Solar & Wind Technoloyy Vol. 7, No. 2/3, pp. 255 260, 1990 0741-983X/90 $3.00+.00 Printed in Great Britain. Pergamon Press plc

DATA BANK

E s t i m a t i o n of hourly clear-sky solar radiation for P.D.R. Yemen

GAMIL M . A B D U L A z I z

Basic Science Department , Faculty of Engineering, Aden University, Aden, P.D.R. Yemen

(Received 3 January 1989; accepted 3 February 1989)

Abs t rac t - -Month ly average hourly clear sky solar radiation for some principal stations in P.D.R. Yemen are evaluated. Hottel 's model is used to predict the hourly clear sky beam and horizontal solar radiation and that of Liu and Jordan for the estimation of clear sky diffuse radiation. The two methods are combined to obtain the clear sky total radiation. M a x i m u m and min imum clear sky total solar radiation are evaluated. The maxima are situated between 21.0 MJ /m 2 and 26.6 MJ /m 1, minima between 15.0 MJ /m 2 and 19.1 MJ /m 2 for Aden and Mukairas respectively. Mean hourly clear-sky solar radiation are computed and discussed. 75% of the estimated radiation on a horizontal surface is obtained between 9 a.m. 3 p.m. The average intensity is about 700 W / m 2 for Aden and 900 W / m 2 for Mukairas.

I N T R O D U C T I O N

To derive the detailed solar radiation climatology of a region and to estimate its solar energy potential, extensive radiation measurements of high quality at a large number of stations covering all major climate zones of the region are essential. Where no radiation measurements or no accurate measure- ments are made with reliable ins t ruments - -which is the case of P . D . R . Y . ~ a t a have to be computed:

(i) from other meterological parameters using regression techniques,

(ii) from the solar constant, allowing for depletion by absorption and scattering by atmospheric gases, dust and aerosols and clouds, or

(iii) from satellite measurements of the solar energy scat- tered and reflected into space by the ear th-a tmosphere system [1].

The first method is empirical, the cloud field being defined by either the total cloud amoun t or the measured number of sunshine hours. This method is used to estimate the monthly global and diffuse solar insolation in Aden [2].

The effects of the atmosphere in scattering and absorbing radiation are variable with time, as atmospheric conditions and air mass change. Since many solar devices require infor- mation on the hourly solar radiation, it is useful to define a standard "clear" sky, and calculate the hourly and daily radiation which would be received on a horizontal surface under these s tandard conditions. Such estimation is help- ful especially for the design and assessment of solar energy conversion systems.

The basic idea of this paper is to present the theoretical values of the estimation of hourly clear sky radiation for some principal characteristic sites in P.D.R.Y. based on Hottel 's method which takes into account zenith angle and altitude for a s tandard atmosphere and for four climate types. Estimation of clear sky diffuse radiation is carried out by using the Liu and Jordan model. Total clear sky radiation is obtained by combining the two methods.

The results of this paper will enable us to predict how much solar radiation can be expected on average at these major sites, hour by hour, during any given mon th of the year and will be of great help for future projects which aim to establish the solar map for the whole country.

H O T r E L ' S M O D E L [3]

In this study, we have not found it worthwhile to use sophisticated clear sky models. On the other hand the use of a too simple approach or of s tandard tables would not give the effect of altitude of the station which is certainly impor- tant in a territory like P.D.R.Y. Such an intermediate model is that proposed by Hottel.

The clear day all wavelength transmittance v of solar radi- ation directly through the atmosphere to a surface at altitude A is found to fit a simple mixed-grey gas model (1 black, 1 grey, 1 clear) with a max imum error of 0.4%. The relation is :

z = a 0 + a l e k/cos0~. (1)

The constants a0, al and k for the standard atmosphere with 23 km visibility are found from a*, a* and k* which are given from altitudes less than 2.5 km by :

a* = 0.4237-0.00821 ( 6 - A ) 2 (2)

a* = 0.5055+0.00595 ( 6 . 5 - A ) z (3)

k* = 0.2711 +0.01858 (2.5 - A ) 2 (4)

where A is the altitude of the observer in kilometers. Cor- rection factors are applied to a~, a* and k* to allow for change in climate types. 0z is the zenith angle and the cosine of the zenith angle is given by the equation

cos 0z = cos 6 cos 0 cos w + sin 6 sin ~b (5)

where 6 is the solar declination, ~b is the latitude of the station and w is the hour angle.

255

256 Data Bank

Thus, the transmittance for beam radiation can be deter- mined for any zenith angle and any altitude up to 2.5 km.

The clear-sky beam normal radiation is then :

Gcn b : zGo. (6)

Go. is obtained from the equation :

Go. = Gsc (1 + 0.033 cos 360n/365) (7)

where Go. is the extraterrestrial radiation, measured on the plane normal to the radiation on the nth day of the year. G~ is the solar constant with a value of 1.353 W/m s and the term in parentheses is the dependence of extraterrestrial radiation on time of year due to the variation of the e a r t ~ s u n distance.

The clear sky horizontal beam radiation is :

Gob = zGon cos 0z. (8)

The hours are designated by the time for the midpoint of the hour, and days are assumed to be symmetrical about solar noon.

LIU AND JORDAN'S METHOD [4]

To get the total clear sky radiation, it is also necessary to estimate the clear sky diffuse radiation on a horizontal sur- face to get the total radiation. Liu and Jordan [4] developed an empirical relationship between the transmission coeffi- cient for beam and diffuse radiation for clear days.

% = 0 .2710-0.2939r (9)

where ra is the ratio of diffuse radiation to the extraterrestrial radiation on a horizontal plane. The data used by Liu and Jordan predated that used by Hottel and may not be entirely consistent with it; until better information becomes avail- able, it is suggested that eq. (9) can be used to estimate diffuse clear sky radiation [5], which can then be added to the beam radiation predicted by Hottel 's to obtain a clear day total radiation.

APPLICATION OF THE PREDICTED M E T H O D S - - R E S U L T S AND DISCUSSION

In Table 1 the geographical positions of the locations under study are given. These regions represent the main climatological variation in P.D.R.Y. and are the most impor- tant sites for eventual applications of solar radiation.

The results obtained show that generally, the maxima are obtained during the months of April, May or June. January and December represent the months fur min imum solar radi- ation for all sites. For the mean hourly clear sky horizontal radiation between 6-8 a.m., [Fig. l(a), (b)] the max imum radiation is during the month of June for all locations.

Table I. Geographical position of the stations

Station Altitude (m) Latitude °N Longitude °E

Aden 5 12.80 45.0 Seiyun 700 16.00 49.0 Beihan 1150 14.88 45.7 Dalaa 1500 13.42 44.7 Mukairas 2042 13.93 45.7

Between 8 9 a.m. [Fig. l(c)] we have practically the same radiation for each site during the months April August with a max imum for the month of May. Between 9 12 a.m. [Fig. 1 (d) (f)] a max imum is obtained for the month of April for all locations. The values of the estimated results are very similar during the summer months (April September). For this period and for each location, the difference of solar radiation does not exceed 30 W/m 2. The highest radiation is obtained in the hours around midday with an average about 830 W/m 2 for Aden, 900 W/m 2 for Seiyun, 940 W/m 2 for Beihan, 970 W/m: for Dalaa and 1000 W/m 2 for Mukairas.

For the results of the mean hourly clear-sky beam radi- ation and between 6-8 a.m. [Fig. 2(a), (b)] we have prac- tically symmetrical curves with a max imum during the mon th of June. A sensible increase of clear sky beam radiation during these 2 hours and for all sites can be noted. Between 1(~12 a.m. [Fig. 2(e), (f)] and for the whole year the hourly clear sky beam radiation can be averaged by 810, 890, 940, 960 and 990 W / m 2 for Aden, Seiyun, Beihan, Dalaa and Mukairas respectively.

The results of the estimation of clear sky diffuse radiation show slight variation through the whole year for each station and for the same hour. To show this the results of the month of January (minimum) and that of April (maximum) are presented in Fig. 3. For a given site, and hour, the mean hourly clear sky diffuse radiation is practically the same, except that for the hour 6-7 a.m., where the variation between the max imum and min imum is 25 W/m 2. In the same manner, the results of the clear sky transmittance and the transmission coefficient for clear sky diffuse radiation are presented in Table 2.

Finally, Fig. 4 shows the variation of monthly average clear sky total radiation which is twice the sum of the esti- mation for clear sky horizontal radiation given by Hottel 's method and that by Liu and Jordan for clear sky diffuse radiation. The same remark can be made for the mean monthly clear sky total radiation. During the summer months (April September), practically the same total radiation is obtained. This radiation can be averaged as 20.7 MJ/m z day for Aden, 23.5 MJ/m 2 day for Seiyun, 24.5 MJ/m: day for Beihan, 25.4 MJ/m 2 day for Dalaa and 26.4 MJ/m 2 day for Mukairas. Min imum is observed in December and January in a somewhat symmetrical way.

To those interested in the use of solar energy for heating, cooling, etc., the frequency of extended period of low radi- ation income is of particular interest. The min imum clear sky total radiation for the whole year is about 15 M J /m: day for Aden, 15.8 MJ/m 2 day for Seiyun, 17.4 MJ/m 2 day for Beihan, 18.6 MJ/m 2 day for Dalaa and about 19.2 MJ/m ~ day lbr Mukairas.

C O N C L U S I O N S

From this study, the following conclusions can be drawn :

(1) Where no sunshine data are available as in the case of P.D.R.Y., solar radiation at the ground on clear sky days is estimated using Hottel 's and Liu and Jordan 's models. The obtained results will be of great interest to establish the solar map for P.D.R.Y. and give a general idea about the potential of solar energy for planning any eventual utilization of solar radiation.

(2) The max imum total clear sky radiation is obtained dur- ing the months of April, May or June, the min imum during December and January. This max imum is situ- ated between 21.0 MJ/m 2 for Aden and 26.6 MJ/m 2 for

Data Bank 257

& (a) 6-7 h • Aden l (b ) 7-8 h

+ Seiyun 14~ o Beihan

z~ Dalaa

4o0 i , , / F ~ ~ • Mukairas

oo~_ / /1 : / ' - "\. %'%. I "#,~/ ~..~

J F M A M J J A S 0 N D J F M A M J J A S 0 N D

(c) 8-9 h

60( --

5oo

4oo

3o0

(d)9-10 h

80(]

°t: ] ~ 1 ~ ] I S l O I I N ~ j F M J I M I ] ~ I J S I O N o '

T (e) lO-11h ~ (f) 11-12h / ~ " ' .

. . . o ~ o _ _ o . . , ~ -

J F M A M J J A S O N D J F M A M J J A S O N D

Fig. 1. (a)- ( f ) Monthly average clear sky horizontal radiation.

258 Data Bank

°~ : o:= [ / ~ \ .

I . \ . \ : to- - - . / / \ / I I I I I J I I I I I I ,. I t I I I I I I I I\,~ .

J F M A M J J A S 0 N D J - F M A M J J A S 0 N D "

9O(;

700

100(]

800

(c)8-9 h (d)9-10h

o ~ - O ~ o I I I L I L I I l I ~' _ I I I I [ I I I I I I I ..

J F M A M J J A S O N D J F M A M J J A S O N D

( e ) 1 0 - 1 1 h T ( f ) 1 1 - 1 2 h

/

+~+~'~'~+'~.~,~+___+..,~..~+,.--+..,~ +~+

m ~ O "'"0,,~.. O . . . . .O~o _ o7- o,.~-o__o-.-" ",,,.o,,..,,,.o

L I I I L I I I I I I [ , J F M A M J J A S O N D

O',~,,~ O

f .,,.,..Q~e__i~,.,. o ..,..q~._..o~q~...,,~o

I 1 I [ I I I I I I I I , J F M A M J J A S 0 N D

Fig. 2. (a)-(f) Monthly average clear-sky beam radiation.

150

lO~

50

0

• A d e n

+ Se iyun o Beihan

J a n u a r y zx Da la r Apri l • Muka i ras

I I I I I h P 6-7 7-8 8-9 9-10 10-11 11-12 6-7 7-8 8-9 9-10 10-11 11-12

Fig. 3. Hourly clear sky solar radiation.

259

Table 2. Clear-sky transmittance and diffuse coefficient

Aden Seiyun Beihan Dalaa Mukairas Hours • T~ T zd • zd z zd z Zd

January (min) 11 12 11~11 9 10 8-9 7 8 6-7

0.584 0.010 0.638 0.084 0.673 0.073 0.697 0.066 0.720 0.060 0.566 0.105 0.622 0.088 0.659 0.077 0.684 0.070 0.707 0.063 0.524 0.117 0.583 0.010 0.624 0.088 0.652 0.079 0.678 0.072 0.443 0.141 0.510 0.121 0.544 0.111 0.588 0.098 0.618 0.090 0.287 0.187 0.354 0.167 0.408 0.151 0.451 0.139 0.486 0.128 0.125 0.234 0.187 0.216 0.224 0.205 0.250 0.198 0.286 0.263

April (max) 11-12 10-11 9 10 8 9 7-8 6-7

0.628 0.087 0.683 0.070 0.712 0.062 0.730 0.056 0.751 0.050 0.614 0.091 0.672 0.074 0.065 0.720 0.720 0.059 0.742 0.053 0.582 0.010 0.645 0.082 0.677 0.072 0.697 0.066 0.721 0.051 0.522 0.118 0.594 0.097 0.630 0.086 0.653 0.079 0.680 0.071 0.408 0.151 0.493 0.126 0.536 0.114 0.563 0.106 0.596 0.096 0.191 0.215 0.283 0.188 0.328 0.175 0.357 0.166 0.399 0.154

20

15

+ Seiyun / y ~ ~ / c ~ = ~ 4 ~ ~ ~ o Beihan

zx Dalaa . ~ i t • Muka i ras

I I I I I t I I I I I I Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Fig. 4. Monthly average clear sky total radiation.

260 Data Bank

Mukairas. The minimum varies between 15.0 MJ/m 2 and 19.1 MJ/m z for Aden and Mukairas respectively.

(3) For the mean hourly clear sky radiation, the maxima are obtained around midday. A best time to have a maximum solar radiation input is obtained during the period 9 a.m.-3 p.m. where about 75% of the solar energy is available. During this period the average inten- sity is about 700 W/m 2 for Aden and 900 W/m 2 for Mukairas.

REFERENCES

I. A. Mani and S. Rangarajan, Solar Energy 31, 577-595 (1983).

2. G. M. Abdul Aziz and M. A. Moqbel, Renewable Energy Conf., University of Alep, 29 September 2 October 1986.

3. C. Hottel, Solar Energy 18, 12~134 (1976). 4. Y. H. Liu and R. C. Jordan, Solar Energy 4, 1 19 (1960). 5. J. A. Duffle and W. A. Beckman, Solar Engineering of

Thermal Processes. John Wiley (1980).