Solar & Wind Technology Vol. 3, No. 3, pp. 223-229, 1986 0741-983X/86 $3.00+0.00 Printed in Great Britain. Pergamon Journals Ltd.

T E C H N I C A L N O T E

Estimation of hourly beam and diffuse solar radiation

K. K. GOPINATHAN and P. POLOKOANA Physics Department, National University of Lesotho, Roma 180, Lesotho

(Received 30 October 1985; accepted 1 December 1985)

Abstract--Measurements of beam and diffuse solar irradiance on a horizontal surface have been utilized to verify simple methods of prediction of solar radiation. Measurements of hourly beam and diffuse solar irradiance on a horizontal surface have been made at Roma, a town 35 km from Maseru, on a few selected clear cloudless days during 1984-85 and the results are presented. The results are compared with those estimated theoretically using the models proposed by Hottel, H. C. Solar Energy 18, 129 (1976) and by Liu, B. Y. H. and Jordan, R. C. Solar Energy 4, 3 (1960). It is suggested that the theoretical models of Hottel and of Liu and Jordan are suitable for estimating hourly beam and diffuse irradiation for any location in Lesotho.

1. INTRODUCTION

The availability of solar radiation is an important factor for consideration in the design of solar energy devices and a reasonable estimate of both global and diffuse irradiation is always important for any solar energy application. However, the mean daily radiation is not always the most appropriate figure to characterize the potential utility of solar energy utilization systems. While designing solar energy systems, one also needs to know insolation values at hourly intervals for inclined and horizontal surfaces. Hourly values of solar radiation allow us to derive very precise information about the performance of solar energy systems. For example, hourly radiation values are more useful in calculating the performance of flat plate collectors than daily radiation values.

Accurate measurements of solar radiation data require delicate and fairly expensive instruments. As such instru- ments are not available at all locations, it is often necessary to compute global and diffuse radiation from theoretical models. In this paper we present the results of measured hourly beam and diffuse radiation for a few selected clear cloudless days during 1984-85. The measurements were carried out at Roma, a town 35 km from Maseru, in Lesotho. Hourly values of beam and diffuse radiation were also estimated for these days, for Roma, using different theoretical models and the results are compared with meas- ured values.

At present, Lesotho has only one solar radiation meas- uring station (Roma) and, as the country is interested in developing solar energy devices, more information on solar radiation data is needed. We have recently reported the results of theoretical estimation of daily mean global and diffuse radiation for four different stations in the country [1]. The main purpose of this paper is to check the applicability of theoretical models for estimating hourly solar radiation data for Lesotho, in preparation for solar energy utilization.

2. SOLAR RADIATION MEASUREMENTS

An Eppley precision pyranometer-integrator system was used to measure global radiation and a similar instrument, fitted with an Epply shadow band, was used to measure diffuse component. Appropriate shadow band corrections were made to the shaded pyranometer readings.

3. METHODS OF ESTIMATION

3.1. Prediction of hourly beam irradiance The model used for the estimation of hourly beam

irradiancc is the one proposed by Hottel [2]. Hottel used a method for estimating the beam radiation transmitted through a clear atmosphere considering the zenith angle and the altitude. According to this model, for periods of an hour, the clear sky horizontal beam radiation is given by

lob = Ion~b cos 0z, where Ion = the extraterrestrial radiation, 0z = zenith angle, Zb = the atmospheric transmittance for beam radiation and % = a 0 + a l e -k/c°'°~. Hottel has given methods for cal- culating the constants a0, aj and k for four different climate types.

3.2. Prediction of diffuse solar irradiance It is also necessary to estimate the clear sky diffuse radi-

ation on a horizontal surface to get the total radiation. An empirical relationship proposed by Liu and Jordan [3] was used for this purpose. According to this model, diffuse radi- ation on a horizontal plane is given by

Id = lo.Zd,

where zd = 0'2710--0'2939%. Hour-by-hour estimates of beam and diffuse radiation are

made, based on the mid-points of the hour.

223

224 Technical Note

4. RESULTS AND DISCUSSION

Table 1 shows the comparison between the measured and calculated hourly values of beam radiation. Table 2 presents the comparison between measured and estimated data of

hourly diffuse radiation. The experiments were conducted in Roma and the data corresponds to 6 clear cloudless days during 1984-85. Figures 1~6 present the variation of beam and diffuse irradiance with time on these days. The time indicated in the tables and figures is solar time. The local

~E

e ~

900

7 0 0 - •

60O

40O

300 8

20(] I I I i 1 I 1 I I 7 8 9 10 11 12 13 14 15 16

I i I 17 18

100

90 7

80 g

70 ~

50

40

30

Solar time (h)

Fig. I. Comparison of experimental and theoretical values of beam and diffuse solar irradiance on a horizontal surface for Roma--9 September 1984. Key: ((3) beam radiation (experimental); ( 0 ) beam

radiation (Hottel) ; (Fq) diffuse radiation (experimental) ; ( i ) diffuse radiation (Liu and Jordan).

I

E

1000

900

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700

6OO

500

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m

I I I I I I I i ~ 8 9 10 11 12 13 14 15 16

I I

17 18

- 1 0 0

- 90 ,.-, 7

E - 80 ~,

8

- 7 0

- 6 0

- 50

- 4 0

3O

Solar time (h)

Fig. 2. Comparison of experimental and theoretical values of beam and diffuse solar irradiance on a horizontal surface for Roma--25 October 1984. See Fig. 1 for explanation of symbols.

Table 1. Hourly beam radiation in MJ m -2

Time (h)

)ay

nber 1984

bet 1984

~ber 1984

nber 1984

mry1985

,ary1985

Method 7-8 8-9 9--10 10-11 11-12 12-13 13-14 14-15 15-16

Experimental 1"88 2.64 3"29 3'85 3-78 3.68 3.20 2-83 1,93 Hottel 1-59 2.40 3.03 3-50 3.74 3.74 3.50 3.03 2.40 % deviation +15.4 +9,1 +7.9 +9.1 +1.1 -1-6 - 9 . 4 -7-1 -24-3

Experimental 1"09 2.05 2-79 3.33 3.43 3.63 3-16 3-0 2.34 Hottel 1.27 2-09 2.78 3.28 3.54 3.54 3.28 2.78 2.09 % deviation -16-5 -1 .9 +0-4 +1.5 - 3 . 2 +2.5 -3 .8 +7.3 +10-7

Experimental 1.75 2.08 2.77 3.07 3-59 3.62 3-68 2-8 2' 51 Hottel 1'62 2.27 2-95 3.43 3.68 3.68 3.43 2.95 2.27 % deviation +7.4 -9-1 -6 .5 - 11-7 -2 .5 - 1.7 +6-8 - 5 . 0 +9"6

Experimental I. 31 2.22 2' 80 3 -26 3' 59 3' 25 3-18 2" 78 2' 18 Hottel 1.57 2.36 3.02 3-49 3.73 3.73 3.49 3.02 2,36 % deviation -19"8 -6 ,3 -7 .9 -7 .1 -3 .9 -14-8 -9 .7 -8 .6 -8 .3

Experimental 1' 21 1.98 3" 0 3,48 3" 69 3" 30 3 -4 l 2- 55 2.22 Hott¢l 1"30 2.11 2.79 3.27 3-52 3-52 3-27 2.79 2,11 % deviation - 7.4 - 6.6 + 7'0 + 6.0 + 4.6 - 6-7 + 4-1 - 9.4 + 4.9

Experimental 1"0 1-99 2,41 2,73 2-94 3.06 2.78 2.46 2.07 0" Hottel 1.07 2.18 2-50 2.77 3.02 3.02 2.77 2,26 2.18 1. % deviation -7 .0 -9 .5 -3 .7 -1-5 -2 .7 +1.3 +0.4 +8-1 -5 .3 -16,

226 Technical Note

.I

.e

1100

1000

900

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700

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300 7

I I I I t 1 I I l 8 9 10 11 12 13 14 15 16

I 1 17 18

100

90

- 80

- - 7 0

- 6 0

- 50

40

30

Solar time (h)

Fig. 3. Compar ison of experimental and theoretical values of beam and diffuse solar irradiance on a horizontal surface for R o m a - - 9 November 1984. See Fig. I for explanation of symbols.

I E

8 ,!

a

r~

time is converted to solar time using the procedure discussed by Duttie and Beckman [4]. The only data used are from 7 a.m. to 5 p.m. (solar time) to eliminate very low sun angles.

The estimated solar radiation is compared with measured radiation to calculate the accuracy and applicability of the

estimate. From Tables 1 and 2 it can be clearly seen that there is a close agreement between the experimental and theoretical values of beam and diffuse radiation. The error does not exceed +_ 10% for any day for the hours of practical interest, and, in most cases, it is much less. There is relatively large disagreement for 1 2 h after sunrise and I-2 h

t

.I

1000

900

800

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~ 0

I I I I t I 7 8 9 10 11 12 13

t I, 14 15 16

I , 1 17 18

100

90

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6O

50

4O

,30

S o l a r t i m e ( h )

Fig. 4. Compar ison of experimental and theoretical values of beam and diffuse solar irradiance on a horizontal surface for R o m a - - 9 December 1984, See Fig. l for explanation of symbols.

I .!

Table 2. Hourly diffuse radiation in MJ m -2

Time (11)

Method 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14--15 15-16 16-

aaber 1984 Experimental 0.184 0-205 0-220 0-234 0.245 0.248 0.227 0.212 0-202 Liu and Jordan 0,178 0.212 0.227 0.236 0.239 0.239 0.236 0.227 0.212 % deviation + 3"3 - 3.4 - 3.2 - 0.8 + 2-4 + 3.6 - 4.0 - 7- l - 4.9

,her 1984 Experimental 0.173 0.230 0.230 0,241 0-252 0.248 0.241 0.212 0.205 0- Liu and Jordan 0,199 0.220 0.230 0-238 0.241 0.241 0.238 0-230 0"220 0" % deviation -15-0 +4 '3 0.0 +1-2 +4.4 +2-8 +1-2 - 8 - 6 -7 -3 - 1 0 .

aaber 1984 Experimental 0-191 0"234 0.223 0.241 0'266 0.274 0-241 0-248 0-234 Liu and Jordan 0-210 0-228 0.238 0-244 0.246 0.246 0-244 0-238 0-228 % deviation -9 -9 +2-6 - 6 , 7 - 1-2 +7-5 + 10.2 - 1-2 +4.0 +2-6

nber 1984 Experimental 0' 184 0-215 0.230 0-264 0.280 0.240 0-270 0.266 0"227 Liu and Jordan 0-209 0.232 0.240 0.244 0,253 0-253 0-244 0-240 0-232 % deviation -13 .6 - 7 . 9 - 4 . 3 +7.6 +9 '6 - 5 - 4 +9.6 +9.8 - 2 . 2

~ary 1985 Experimental 0.175 0.210 0.227 0-234 0,244 0-252 0.238 0.234 0.230 Liu and Jordan 0.202 0-220 0-236 0.242 0.244 0.244 0.242 0.236 0-220 % deviation -15 .4 - 4 . 8 - 4 -0 - 3 . 4 0.0 +3.2 - 1 . 7 - 0 . 8 +4 '3

ary 1985 Experimental 0.217 0.220 0-252 0-216 0-259 0-271 0,250 0-225 0"210 Liu and Jordan 0.210 0-227 0-240 0-243 0-246 0.246 0.243 0.240 0.227 ° d e v i a t i o n +3-2 - 3 ' 2 +4,8 -12 .5 +5.0 +9-2 +2-8 - 6 . 7 -8 .1

228 Technical Note

1000

900

= 700

500

4O0

300 f d I I 1 I I I I I I 1

8 9 10 11 12 13 14 15 16 17

5. C O N C L U S I O N

100

90

80

70

60

50

- 40

30

S o l a r t i m e ( h )

Fig. 5. Compar ison of experimental and theoretical values of beam and diffuse solar irradiance on a horizontal surface for R o m a - - 1 7 January 1985, See Fig. 1 for explanation of symbols.

8

before sunset on some days. As very little solar radiation is available during those hours, they are not of much practical interest. It can be seen from Figs 1-6 that the measured and estimated values of beam and diffuse irradiance show the same pattern o f variation with time on all 6 days.

0

The prediction of hourly beam and diffuse radiation using the models of Hottel and of Liu and Jordan is a good pro- cedure for cases without meteorological stations or recording

I 18

1100

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300 I I I I I 1. I I L L 1 8 9 10 l l 12 13 14 15 16 17 18

- - 1 0 0

- - 9 0

- 8 0

- 7 0

- - 6 0

50

40

30

Solar time ( h )

Fig. 6. Compar ison of experimental and theoretical values of beam and diffuse solar irradiance on a horizontal surface for R o m a - - 3 0 January 1985. See Fig. 1 for explanation of symbols.

f i - E

Technical Note 229

equipment and data. The predicted results using the Hottel model for beam radiation and the Liu and Jordan model for diffuse radiation are of a high standard and in close agree- ment with the measured values. The difference between cal- culated and observed values is never more than + 10% for the hours of practical interest. These models have an advan- tage that they do not need any measured meteorological data for estimating solar irradiance and if their universal applicability is verified they can be the most suitable equa- tions in solar energy research.

Acknowledgements---One of the authors (K.K.G.) would like to thank Professor Abdus Salam, the International Atomic Energy Agency and UNESCO for the hospitality at the International Centre for Theoretical Physics where the cal- culations involved in this work were done. Thanks are also due to Professor G. Furlan oflCTP for his continued interest

in the work. The measurements reported in this paper have been possible through a UNDP grant which enabled us to purchase the Eppley pyranometers.

REFERENCES

1. K. K. Gopinathan and J. Mwanje, Estimation of solar radiation over Lesotho. INTERSOL 85, June 23-29 (1985).

2. H. C. Hottel, A simple model for estimating the trans- mittance of direct solar radiation through clear atmo- spheres. Solar Energy 18, 129 (1976).

3. B. Y. H. Liu and R. C. Jordan, The interrelationship and characteristic distribution of direct, diffuse and total solar radiation. Solar Energy 4, 3 (1960).

4. J. A. Duffle and W. A. Beckman, Solar Engineering of Thermal Processes. John Wiley, New York (1980).