiness. The effect of astronomic factors can be eliminated when (s) is normalized with respect to (N). The ratio ( s / N ) is referred to as the relative duration of sunshine. In computations of average global daily solar radiation using Angstrrm's method, a functional dependence is assumed between (H/Ho) and ( s / N ) as pre-

thus, eqn ( 1) takes the form

(H) Hop

=0"18 + 0 . 6

2(s) ~

.

(4)

Later, Glover, and McCulloch[16] have included the latitude (th) of the place in eqn ( 1) and proposed the following relation for 4~ < 60 °

0

os0+ 0

(5)

In this study the regression constants a and b are determined for Bahrain and their interpretation to the

115

F. H. AL-SADAHand F. M. RAGAB

116 APR 8 72

MAY

Table 1. RMSE and a, b ofeq (8) MAR

Month

a

JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV

0.231 0.265 0.306 0.310 0.323 0.416 0.427 0.489 0.442 0.323 0.275 0.183

JUN

e u L K~11111llIIII[ l l l l [ l l l l M l l l

SEE 1024

OCT 9 94

Fig. 1. Average sunshine hours over Bahrain (hours).

DEC

physical parameters of the atmosphere is evaluated. The data obtained from theoretical model of clearness index are compared to those obtained from actual measurements for Bahrain.

b

RMSE

0.467 0.454 0.378 0.400 0.334 0.287 0.267 0.187

0.940 1.130 1.460 1.463 1.490 0.882 1.041 0.645 0.468 0.833 0.544 1.097

0.258

0.331 0.392 0.486

and 2~ c o s _ l [ _ t a n 6 tan ~b]. N = 1---

(7)

2. METHODOLOGY The mean monthly daily global solar radiation obtained for the period 1983-1987 was correlated with the available data of corresponding sunshine duration. A computer program was written for the analysis. Extraterrestrial radiation (11o) and m a x i m u m sunshine hour (N) were computed from eqns (6) and (7), respectively. /360D]

The correlation between (H/Ho) and (s/N) was found to be a linear relation in the form -

Ho

RMSE = ×

.

(cos ~ cos 6 sin ~0) + ~3-3-~)sln 4) sin 6]

.

(8)

The constants a and b alongside with the root mean square error (RMSE) were obtained for every month of the year. RMSE is expressed as

Ho=(2~4r)G~c[l + 0.033 c o s ~ - - ~ - } ] (2r~o~

a+b

V E (Hi,=, - H i , ~ ) 2

(6) a, b and RMSE are given in Table 1.

l

1983

~

1984

~

1985

1986

~

1987

--

MONTHLY AVERAGE

Thousands (W-h/m"2)

10 9 8

7 6 5 4 3 2 1 J

F

M

A

M

J

J

A

S

0

Month Fig. 2. Average monthly daily global radiation over Bahrain.

N

D

(9)

Global daily solar radiation in Bahrain

117

'!

'!

H/Ho

H/Ho

0.a[

0.8 0.6~

0.6 ~

....

~--~

0.4 i[ 0.4

0.21

!

0[

0,2

0

0,2

0,4

0.6

- - - 0.5

0,8

~

____

0.6

i

z

L

0.7

0.8

0,9

s/N

s/N Fig. 3. Variation of global daily solar radiation with sunshine hours (February). 3. RESULTS AND DISCUSSIONS The monthly daily average sunshine hours in Bahrain is shown in Fig. 1. Maximum sunshine duration occurs in the month of June reaching a value of 11.17 hours. On the other hand, minimum sunshine hours are usually recorded during the month of December with a value of 7.19 hours. This figure clearly indicates that the country enjoys clear sky conditions most of the year apart from occasional winter cloud covers. Figure 2 shows the monthly daily average total solar radiation for the country in ( W - h / m 2) during the period 1983-1987. This figure portrays the abundance of solar radiation in the Island with a peak value oc-

Fig. 5. Variation of global daily solar radiation with sunshine hours (June).

curring around June of each year and a minimum value in December. The parameter (H/Ho) is plotted as a function of (s/N) for the months of February, May, June, September and December in Figs. 3-7, respectively. The plots demonstrate the linear trend of the AngstrOm type regression. The regression constants a and b as shown in Table 1 have been found to be in good agreement with those reported in refs. 17 and 18. Reference 17 has reported values of a and b for five cities in Egypt which vary from 0.17-0.70 and from 0.03-0.61, respectively. On the other hand, ref. 18 has reported values of a and b for Iran as 0.23 and 0.54 for the entire

H/Ho

H/Ho

1

0,7

0.6

0.8 0.5

~LJ ~J

j-

fJ

0.4 f7

/"

• ..

0.6

°.

•

• °

,

• .

0.3 ~

0,2

0.4

0.1

0 0,2

±

L

0,4

0,6

J

0.8

s/N Fig. 4. Variation of global daily solar radiation with sunshine hours (May).

0.2

i 0.7

_ _ _ 1

0.8

0.9

s/N Fig. 6. Variation of global daily solar radiation with sunshine hours (September).

118

F.H. AL-SADAHand F. M. RAGAB H/Ho

H/Ho

'f

Measurements

- -

predictions

0.8

0.8

0.6

m

m

m

0.6 0.4 0.4 0.2 0.2 0

0.2

0.4

0,6

0.8

s/N Fig. 7. Variation of global daily solar radiation with sunshine hours (December).

0

0

i

I

k

5

10

15

I

20 DAYS

I

I

25

30

35

Fig. 9. Clearness index (April). year. The values of a and b reported in this paper are within these limits considering the differences in latitude, longitude, and elevation. The transmissivity of the atmosphere for global radiation under clear sky conditions can be interpreted from the summation o f the regression coefficients a and b[19]. The accuracy of the results presented in these figures are tested by the root mean square error ( R M S E ) as shown in Table I. In general, the lower the R M S E the more accurate the estimate is. The daily variations of the measured clearness index

(H/Ho) are presented in Figs. 8-11. These graphs are compared to the theoretical predictions of Hottel [ 20 ] and Liu and Jordan[21]. It is noticeable that the agreement is good during s u m m e r months where clear sky conditions prevail, while the comparison is fair during winter months since the models of refs. 20 and 21 are based on clear sky conditions. Nonetheless, the comparison is significant for such comprehensive study. In addition, the results presented in this investigation compare well with previous results reported by the authors elsewhere [ 22-24 ]. H/Ho

H/Ho •

Measurements

Measureraents

predictions

- -

predictions

0.8

0.8 B

m

i I

m

g

0.6

D

0,6

m O

0.4

0.4

0.2

0.2

I

I

I

I

I

5

10

15 DAYS

20

25

Fig. 8. Clearness index (February).

t

0 30

0

5

J

10

I

I

I

15 DAYS

20

25

Fig. 10. Clearness index (June).

30

119

Global daily solar radiation in Bahrain REFERENCES

H/Ho •

M e a s ~ t r o m e n t s

0.6

•

-

-

predictions

•

•

m

0.4 m

I

0.2

0

5

10

15

20

25

30

35

DAYS

Fig. 11. Clearness index (December). 4. CONCLUSIONS In this investigation a study is carried out to correlate the m o n t h l y daily average global solar radiation o n a horizontal surface in Bahrain with the s u n s h i n e h o u r s for the period 1983-1987. T h e regression constants a a n d b are d e t e r m i n e d for each m o n t h of the year. T h e m o n t h l y daily average variations o f the clearness index in B a h r a i n are c o m p a r e d with those o f refs. 20 a n d 21. It is shown t h a t the c o m p a r i s o n is fairly significant d u r i n g s u m m e r m o n t h s a n d falls to a lesser extent d u r i n g winter m o n t h s . It is believed that this investigation could be extended to cover the adj a c e n t countries in the G u l f having similar meteorological a n d a s t r o n o m i c conditions as Bahrain.

a,b D G,c Ho H Hc Hi.est H~.,,~ n N s

NOMENCLATURE constants in eqn (8) the day-number in the year, 1 < D < 365 solar constant, W / m 2 daily average extraterrestrial radiation, M J / m 2 daily average global radiation, M J / m 2 clear sky global radiation, M J / m 2 ith estimated value of global radiation, M J / m 2 ith measured value of global radiation, M J / m 2 number of observations maximum daily sunshine duration, hr daily average sunshine duration, hr

Greek ~o sunset hour angle declination angle q~ latitude angle

1. A. Angstr/Jm, Solar and terrestrial radiation, Q. J. Roy. Met. Soc. 50, 121 (1924). 2. J.A. Prescott, Evaporation from water surface in relation to solar radiation, Trans. Roy. Soc. Austr. 64, 114 (1940). 3. A. A. M. Sayigh, Solar energy engineering, Academic Press, New York (1977). 4. K. K. Gopinathan, A new model for estimating total solar radiation, Solar & Wind Technology 5, 107 (1988). 5. D. S. Chuan and S. L. Lee, Solar radiation estimate in Malaysia, Solar Energy 26, 33 ( 1981 ). 6. A. Khogali, Solar radiation over Sudan--Comparison of measured and predicted data, Solar Energy 31, 45 (1983). 7. P. C. Jain, Solar irradiation over Zambia, ICTP internal report, IC/83/213 (1983). 8. F. Neuwirth, The estimation of global and sky radiation in Austria, Solar Energy 24, 421 (1980). 9. G. O. Lrf, J. A. Duffle, and C. O. Smith, World distribution of solar radiation. Report no. 21, Solar Energy Lab. University of Wisconsin, Madison, Wl (1966). 10. T. N. Gosh, Statistical study of solar radiation information in an equatorial region, Solar Energy 22, 105 (1979). 11. M. R. Rietveld, A new method for estimating the regression coefficients in the formula relating solar radiation to sunshine, Agric. Meteor. 19, 243 (1978). 12. M.A. Atwater and J. T. Ball, A numerical solar radiation model based on standard meteorological observations, Solar Energy 21, 163 (1978). 13. C. T. Leung, The fluctuations of solar irradiance in Hong Kong, Solar Energy 25, 485 (1980). 14. P. C. Jain, Comparison techniques for estimation of hourly global irradiation, Solar & Wind Technol. 1, 123 (1984). 15. J. E. Hay, Calculation of monthly mean solar radiation for horizontal and inclined surfaces, Solar Energy 23, 301 (1979). 16. J. Glover and J. McCulloch, The empirical relation between solar radiation and hours of bright sunshine, Q. J. Roy. Met. Soc. 84, 172 (1958). 17. S. M. Ibrahim, Predicted and measured global solar radiation in Egypt, Solar Energy 35, 185 (1985). 18. K. Jafarpur and M. Yaghoubi, Solar radiation for Shiraz, lran, Solar & Wind Tech. 6(2), 177 (1989). 19. K. Revfeim, An interpretation of the coefficients of the AngstrOm equation, Solar Energy 31,415 (1983). 20. H. C. Hottel, A simple model for estimating transmittance of direct solar radiation through clear atmospheres, Solar Energy 18, 129 (1976). 21. B. Y. Liu and R. C. Jordan, The interrelationship and characteristic distribution of direct, diffuse and global solar radiation on horizontal surfaces, Solar Energy 4(3), 1 (1960). 22. F. H. A1-Sadah, F. M. Ragab, and M. K. Arshad, Hourly solar radiation over Bahrain, Energy 15 ( 5 ), 395 (1990). 23. F. M. Ragab, F. H. Al-Sadah, and M. K. Arshad, Estimation of direct, diffuse and global daily solar radiation in Bahrain, The second Int. Conf. on solar application, Cairo, Egypt, (in press). 24. F. H. A1-Sadah, F. M. Ragab, and K. Arshad, A comparative study of hourly solar radiation in Bahrain, The second Int. Conf. on solar application, Cairo, Egypt (in press).