Emgy Vol. 15, No. 5, pp. 395-402, 1990 Printed in Great Britain. All rights reserved

03&M442/90 $3.00 + 0.00 Copyright@ 1990 Pergamon Press plc

HOURLY SOLAR RADIATION OVER BAHRAIN

FAYEZ Ii AL-SADAHt FAROUK M RAGABtt and MIRZA K ARSHAD

tDepartment of Mechanical & Chemical Engineering, College of Engineering, University of Bahrain,

BOX 32038, Bahrain. ttDepartment 0:.Physics, College of Arts & Sciences.

(Received 15 February 1989; received for publication 25 January 1990)

Abstract - An empirical formula for estimating hourly solar radiation has been developed. The average hourly total solar radiation has been computed as a function of local time. The results compare well with experimental data measured at latitude @=26'~. There is also good agreement between our model and that of other authors.

A 0' A1' A2

a, b, c

G SC

HO

IO

'b Id

IT n

SD

wl' w2 Z

6

6

JI

'b

'd

NOMENCLATURE constants in Eq. (1)

constants in Eq. (9)

solar constant (W/m2)

daily average total solar radiation (J/m2)

hourly extraterrestrial radiation (J/m2)

hourly beam radiation (J/m2)

hourly diffuse radiation (J/m2)

hourly total radiation (J/m21

day-number of the month

standard deviation (%)

hour angles

zenith angle

declination angle

latitude angle

local time

beam transmissivity

diffuse transmissivity

INTRODUCTION Energy derived from solar radiation promises to play an important role in renewable energy development. The radiation data needed for applications are average hourly and daily beam, diffuse and total intensities on a horizontal surface.

Bahrain is an island situated in the Arabian Gulf at 26'N latitude and 50"E longitude. The average rainfall is 90 mm per year. conditions prevail throughout the year,

Clear sky with occasional cloud cover in

some winter months. The turbidity is low, Shamal winds that may last up to many days.

except during the time of The temperature may reach

up to 46°C in the summer and decreases to 4'C in winter. The relative humidity is over 90% during the summer months.

Solar radiation is abundant, with 11 hours of average daily sunshine.

395

3% FAYEZ H. AL-SADAH et al

The maximum amount of daily solar radiation ranges between 29 and 13 MJ/m2day during June and December, respectively. Solar energy is therefore available in excess of needs.

Insolation data are of fundamental importance for solar technology implementation. In the absence of sufficient monitoring stations, accurate mathematical simulation for estimating data is invaluable. The simulation correlates all meteorological variables that influence the incident solar radiation.

Different models exist for calculating mean hourly solar radiation on a flat surface. The'model utility depends on the accuracy of the predicted data and the ease of application. The model of Hottell has been used together with that of Liu & Jordan' to derive the information discussed in this paper.

Earlier attempts to ana yze hourly radiation were made by Whillier' and by Hottel & Whillier. a These authors presented results for each hour from 9:00 AM to 3:OO:PM. Liu & Jordan5 extended the hours of calculation and also obtained an analytical expression for hourly-to- daily ratios, which agreed with their measured data. Collares-Pereira and Rab16 used the corrected data for five locations in the USA and employed the graphs of Liu & Jordan to develop an analytical expression for hourly-to-daily ratios in terms of the sunset hour angle. Jain7 used measured average hourly global irradiation data for Trieste (Italy) and showed that a normal curve could be well fitted to the data for all months of the year. In 1988, Jain8 used this technique again to analyze hourly direct and diffuse radiation for Montreal (Canada). In our present study, we derive a useful empirical model as a function of local time from measured data.

THEORETICAL MODEL Hourly solar radiation on a horizontal surface has been estimated by

using several models. A convenient model' has been developed for estimating the direct radiation transmitted through a clear atmosphere as a function of zenith angle and altitude. This model is only valid for a standard atmosphere and for four different climate types.' The atmospheric transmissivity for direct radiation is

'b = Ao+A,exp(A2/cosz), (1)

where A,, A, and A2 are constants for a standard atmosphere with 23 km visibility. These constants refer to altitudes < 2.5 km. They may be used for Bahrain (altitude < 0.1 km). The constants for Bahrain are

Ao= 0.1339, A,= 0.7417, A2= 0.3803.

Equation (1) may be rewritten as

TV= 0.1339 + 0.7417 x exp(-0.3803 / cosz). (3)

The clear-sky hourly direct solar radiation may be expressed as

'b = IO x Tb,

where

IO = (12 x 3600/n) Gsc[l+0.033 cos(360 n/365)1

x {co& toss (sinW, - sinW2) + [2*(W2-W,)/3601 sind sin6), (5)

and Gsc = 1367 W/m2.

It is also important to estimate the diffuse hourly radiation on a horizontal surface in order to obtain the total hourly radiation incident at a given location. Liu & Jordan2 presented an empirical correlation between the diffuse and beam transmissivity parameters as

Hourly solar radiation over Bahrain 397

*d = 0.2710 - 0.2939 TV. (6)

The clear-sky hourly diffuse radiation on a horizontal surface is

'd = IO x rd.

The total clear-sky insolation is

IT = Ib + Id_

Based on the measured data, an empirical relation for the estimation of total hourly solar radiation over Bahrain has been developed. This relation is

IT =a + bJ)+ c$

2 for 6:00 5 JI < 18:O0. (9)

Here, a, b and c are constants which are given in Table 1 together with the standard deviation for all months of the year, except for May. Results obtained from this model are discussed in the next section.

Table 1. Constants in Eq. (9).

Month a bx10-2 cx10-3 SDxlO_2

JAN -0.5430 -11.29 -4.65 1.87 FEB -0.5440 9.17 -3.76 0.70 MAR -0.4546 9.59 -3.92 2.29 APR -0.4290 9.17 -3.76 0.69 JUN -0.3490 7.73 -3.18 0.38 JUL -0.4179 8.79 -3.54 1.40 AUG -0.3634 7.98 -3.27 0.62 SEP -0.4069 8.87 -3.68 0.53 OCT -0.4408 9.61 -4.02 0.85 NOV -0.4927 10.63 -4.47 1.50 DEC -0.5282 11.21 -4.68 1.80

RESULTS AND DISCUSSION Direct solar-radiation ratios for the months of April, June, and

September are plotted in Figs. l-3. The direct hourly component of solar radiation divided by the average daily direct component is plotted as a function of local time. In Figs. 4 and 5, we show ratios of the hourly solar diffuse components divided by the average daily diffuse components for the measured data as well as predictions from the formulae of Hottel and Liu & Jordan.

Measured values are not readily available at many places in the Gulf. At locations where no records exist, one may use the theoretical models for estimations.

It is apparent from Figs. 1-3 that there is good agreement between measured data and predictions for the formulae of Refs. 1 and 2. However, Fig. 2 shows that while Hottel's model is symmetrical around the solar noon, the experimental data indicate some asymmetry during the summer season. This discrepancy may be attributed to many factors, viz. (i) variable amounts of scattering and absorption by gases and particulates in the atmosphere and turbidity; (ii) different atmospheric conditions, mainly due to the effects of dust particles that are prevalent in this region during summer time; (iii) changes of the irradiance from the ground. Other meteorological and climatic factors are generally systematic. Environmental factors may produce systematic variations of parameters during the day that cannot be generalized. Interestingly, we find the Liu & Jordan model for estimating diffuse radiation to be in good agreement with our measurements (Figs. 4 and 5).

398 FAYEZ H. AL-SADAH et al

m Hottel m Experiment

0.00 I__ 5 6 ti 12 13 14 15 16 1: 18 19

Time

20

Fig. 1. The direct hourly solar radiation ratio for April.

_ Ho&l EZB Experiment

0.20 [

Fig. 2. The direct hourly solar radiation ratio for June

Hourly solar radiation over Bahrain 399

m Hottel m Experiment

0.20 r

10 ii 12 13 14

Time

15 16 17

Fig. 3. The direct hourly solar radiation ratio for September.

w Liu 6 Jordan m Experiment

0.12

0.10 -

0.08 -

0.06 t

0.04

I

0.02

0.00 'I 5 7 8 9 10 ii 12 13 14 15 16 17

Time

Fig 4. The diffuse hourly solar radiation ratio for June.

400 FAYEZ H. AL-SADAH et al

m Liu 6 Jordan B Experiment

Fig. 5.

5 6 7 8 910 11 12 13 14 15 16 17 18 19 20

Time

The diffuse hourly solar radiation ratio for September.

In Figs. 6-8, we present our model for the hourly total solar radiation. The ratios of hourly total radiation to dail radiation are plotted and compared with those of Hottel. Y

total Our present

model has been derived from local measurements at 26ON latitude. The peak values for the graphs of the total solar hourly radiation ratio for the different months are somewhat less in magnitude than the corresponding estimated theoretical values of Hottel's model. We believe that this peak difference is due to the fact that our model is derived from local measured data while Hottel's is a partial theoretical prediction for a different locality than ours (the Gulf region).

Minor differences may be explained by the fact that both models yield symmetrical forecasts. However, physical phenomena, when all variables are accounted for, are rarely symmetrical. Therefore, the time lag of occurrence of those variables and in particular due to clouds could be different for both models. This phenomenon is clear when comparing Figs. 7 and 8 that characterize summer and winter conditions, respectively.

Our study suggests that whereas Hottel's model is useful, an empirical model based on measured data provides increased accuracy in estimating the intensity of solar radiation at different places. GopinathanlO has followed the same

E rocedure by using the theoretical

model of Collares-Pereira and Rabl. His model is

rt = (a/24) (a+b COSW) { [cosW - cosW,l / [sinWs

- (2nWs/360) cosWsll, (IO)

where r = the ratio of hourly to daily global radiation, W = hour angle ih degrees, Ws = sunset hour angle, a = 0.409+0.5016 sin (Ws-60),

Hourly solar radiation over Bahrain

......’ tiottel - Present model

401

0.20

i

0.15 L

Time

Fig. 6. The total hourly solar radiation ratio for March.

.....*. Hottel - Present model

0.12 -

0.10 -

I 5 6 7 8 9 10 11 12 13 14 15 16 17 la 19 20

Time

Fig. 7. The total hourly solar radiation ratio for June.

FAYEZH. AL-SADAH~~~I

..****. Hottel - Present model

0.20 -

I 5 6 7 8 9 10 !i1213!6 17 18 19 20

Time

Fig. 8. The total hourly solar radiation ratio for December.

b= 0.6609-0.4747 sin(W,-60). This model was applied to Lesotho in South Africa in 1988 to compare measured and estimated data of global solar radiation as a function of solar time.

CONCLUSIONS Our model depicts insolation prevailing in Bahrain and adjacent

countries in the Arabian Gulf. The utility of our model is the result of the fact that meteorological conditions in the Gulf region are generally stable. Our measurements are based on local times.

REFERENCES 1. H.C. Hottel, Solar Energy 18, 129 (1976). 2. B.Y.H. Liu and R.C. Jordan, Solar Energy 4, 1 (1960). 3. A. Whillier, Arch. Meterol. Geophys. Bioclimatol. Ser. B7, 197

(1956). 4. H.C. Hottel and A. Whillier in Transaction of Conference on the Use

of Solar Energy, The Scientific Basis, II, Sec. A, 74 (1955). 5. B.Y.H. Liu and R.C. Jordan, Solar Energy 7, 53 (1963). 6. M. Collares-Pereira and A. Rabl, Solar Energy 22, 155 (1979). 7. P.C. Jain, Solar & Wind Technology 1, 123 (1984). 8. P.C. Jain, Solar & Wind Technology 5, 7 (1988). 9. J.A. Duffie and W.A. Beckman, Solar En ineerin

Processes, John Wiley & Sons, ml9 0). -$----9 of Therma1 10. K.K. Gopinathan, Solar & Wind Technology 5, 661 (1988).