Solar Energy Vol. 48. No, I,pp. 3-5, 1992 00384)92X/92 $5.00+ .00 Printed in the U.S.A. Copyright © 1991 Pergamon Press plc

ESTIMATION OF HOURLY GLOBAL AND DIFFUSE SOLAR RADIATION FROM HOURLY SUNSHINE DURATION

K. K. GOPINATHAN Department of Physics, National University of Lesotho, Roma, Lesotho, Africa

Abstract--A statistical procedure has been employed to develop correlations of monthly-mean-hourly global and diffuse solar radiation on a horizontal surface to hourly sunshine duration. Several years of measured data on solar radiation and sunshine duration, reported in the literature for two stations in the southern African region, is employed for this purpose. The applicability of the developed correlations is tested by estimating solar radiation for a new location. The excellent agreement between the measured and estimated data for that station suggests the wide applicability of the method.

I. INTRODUCTION

Information on the availability of solar radiation is needed in many applications dealing with the exploi- tation of solar energy. A knowledge of monthly-mean- daily global and diffuse radiation on a horizontal sur- face is essential to design any solar energy system. However, the mean daily radiation is not always the most appropriate figure to characterize the potential utility of solar energy. While designing solar energy systems, one also needs to know insolation values at hourly intervals for inclined and horizontal surfaces. Hourly values of radiation allow us to derive very pre- cise information about the performance of solar energy systems.

Most of the locations in the southern African region receive abundant solar radiation, and solar energy uti- lization technology can be profitably applied to this region. However, information on measured solar ra- diation data are not available for most of the locations in this part of the continent. Measurements of solar radiation on an hourly basis are rarely carried out in meteorological stations here.

For stations where no measurements exist, hourly radiation can be estimated by using empirical corre- lations developed from the measured data of nearby locations having similar climatological conditions. At- tempts have already been made by many investigators to predict hourly global and diffuse radiation from various measured parameters. The first attempt to an- alyze the hourly global radiation data was done by Whiller [ 1 ] and Hottel and Whiller [ 2 ], who used data of widely separated locations to obtain the curves of hourly to daily radiation ratio against the sunset hour angle. Liu and Jordan[3] extended the day length of these curves. By using the corrected data of five U.S. locations, Collares-Pereira and Rabl [4] developed an analytical expression for the ratio of hourly to daily global radiation (rt) in terms of the sunset hour angle. The hourly correlations of Boes[ 5], Orgill and Hol- lands [ 6 ], Bruno [ 7 ], and Bugler [ 8 ] can be expressed as relationships for estimating the ratio of hourly diffuse to hourly global radiation. The relationship suggested by Liu and Jordan [ 3 ] estimates the hourly distribution of diffuse radiation from daily data.

The possibility of estimating the hourly distribution of global and diffuse radiation from hourly sunshine duration is, however, more attractive for stations to utilize where measured data are not available. Reports are already available[9] on the estimation of hourly radiation from sunshine duration. The main advantage of computing the hourly global or diffuse radiation from sunshine data is that there are more sites available with measured sunshine duration than solar radiation measurement. Though measured radiation data are not available for most of the southern African locations, long-term measured sunshine duration values are available for many stations in this region. For example, Lesotho, which has only one solar radiation measuring station, has about 13 locations where sunshine duration is recorded.

The purpose of the present study is to develop cor- relations for estimating monthly-mean-hourly global (I) and diffuse (ID) radiation on a horizontal surface from measured hourly sunshine (S), for locations in southern Africa, in general, and for Lesotho in partic- ular.

2. M E T H O D OF ESTIMATION

Correlations of the following form are assumed to connect the monthly-mean-hourly global and diffuse radiation on a horizontal surface with monthly-mean- hourly sunshine duration.

I / I o = a + b ( S / S o ) ( 1 )

I D / l o = c + d ( S / S o ) (2)

I o / I = e + f ( S / S o ) (3)

where Io is the hourly extraterrestrial radiation, S o is the maximum possible sunshine duration and a, b, c, d, e, f are all constants. S / S o is the minutes of bright sunshine in the hour divided by the total number of possible minutes. Equations ( 1 ) and (2) need only one measured variable, the sunshine duration, for esti- mation purposes. Equation (3) can be employed when measured hourly global radiation values are also avail- able in addition to sunshine duration. A statistical pro-

K. K. GOPINATHAN

cedure has been employed here to compute the con- stants of the above equations. Long term measured hourly solar radiation and sunshine duration data, re- ported in the literature [ l 0 ] for two locations in south- ern Africa are employed for this purpose. Measured monthly-mean-hourly data during the months of Jan- uary and July from Bloemfontein and Pretoria are used in a linear regression analysis to obtain the constants of eqns ( I -3) . A total of forty-six sets of hourly data are employed in the regression analysis. January and July are the two typical summer and winter months for the southern African region. Io and So values needed for the study were evaluated using the proce- dure given by Duffle and Beckman [ 11 ]. Proper com- puter programs were written for the regression analysis.

3. RESULTS AND DISCUSSION

A linear regression was performed on the data from the two locations and the following equations are de- veloped to express the dependence of hourly solar ra- diation on sunshine duration.

I /Io = 0.406 + 3.043(S/So) (4)

IHIo = 0.260 - 1.312(S/So) (5)

ID/I = 0.550 - 3.819(S/So). (6)

A good linear fit is obtained in all three cases. To test the applicability of the developed correlation

for Lesotho, a set of measured data from Roma (in

Lesotho) is used. The developed correlations are then tested by estimating hourly global and diffuse radiation values during January and July and then comparing them with the measured data. The estimated and mea- sured values of I and 1,9 for Roma are presented in Figs. 1 and 2, respectively. The time shown in the fig- ures is solar time. The local time is converted into solar time using the procedure given by Duffle and Beckman [ 11 ]. The radiation values are plotted at the midpoint of each hour. In the figures, Ioj represent the hourly diffuse radiation values estimated from eqn (5) and lo2 are those estimated from eqn (6).

The results presented in the two figures clearly demonstrate the accuracy of the estimated data. The measured and estimated radiation values always agree very well and the errors involved in the estimation are very low. This is true for both global and diffuse ra- diation. Both Iol and ID2 give very accurate estimates of diffuse radiation and any of the above two equations can be employed for estimation purposes. However, eqn (6) needs two measured variables to estimate hourly diffuse radiation whereas eqn ( 5 ) requires only one measured quantity. Equation (5) should be thus more acceptable for countries like Lesotho, where hourly radiation measurements are not carried out at many locations. The two stations, Bloemfontein and Pretoria, are chosen here to develop the correlations for the following reasons. Since Lesotho is a small country surrounded by South Africa on all sides, the two stations are very near to Lesotho and their climatic conditions are very similar to that of most locations in Lesotho. For example, the station Bloemfontein, is only 135 km away from Roma, the station in Lesotho

#,0

~'E3,0

I

o =

~ 2,0

< re

~ 1,0

_ _ _ M E A S U R E D GLOBAL

ESTIHATED GLOBAL

. . . . . . . HEASURED DIFFUSE

J l ~ I _ J 1 ~ I i I I I 6 8 10 12 1/~ 16 18

SOLAR TIHE

Fig. I. Comparison ofe×perimental and theoretica! values of monthly-mean-hourly global and diffuse solar radiation on a horizontal surface for Roma during January.

Estimation of hourly global and diffuse solar radiation

C~

'E2, 3-

l Z 0

~1,5 _< r-1 .< ,v

a~ 1.0 < --J (21

0,5

. . . . MEASURED fiLOBAL

-o--o--o ESTIMATED GLOBAL

. . . . . . MEASURED DIFFUSE

I I I I I I i . J _ J 7 9 11 13 15

SOLAR TIME

I I 17 19

Fig. 2. Comparison of experimental and theoretical values of monthly-mean-hourly global and diffuse radiation on a horizontal surface for Roma during July.

selected for study. The lati tude and elevation of Bloemfonte in and Pretoria are 29.12°S, 1422 m and 25.75°S, 1369 m, respectively and most of the locations in Lesotho lie in this lati tude and alt i tude range. Cor- relations developed from Bloemfonte in and Pretoria should thus be acceptable for locations in Lesotho.

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

The following equations are recommended to estimate m o n t h l y - m e a n - h o u r l y global and diffuse radiat ion on a hor izonta l surface, for locations in Lesotho and the southern African region in general, where hourly sun- shine dura t ion data are available.

I / I o = 0.406 + 3.043(S/So)

ID/lo = 0.260 - 1.312(S/So).

If measured hourly global radiation is also available, in addi t ion to sunsh ine durat ion, the equat ion of the

form

ID/I = 0.550 - 3.819(S/So)

may be useful. The accuracy of the estimated data from these three equations is quite high and these equations, in the present form, are applicable to any location in Lesotho.

R E F E R E N C E S

1. A. Whiller, The determination of hourly values of total solar radiation from daily summation, Arch. MeteoroL Geophys. Bioklimatol. Ser. B. 7(2), 197 (1956).

2. H.C. Hottel and A. Whiller, Evaluation of flat plate solar collector performance, Transactions of the conference on use of solar energy, The Scientific Basis Vol. II (I), Section A, 74, University of Arizona Press (1958).

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

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

5. E.C. Boes, Estimating the direct component of solar radiation, Sandia Report, SAND75-0565 Sandia National Laboratories, Albuquerque, NM ( 1975 ).

6. J. F. Orgill and K. G. T. Hollands, Correlation equation for hourly diffuse radiation on a horizontal surface, Solar Energy 19, 357 (1977).

7. R. Bruno, A correlation procedure for separating direct and diffuse insolation on horizontal surface, Solar Energy 20, 97 (1978).

8. J. W. Bugler, The determination of hourly insolation on an inclined plane using a diffuse radiation model based on hourly measured global horizontal insolation, Solar Energy 19, 477 (1977).

9. Solmet, Volume 2. Final Report, Hourly solar radiation. surface meteorological observations, US National Cli- matic Center, Asheville, NC, TD-9724 ( 1979 ).

10. A. J. Drummond and E. Vowinckel, The distribution of solar radiation throughout Southern Africa, Z Meteorol. 14, 343 (1957).

1 I. J. A. Dut~e and W. A. Beckman, Solar engineering of thermal processes, Wiley, New York (1980).