correlation between estimated and measured hourly and daily solar fluxes over bahrain

Applied Energy 40 (1991) 83-89

Correlation between Estimated and Measured Hourly and Daily Solar Fluxes Over Bahrain

F. M. Ragab & A. K. Som

Physics Department, College of Science, University of Bahrain, PO Box 32038, State of Bahrain

ABSTRACT

Global radiation predictions can be carried out by many methods. However, the simplest method is the addition of direct and diffuse components of the solar.flux. In this paper, the actual data .for the direct, diffuse and global radiations as measured by Eppley precision pyranometers have been anaO'sed.

Correlations for the hourly fluxes were carried out. The comparison of the predicted and measured data for the two months of April and September 1990 is significant, except for low sun angles. The presence of clouds decreases the direct .flux and relatively increases the diffuse flux.

1 INTRODUCTION

Accurate and reliable information about the amount of solar radiation falling on a horizontal plane is a prerequisite to the study of the workability of various solar energy appliances and devices. However, such data are not always readily available for as many locations as are desired. Therefore, estimations of the hourly and daily fluxes at such locations are very useful in assessing the local potential of solar energy utilization. However, the average daily radiation is not always the most appropriate parameter to characterize the potential applicability of solar energy.

A knowledge of probable incident solar-flux values at hourly intervals on horizontal and inclined surfaces is essential in designing solar energy devices. Data for hourly radiation received are more significant in evaluating

83 Applied Energy 0306-2619/91/$03"50 © 1991 Elsevier Science Publishers Ltd, England. Printed in Great Britain

84 F. M. Ragab, A. K. Sore

the performance of flat-plate collectors than daily radiation values. However, to measure solar radiation accurately one requires expensive and sensitive instruments. As the availability of such instruments is scarce in any country, it is often necessary to compute the direct, diffuse and global fluxes from theoretical models.

In this paper results are presented for hourly direct, diffuse and global radiations for two selected days of April and September 1990. These results are compared with predictions from the theoretical models of Hottel ~ for direct flux, Liu and Jordan 2 for diffuse flux and then from the two models, for the global flux. For the three fluxes, the theoretical estimations of A1-Sadah et al. 3 are also applied for comparison with the actual measured data.

The predicted daily variation of the three fluxes for April and September are presented; also, the average minimum and maximum daily temperature variations for the two months are shown. Actual,global-radiation data were measured by an Eppley pyranometer- integrator system and a similar instrument, fitted with an Eppley shadow band, was used to measure the diffuse component. Suitable shadow-band corrections were made to the shaded pyranometer readings. These Eppley pyranometers were placed on the roof of the Physics Depar tment of the University of Bahrain.

2 M E T H O D S OF P R E D I C T I O N

2.1 Estimation of hourly direct flux

The first model used for the estimation of the hourly direct-radiation is the one proposed by Hottel.1 According to this model, the hourly flux of direct radiation I b under clear-sky conditions as a function of the zenith angle and the altitude is given by

I b = IoTb cos ®z (1)

where I o is the extraterrestrial radiation, and ®z is the zenith angle. The atmospheric transmittance 4 is given by the expression

T b = 0-1338 + 0.7417 exp ( - 0-3803/cos Oz) (2)

The second model, for the same purpose, was proposed by A1-Sadah et

al. 3 in the form

T b / H b = a 1 + bi t + cl t 2 (3)

for 6"00 < t < 18"00 where al, bl and c x are constants and t is the local time in hours. For the month of April, expression (3), for Bahrain, can be written a s 4

l b / H b = --0"5130 + 0.1063 t -- 0"0043 t 2 (4)

Hourly and daily solar fluxes over Bahrain 85

2.2 Estimation of hourly diffuse flux

An empirical relationship, as proposed by Liu and Jordan, 2 was used to estimate the clear-sky diffuse radiation on a horizontal surface. According to their model, the hourly flux of diffuse radiation I d is given by

1 o = loT o (5)

where T o is the atmospheric transmittance for diffuse radiation which can be expressed in terms of T b as

T o = 0-2710 - 0-939 T b (6)

Again, using expressions given in Refs 3 and 4, then for the month of April, in Bahrain,

Io /H o --- - 0 2 9 4 3 + 0"0683 t - 0 0 0 2 8 t 2 (7) for 6"00 < t < 18"00 where H 0 is the daily flux of diffuse radiation.

2.3 Estimation of hourly global flux

Also I T / H T on expressed as;

One of the many methods available for the estimation of hourly global flux is the simple addit ion of the two components I b and 1 o. So for Bahrain, under clear-sky conditions, the hourly global radiation flux I v is given by;

1T = tb + Zo (8)

a horizontal plane 3'4 for Bahrain during April can be

I T / H v ~- --0"2943 + 0-0917 t --0"0037 t 2 (9)

for 6"00 < t < 18"00 where H T is the daily flux of global radiation. For the month of September 1990, equations similar to eqns (4), (7) and (9) exist for Ib /H b, I o /H d and I v / H v but with different constants. 3"4

3 R E S U L T S A N D D I S C U S S I O N

3.1 The hourly solar flux

Tables 1 and 2 show the measured solar-flux data for direct, diffuse and global radiation over Bahrain for each hour of 16 April and 16 September 1990, respectively. The flux is measured in Wh/m 2 when it is received on a horizontal surface and the hourly values are integrated to give the daily sum of each component . The ratios (Ib/Hb), (ld/Hd) and (IT/HT) are presented in Tables 3 and 4. The time indicated in the tables is the local time. The data

86 F M. Ragab, A.K. Som

T A B L E 1 Data of the Direct, Diffuse and Globa l Radia t ions in W h / m z for 16 April

1990 at the Weather Station, Bahra in Universi ty"

Time (h) Global Diffuse Direct

6 28 12 16 7 190 132 58 8 409 328 81 9 619 381 238

10 724 159 565 11 879 146 733 12 917 137 780 13 879 127 752 14 758 115 643 15 592 104 488 16 391 90 301 17 189 65 124 18 37 27 10

Total 6 612 I 823 45 789

" 0 = Midn igh t = 24h local time.

T A B L E 2 Data of the Direct, Diffuse and Globa l Rad ia t ions in W h / m 2 for 16

September 1990, at the Weather Stat ion, Bahra in Universi ty"


6 17 4 13 7 167 44 123 8 388 89 299 9 595 121 474

10 750 128 622 11 850 132 718 12 884 132 752 13 853 123 730 14 753 106 647 15 596 92 504 16 391 79 312 17 167 52 115 18 11 14 3

Total 6424 1116 4 652

" 0 = Midn igh t - 24h local time.

Hourly and daily solar fluxes over Bahrain

TABLE 3 Solar Radiation Ratios for 16 April 1990"

87


6 4.23 x 10 3 6-582 × 10 -3 3.34 x 10 -3

7 0.028 7 0.072 4 0.012 1 8 0.061 8 0.1799 0.0169 9 0.083 6 0.208 9 0.049 6

10 0.1094 0.087 2 0.117 9 11 0.1329 0.08 0-153 12 0.138 6 0-075 1 0.162 8 13 0.1329 0.0696 0.157 14 0-1146 0.063 0.1342 15 0-089 5 0.057 0-101 9 16 0"059 1 0'049 3 0.062 8 17 0.025 8 0.035 6 0.025 8 18 5"595 x 10 . 3 0"0148 2"088 >( 10 3

" 0 -= Midnight -= 24 h local time.

used are from 6 am to 6 pm each day. Compar isons of each ratio with the values predicted from the corresponding empirical models 1 -3 were made.

3.2 Direct flux

Figures 1 and 2 represent the direct solar-flux ratios for the chosen months. The ratio of the measured hourly average fluxes (Ib/Hb) is plotted as

TABLE 4 Solar Radiat ion Ratios for 16 September 1990"


6 2-646 x 10 -3 3"584 x 10 3 2"794 x 10 -3

7 0"025 6 0"039 4 0"026 4 8 0"060 3 0"079 7 0"064 2 9 0-0926 0"1084 0"101 9

10 0"1167 0"1146 0-1337 11 0"132 3 0"118 2 0-154 3 12 0-137 6 0-118 2 0"161 6 13 0-1327 0'1102 0"1569 14 0"117 2 0-095 0"139 15 0"092 7 0"082 4 0" 108 3 16 0"060 8 0"070 7 0-067 17 0"025 9 0'046 5 0"024 7 18 1"712 x 10 -3 0"0125 6"4 x 10 -3

a 0 - Midnight - 24 h local time.

88 F. M. Ragab, A. K. Som

D I R E C T R A D I A T I O N 1 6 . 4 . 9 0

0.1(

0.1,1 I

0.12

£ I- ~ 0.10

z O

o.oe

a <

0.o6

O,04

0.o2 i

6 7 8 9 10 1 1 12 13 14 15 16 17 18

T I M E HOUR

Fig. 1. Direct solar-flux ratios for 16 April 1990. O, Ratio of measured hourly average fluxes (lb/Hb) plotted as a funciton of time; A, theoretical estimation of Ref. 1; I , theoretical

estimation of ReE 3.

0-11 D I R E C T R A D I A T I O N 1 6 . 9 . 9 0

0.16

0.14

2-a 0.12 £ I,,,

0.10

Z £ I-. 0.06

a , (

{= 0.06

0.04

0.02

6 7 8 9 10 1 ] 12 13 1"- lS 16 17 18

T I M E HOUR

Fig. 2. Direct solar-flux ratios for 16 September 1990. O, Ratio of measured hourly average fluxes (Ib/Hb) plotted as a function of time; A, theoretical estimation of Ref. 1; I , theoretical

estimation of Ref. 3.


a function of the actual time t and is indicated by a solid circle. The ratio is then compared with the theoretical estimation of Ref. 1 as indicated by the solid triangle, and of Ref. 3 as indicated by the solid square.

It can be seen that there is a close agreement between experimental and theoretical values of the direct flux. The agreement is more pronounced between the peaks of measured and predicted values 3 for April than for September. The latter deviates by 13% from the estimated values given in Refs 1 and 3. For the rest, the figures show a small discrepancy, less than 6%, between the estimated and the measured ratios. This discrepancy may be due to the presence of clouds but they do not normally form in the months chosen. The ratio is then compared with the theoretical estimation of Ref. 1 as indicated by the solid triangle, and of Ref. 3 as indicated by the solid square. Part of the discrepancy may be due to non-uniform absorption and scattering by atmospheric particulates and gases or by the ground irradiance.

The comparison leads to the fact that predictions given in Ref. 1 and 3 are valid within acceptable limits when applied in estimating the hourly solar flux in Bahrain and the Arabian Gulf region at large. 4

3.3 Diffuse flux

The ratios (Id/Hd) are shown in Figs 3 and 4 for April and September. They were compared with the estimated values obtained from models 2 and 3. The

0.20

0.18

0.16

2 ..:o 0.14

o

0.12 E Z O F- 00J

Q

• 0.01

0.06

0-04

Fig. 3.

D I F F U S E R A D I A T I O N 1 6 . 4 . 9 0

6 7 8 9 10 11 12 13 14 15 16 17 18 T I M E HOUR

Diffuse flux ratios (Id/Hd) for 16 April 1990: 0 , measured ratio; A, ratio from model 2; I , ratio from model 3.


0.2(

O.1E

0.16

--~ 0.14

_.£ I-

0.12 E Z £ I-,- 0.10

a

0.08

0.06

0.04

D I F F U S E R A D I A T I O N 1 6 . 9 . 9 0

6 7 tl 9 10 1 l 12 13 14 lS 16 17 18

T I M E HOUR

Fig. 4. Diffuse flux ratios (la/tla) for 16 September 1990: 0, measured ratio; A, ratio from model 2; m ratio from model 3.

measured ratios are indicated on the graphs by a solid circle, while those for model 2 are indicated by a solid triangle and for model 3 by a solid square.

The measured data at low morning sun angles deviate significantly from the estimated data for April, but tbr later in the day, the graphs have the same shape and the deviation, if any, is less pronounced.

For September the measured data and the predicted data agree within acceptable limits; the variation being within 12%. A good correlation is obtained which is an accurate comparison for solar radiation under prevailing environmental conditions in Bahrain and the neighbouring Gulf countries. ~

3.4 Global flux

The ratios of actual and estimated hourly global radiations are presented in Figs 5 and 6 for April and September. The comparison in this case is carried out between the measured data and the calculated theoretical data using the models described in Refs ! and 2: the two components I b and I d are summed.

The ratios are also compared with predictions obtained using model 3. The actual data ratios are indicated by solid circles while those from models 1 and 2 are indicated by solid triangles and from model 3 by solid squares.

A deviation of about 18% is noticed at low sun angles, whereas the peak values which occur between 11 and 13 h deviate less than 7% for April. The


0.14

I 2~.

0.12

9 0.1~

E z 0 r-- o.oe <

< ee 0.0(

0.04

Fig. 5.

0.02

G L O B A L R A D I A T I O N 1 6 . 4 , 9 0

6 7 8 9 10 11 12 13 14 15 16 17 10

T I M E HOUR

Global flux ratios for 16 April 1990: Q, measured data; &, ratio from models 1 and 2; II, ratio from model 3.

0.18

0.16

0.14

Z _o I - 0,08 <

<[ oc 0-O6

Fig. 6.

0,04

0.02

G L O B A L R A D I A T I O N 1 6 . 9 . 9 0

6 7 8 9 10 11 12 13 14 15 16 17 18

T IME HOUR

Global flux ratios for 16 September 1990: Q, measured data; A, ratio from models 1 and 2; I[, ratio from model 3.


deviation for September is less pronounced and the actual data compare well with those predicted from model 3: a deviation of ,-~10% ensues. The differences noticed in the graphs of hourly global-flux can be explained by the fact that models 1 and 2 are symmetrical forecasts and model 3 is nearly symmetrical. However, astronomical and meteorological phenomena are rarely symmetrical. Therefore the frequency of occurrence of these variables could be different for three models.

Some other models for the calculation of indirect, diffuse and global radiations each hour of the day exist. 5'6 Recently, more theoretical models 7 - 9 have been proposed to account for the cloudiness which prevails in most locations. Gopinathan t° has followed the same procedure by using the theoretical model of Collares-Pereira and Rabl xx and presented a comprehensive estimation of (Iv/H1.) in the form:

{ cosw } (I~/HT) = (a + b cos w~) sin w~ - (2rows360) cos w s

where w = hour angle in degrees w s = sunset hour angle a = 0-409 + 0.5016 sin (w~ - 60) b = 0"6609 - 0.4747 sin (w~ - 60).

In 1988 l° the model proposed by Gopina than was used to compare measured and estimated data of global radiation in Lesotho (Southern Africa) as a function of time. His results compare well with the results o f the present paper. However, his investigations were about solar flux for latitude 29 ° S in the Southern Hemisphere whereas the present study is for latitude 26°N in the Northern Hemisphere.

3.5 Daily solar flux

Tables 5 and 6 show the total solar radiation flux in Wh/m 2 for the months of April and September, respectively. The tables also show the diffuse and direct components of the radiation flux. The daily diffuse flux is indicated on Figs 7 and 8 by solid circles, the direct flux by solid triangles and the global flux by solid squares. Figure 7 presents the daily variations of the three types of radiation for April 1990, while Fig. 8 shows the daily variation of the three radiation fluxes for September 1990.

The graphs for the month of April show more distinct variations in the peaks than those for September. Also, the effect of clouds is easily detected on, e.g. days 4, 9, 14 and 23 of the month where both the direct and global fluxes are drastically reduced, whereas the diffuse flux increases. This also agrees with the present observations.

Hourly and daily solar fluxes over Bahrain

TABLE 5 Total Solar Radiation for Each Day in W/m z for the month of April 1990

93

Day Global radiation Diffuse radiation Direct radiation

1 5 827 - - - - 2 4835 1 728 3 107 3 5911 1 610 4301 4 2767 1 481 1 286 5 5 830 1 837 3 994 6 6921 1 214 5 707 7 6905 1 231 5 674 8 5 347 1 917 5430 9 3414 1 154 2260

10 6561 1632 4930 11 6961 713 6248 12 6757 1 714 5043 13 6047 2013 4034 14 3923 576 3348 15 5272 952 4320 16 6934 1823 5111 17 7090 1898 5192 18 7166 1416 5750 19 6709 1526 5183 20 6286 1677 4 609 21 6150 1403 4 747 22 5308 1755 3553 23 5022 2211 2811 24 6789 1636 5153 25 6250 1763 4487 26 7022 1 470 5 552 27 6412 1870 4542 28 3467 2118 1349 29 4 654 2496 2193 30 6358 1596 4762

Table 7 shows the changes in t empera tu re o f each day dur ing Apri l and

September . F igures 9 and 10 represent the m a x i m u m and m i n i m u m

tempera tu res du r ing Apri l and September , respectively, in Bahrain. The global r ad i a t ion cou ld be co r re la t ed to the m a x i m u m t empe ra tu r e

qual i ta t ively on the two g raphs for each month . The cor re la t ion is within 20% in each case. M a n y a t t empts have been m a d e to develop theoret ical models to es t imate the different dai ly fluxes. A general equa t ion has recently been put fo rward by Bird and H u l s t r o m 9 to calculate the global r ad ia t ion Hv on a ho r i zon ta l surface in the fo rm:

Hv = [ g , - H b cos i + H d cos2(O/2)]/[r , sin2(0/2)] (10)


w h e r e H~ = g lobal flux o n an incl ined p lane H b = direct flux c o m p o n e n t H a = diffuse flux c o m p o n e n t

i = inc ident angle o f direct b e a m 0 = the inc l inat ion o f the surface to the h o r i z o n t a l rg = the g r o u n d a lbedo.

The direct flux H b is related to the prevai l ing a t m o s p h e r i c c o n d i t i o n s by

H b = 0"9662 Ho(T m -- a w ) T a (11)

where T m is the transmiss iv i ty o f the a t m o s p h e r i c gases (except water

TABLE 6 TotalSolarRadiation ~reachday in W/m 2 ~ r t h e monthofSeptember1990

Day Global radiation D!ffi~se radiation Direct radiation

1 6 231 1 406 4 825 2 6 455 1 156 5 299 3 6 718 872 5 846 4 6903 758 6145 5 6 567 1056 5 511 6 6658 771 5887 7 6331 930 5401 8 6 399 746 5 653 9 6 544 970 5 574

10 6340 1120 5220 11 6293 1010 5283 12 6362 888 5474 13 6293 962 5331 14 6415 864 5551 15 6089 901 5188 16 6099 1 116 4983 17 6426 987 5439 18 6297 946 5351 19 6382 987 5395 20 6077 1197 4880 21 5634 1 229 4405 22 5792 1 195 4597 23 5953 850 5103 24 5 988 1044 4944 25 5703 1287 4416 26 5779 1169 4610 27 5 687 635 5052 28 5 274 1014 4 260 29 5644 882 4 762 30 5818 966 4852


v a p o u r , a w is t he p e r c e n t a g e a b s o r b e d b y w a t e r v a p o u r . T a is t he

t r a n s m i s s i v i t y d u e to a b s o r p t i o n a n d s c a t t e r i n g b y p a r t i c l e s .

T h e t h r e e f luxes w e r e a n a l y s e d b y t h e m o d e l p r o p o s e d b y A 1 - S a d a h et al. 3

w h o u s e d t h e m o d e l s o f H o t t e l 1 f o r d i r e c t r a d i a t i o n , a n d t h a t o f L i u a n d

J o r d a n 2 f o r d i f fuse r a d i a t i o n to o b t a i n t he g l o b a l r a d i a t i o n b y a d d i n g the

d i f fuse a n d d i r e c t c o m p o n e n t s . G l o b a l s o l a r r a d i a t i o n a n d i ts f l u c t u a t i o n in

B a h r a i n w a s a l s o m e a s u r e d b y A l n a s e r a n d S o m ~2 o v e r a n u m b e r o f yea r s .

TABLE 7 Maximum and Minimum Temperatures (in C ) recorded for the months of

April and September 1990

Day September April

Maximum Minimum Maximum Minimum

1 23"6 19 37"2 28"9 2 25"7 19"6 40-5 27"6 3 32-6 21 38"1 28"7 4 23"5 20"7 39"3 28 5 25"9 l 8'9 40.5 28 6 25'5 19"6 40 28 7 25'5 17' 1 36 26"9 8 28"5 16"6 37"5 26-8 9 26 20"9 40"8 28" 1

10 30"4 16"5 40 28-6 11 28'9 21 2 37"8 27"3 12 31'4 19"5 38"9 26"4 13 36'3 19.1 39"1 26"9 14 41"3 24"5 37"1 27"6 15 42"2 25-3 35"9 25"6 16 27"9 21"6 35"2 26"5 17 28"2 23-3 36"6 25"5 18 27"5 23"6 34-9 26'3 19 29"3 19"6 36 26"7 20 30 21 "6 34-9 24.9 21 31"2 20"6 34'5 25.34 22 29-4 21 36"8 26"7 23 33"3 24 35.2 25.2 24 28"7 23.5 37.3 26.2 25 30"8 23"4 39-3 27"6 26 31"4 23.6 39.7 27.7 27 31-6 21.9 38 25.9 28 33 23.3 37-6 26 29 37.2 26-6 36.1 25-3 30 29"2 26"6 39-4 25"5

Average 29"92 21 "43 37"9 26"82


70

10

2 8 1 14 18 20 2 24 26 28 Days of the month

Fig. ?, D i rec t , d i f fuse and g l oba l r a d i a t i o n f o r A p r i l 1990; O , da i l y d i f fuse f lux ; A , d i rec t

flux: II, global flux.

60 &-

5o

4o

3o

n- 20

70

60

E 5O

40 o

30 _~ ~3

20

10

' ' ' ~ ' & ' , 2 , ' 4 ' ' ' ' 2 ' o ' ' ' ~ ' ' ' ' ' 2 4 10 16 18 22 4 26 28 Days of the month

Fig. 8. Direct, diffuse and global radiation for September 1990: O, daily diffuse flux; A, direct flux; II, global flux.


45

40

35

30

0 25 o

15

10

5

0 I I I I I I I I I I I I r L I J ; I 2 4 e 8 ,'o ,2 1'4 ,'~ ,• 2'0 ~2 44 46 ' 28

Days of the month

Fig. 9. Maximum 1 0 ) and minimum (A) temperatures for April 1990.

40

35

3C

25

¢ 2c I--

15

,o] 5

I I ~ I I I I I I I ~ ~ I I l 0 2 4 6 ' 8 1'0 1'2 ll4 1'6 18 20 22 ' 24 28 26

Days of the month

Fig. 10. Maximum (O) and minimum (A) temperatures for September 1990.


The comparison between the daily estimated and measured radiation data for Bahrain was carried out recently by Ragab et al.: 13 the deviation recorded was in the region of 14%. According to this study the absolute values of Hb, H d and HT correlate well with the corresponding predicted values calculated from the three models. This agreement provides good background information for the utilization of solar energy in Arabian Gul f States, which have similar weather conditions all the year round.

4 C O N C L U S I O N S

The data of the direct, diffuse and global radiations in Bahrain as measured by Eppley pyranometers have been compared with predicted data of the same fluxes obta ined using three different models. 1-3 The comparison for the hourly flux is significant except at low sun angles, for which a pronounced deviation of diffuse radiation during April was observed.

From the study of the graphs of the daily variations of the solar fluxes during April and September, it is evident that the presence of clouds decreases the direct flux and increases the diffuse flux qualitatively. The maximum global flux for a particular day could be correlated well with the maximum temperature recorded on the same day.

R E F E R E N C E S

1. Hottel, H. C., A simple model for estimating transmittance of direct, solar radiation through clear atmospheres. Solar Energy, 18 (1976) 129.

2. Liu, B. Y. & Jordan, R. C., The interrelationship and characteristic distribution of direct, diffuse and global solar radiation on horizontal surfaces. Solar Energy, 4(3) (1960) 1.

3. A1-Sadah, F. H., Ragab, F. M. & Arshad, M. K., Hourly solar radiation over Bahrain. Energy, 15(5) (1990) 395.

4. AI-Sadah, F. H., Ragab, F. M. & Arshad, M. K., A comparative study of hourly solar radiation in Bahrain. The Second International Conference on Solar Applications, Cairo, Egypt, (in press).

5. Bird, R. & Riordan, C., Simple solar spectral model for direct and diffuse irradiance on horizontal and tilted planes at the Earth's surface for cloudless atmospheres. US Solar Energy Research Institute Technical Report TR-215- 2436, Golden, Colorado, 1984.

6. Justus, C. G. & Paris, V., A model for solar spectral irradiance and radiance at the bottom and top of a cloudless atmosphere. J. Clim. App. Meteor., 24 (1985) 193-201.


7. Doginiaux, R., Eclairment Energetique Solaire Direct, Diffuse Et Global Due Surfaces Orient6es et Inclin6es, I.R.M. Misc. Seire B, 59 Brussels, 1984.

8. Page, J. K., Prediction of solar radiation on inclined surfaces. Solar Energy R & D in the European Community, Series F, Vol. 3, Reidel, Dordrecht, 1986.

9. Bird, R. & Hulstrom, R. L., A simplified clear-sky model for direct and diffuse insolation on horizontal surfaces. US Solar Energy Research Institute Technical Report TR-642-761, Golden, Colorado, 1981.

10. Gopinathan, K. K., Diurnal variation of the hourly hemispherical insolation. Solar and Wind Technology, 5(6) (1988) 661.

11. Collares-Pereira, M. & Rabl, A., The average distribution of solar radiation correlations between diffuse and hemispherical and between hourly and daily insolation values. Solar Energy, 22 (1979) 155.

12. Alnaser, W. E. & Sore, A. K., Solar energy fluctuation over Bahrain. Proceedings of the 1989 Congress of lSES, Kobe, Japan 1989, Clean and Safe Energy Forever, ed. T. Horigome, K. Kimura, T. Takakura, T. Nishino & I. Fujii. Vol. 3, pp. 1977-80, Pergamon Press, London.

13. Ragab, F. M., Al-Sadah, F. H. & Arshad, M. K. Estimation of direct, diffuse and global daily solar radiation in Bahrain. The Second International Conference on Solar Application, Cairo, Egypt (in press).

correlation between estimated and measured hourly and daily solar fluxes over bahrain

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