Estimation of daily and monthly direct, diffuse and global solar radiation in Rabat (Morocco)

Renewable Energy Vol. 3. No. 8, pp. 923930, 1993 Printed in Great Britain.

0960-1481/93 $6.00+.00 ! 1993Pergamon Press Lid

DATA

BANK

Estimation of daily and monthly direct, diffuse and global solar radiation in Rabat (Morocco) H. NFAOUI and J. BURFT Solar Energy Laboratory, Faculty of Science, B.P. 1014 Rabat, Morocco

(Received 15 Februat?' 1993 : aecepted 30 March 1993) A b s t r a c ~ I n Morocco, the bright sunshine hours are measured in 30 meteorological stations, but the global irradiation is measured only in three stations within the country. The direct and diffuse components are not measured in any meteorological station. Therefore, we have established correlations for the estimation of the direct, global and diffuse radiation from the sunshine duration, n, or the clearness index, Kt, based on the measurements of the solar radiation components in Rabat. We have also made a comparison between our results and those of other researchers.

1. I N T R O D U C T I O N To determine the a m o u n t of solar energy received by a horizontal surface at any specified location a large series of measurements are required ; but they are rarely available for the different components of solar radiation. Meteorological stations around the world currently measure the daily sunshine hours, n, and also the daily global radiation, H, on a horizontal surface. The values o f the diffuse radiation are seldom available and they need to be controlled to verify if the shadow band correction is included. If not, the diffuse radiation is underestimated. Due to the cost of the pyrheliometer and the care needed for regular adjustment as the sun gets inside the 2.8" acceptance half angle, the direct component is almost never measured in meteorological stations. That is why, generally, the direct component is calculated from the global and diffuse components. For all these reasons the correlations between the solar radiation components and the sunshine hours (n) or the global radiation are very useful for the estimation of the parameters which are not measured and for the extrapolation of missing data. During the last 10 years these correlations have been studied in a large number of locations [1 6]. The results vary with the climate of each zone and despite a great number of research works, a universal formula has not yet been found.

standard deviation a,: are used to test the accuracy of the predictive models. 3. M E A S U R E M E N T S The present study is based on measurements carried out in the University of Rabat (4~ = 34~'N, L = 6<45'W) during 3 years from 1 August 1982 to 31 July 1985. The measured parameters are the daily values of the number (n) of bright sunshine hours of the global irradiation (H) of a horizontal plane and of the beam normal irradiation (Hb,). The diffuse radiation on a horizontal plane is obtained from global and direct radiation which allows a better estimation of the diffuse radiation than the measurements using a pyranometer with a shadow band. The instruments used are a CampbellStokes heliograph, an Eppley black and white pyranometer and an Eppley normal-incidence pyrheliometer (NIP). The daily values over a period of 3 years have been controlled and then stored on HP discs. 4. STUDY OF T H E D I M E N S I O N L E S S C O E F F I C I E N T S , Kt and Kd The dimensionless coefficients vary only with climatic and meteorological fluctuations.

4.1. Sunshmejraction ~r The daily sunshine fraction, cr, is defined as the ratio n/N between the daily bright sunshine hours, n, and the m a x i m u m day length, N. It is strongly dependent on cloudiness and atmospheric turbidity, linked to the concentration of the aerosols and atmospheric water vapour. For a very clear sky day : n = N and a = 1. For a cloudy day : n = 0 and er = 0. In a given latitude, N varies regularly within 1 year with a m a x i m u m for the summer solstice and a m i n i m u m for the winter solstice. The study of n shows a regular variation essentially for the maxima because n converges towards N. This astronomic regularity is superposed by random climatic behaviour. The

2. M E T H O D O L O G Y The solar radiation arriving on the ground presents a periodic variation linked to the variations of the declination, 3, and the latitude, 4~. To eliminate this variation one generally uses dimensionless coefficients such as the sunshine fraction, a = n/N, or the clearness index, K~ = H/Hob. The values of a and K, then vary only for climatic fluctuation reasons. The correlations between the coefficients are obtained by the least-square method using linear or polynomial functions. The correlation coefficient, R, and the 923

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Fig. 1. Plot of sunshine fraction versus day number. ratio n/N eliminates the regular variation and keeps the climatic effects only (Fig. 1). The maxima around 1 correspond to cloudless days, whereas the minima around 0 characterizes the m a x i m u m cloudiness. The variation of the monthly mean values does not show any regularity.

The average value of K, over the 3 years is about 61% (Fig. 2). 4.3. Diffusefraction, Ka K d represents the diffuse fraction part of the global radiation on a horizontal surface and shows the same variation as the total cloud cover, C. For a totally cloudy day, Ha = H and Kd = 1, and therefore the total cloud cover C = 1. For a clear day, Hd reaches its m i n i m u m value and H its maximum. It should be noted that K~ = 1--Hb/Hoh. Kd increases while K~ and (r decrease. The maxima values are around 1 and the minima are about 20%, while the monthly average variation is irregular (Fig. 3). The average value of Kd over the 3 years is around 45% which shows a large a m o u n t of solar diffuse radiation in Rabat, probably due to its location on the Atlantic coast.

4.2. ClearnessIndex K, Liu and Jordan [2] have shown that the solar climate of a particular location can be characterized by the clearness index, Kt, which is the ratio of the daily global radiation, H, on a horizontal surface to the extra-terrestrial daily radiation, Hob, on the same surface. The maxima of K, correspond to the clear days and the minima to the cloudy days. The accumulation of the plots around small values during winter reflects the cloudiness effect. The maxima linked to the atmospheric turbidity are always under the value of 80%.

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5. C O R R E L A T I O N S BETWEEN THE SOLAR RADIATION COMPONENTS The diffuse, global and direct radiation correlations with global radiation and sunshine duration are presented in Table 1 and Figs 4 12. These results lead to the general conclusion that the passage from the daily average values to

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the monthly mean values always decreases both the correlation coefficient, R, and the standard deviation, a,:. This is due to the smaller n u m b e r of observed values (36 values instead of 1095) and also to the reduced dispersion of the data. The monthly mean values of g or Kt are ranging within a

Table 1. Correlation of global, diffuse, and direct radiation on horizontal surface with or K, (3 years of measurements August 1982 to July 1985 in Rabat)

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Fig. 5. Variation o f the direct horizontal radiation as a function of the sunshine fraction (daily values)•

small interval compared with the daily ones. We can give an example for a :

For diffuse and direct radiation, the correlations with Kt are more valuable than those with a. This shows that the clearness index, K,, is more representative of the solar radiation than a. This result can be explained by the fact that a is calculated from the measurements of n which give only the information that the direct radiation is higher than 120 W/m2; but n cannot give any information about the value of direct radiation which is linked to the atmospheric turbidity and the zenith angle.

daily values monthly means

0 ~< a ~< 1, 0.4 < 6 < 0.8.

The correlation between the monthly mean values is valid only within this interval which is strongly dependent on the climatic conditions•

Hb/Hoh = 0 . 1 3 - 0 . 9 5 H / H o h +2.02 (H/Hoh) 2 H / H o h - 0 . 2 5 Hb/Hoh = 0 H/Hoh~0.25 l0

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Fig. 6. Variation of the direct horizontal radiation as a function of the clearness index (daily values).

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Fig. 7. V a r i a t i o n of the clearness index as a function of the sunshine fraction (daily values).

On the other hand, the clearness index, K,, c o m p a r e s the global r a d i a t i o n o n the g r o u n d with the c o r r e s p o n d i n g extraterrestrial r a d i a t i o n a n d d e p e n d s strongly on a t m o s p h e r i c turbidity• C o m p a r i s o n s of our results with other authors" studies have not been d o n e for the direct n o r m a l r a d i a t i o n because this c o m p o n e n t is rarely studied due to the nonavailability of its m e a s u r e m e n t s . F o r the global a n d diffuse r a d i a t i o n c o m p o n e n t s m a n y results have been found and we have selected some c o r r e l a t i o n s to c o m p a r e them with ours•

H/l~oh = O.17+0.66R/N

In the case o f global radiation, the c o r r e l a t i o n s are closed and can be used for a wide climatic area. F o r the different climatic zones in M o r o c c o we found the following correlations between the daily values o f K~ a n d ~ : H/H,,h = 0.25+0.50 ~ C a s a b l a n c a q~ = 33 34"N [3] H / H , , h = 0 . 2 5 + 0 . 4 9 (7 B~ni M e l l a l ~p = 32 22'N [4] H / H o h - 0 . 2 5 + 0 • 5 1 c~ Marrakech ~0 = 31 3 7 ' N [5] H/H,,h = 0 . 1 7 + 0 . 4 9 (7 Tetouan q~ = 35 35'N [6] H / H o h = 0 . 2 6 + 0 . 5 2 c~ Rabat @ - 34 03'N.

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global radiation (Hd/H) is strongly dependent on the climate, which explains the large number of correlations found by the authors and the discrepancy between our work and the results of other groups. For a given value of K t the value of (Hd/H) for Rabat is larger than for other regions• This is probably due to the large a m o u n t of diffuse radiation in Rabat. For Casablanca with a similar climate the values of H0 are underestimated

< 0.80

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function of the sunshine fraction (daily values).

These five Moroccan locations have very closed latitudes but different climates and the correlations are very similar. From these results we can conclude that the correlation is mostly dependent on ~ but not on the climate which confirms the work of Glover and MacCulloch [7]. It should be mentioned that for ~r = I, we find the m a x i m u m value of K~ to be about 0.75. On the other hand, the ratio between the diffuse and the

= 0,89-0.66n/N

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Fig. I 1. Variation of the ratio Hd/H as a function of the clearness index (daily values)•

compared with those obtained for Rabat. The discrepancy between them lies in the shadow band correction which has not been made for the data of Casablanca.

the Atlantic coast area which has a similar climate. For

continental climate areas these relations have to be modified.

6. CONCLUSION

For the global radiation estimation from the bright sunshine hours, we can propose one correlation available for all the country :

The correlations obtained for the diffuse and the direct radiation are only valid for Rabat, but one can use them for

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Fig. 12. Variation of the ratio Hd/H as a function of the clearness index (monthly means).

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Data Bank NOMENCLATURE

Hbn =

Ha = H = Ha = Ho,1 = Hob = n = N = a= Kt = Kd = R = a,: =

daily direct radiation on a surface normal to rays of the sun daily direct radiation on a horizontal surface daily global radiation on a horizontal surface daily diffuse radiation on a horizontal surface daily extra-terrestrial radiation on a surface normal to rays of the sun daily extra-terrestrial radiation on a horizontal surface daily number of bright sunshine hours m a x i m u m day length n/N = daily sunshine fraction H/Hob = daily clearness index Ha/H = daily diffuse fraction correlation coefficient standard deviation. REFERENCES

1. J. M. G o r d o n and T. A. Reddy, Time series analysis of daily horizontal solar radiation. Solar Energy 41,215 226 (1988). 2. B. Y. H. Liu and R. C. Jordan, The interrelationship and characteristic distribution of direct, diffuse and total solar radiation. Solar Energy 4, 1 (1960). 3. M. L. Ben K a d d o u r and A. A. Sfeir, Etude du gisement solaire au Maroc en vue de son exploitation dans l'habitat. Travail de fin d'6tudes. Ecole Nationale des Travaux Publics de l'Etat, Lyon (1980). 4. F. Lemmini, Etude du rayonnement global ~i B6ni Mellal. Rapport interne. Facult6 des Sciences de Rabat (1983). 5. P. Pulverail, A. Idliman and A. Jamali, Etude du gisement solaire fi Marrakech. Rapport interne. Ecole Normale Sup6rieure de Marrakech (1986). 6. El H. Aroudam, M. E1 H a m m o u t i and H. Ezbakhe,

7.

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13.

14.

15.

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