Renewabh, Eneryy Vol. 1, No. 1, pp. 109 113~ 1991 0960~1481/91 $3.00+.00 Printed in Great Britain. Pergamon Press plc

D A T A B A N K

Monthly average daily global solar radiation in P.D.R. Yemen

S. M. BIN GADHI, R. S. MEGDAD and S. A. A. ALBAKRI Mechanical Engineering Department , Faculty of Engineering, University of Aden,

P.D,R. Yemen

(Received 13 September 1989 ; accepted 21 October 1989)

Abst rac t - - In this paper a study has been made to estimate average global radiation using hours of bright sunshine and measured solar radiation data available for six locations in P.D.R. Yemen. For Aden, data were obtained from Aden Airport, For other locations in P.D.R. Yemen data were obtained from Agricultural Research Center 's meteorological sections. Linear regression analysis of the monthly average global radiation and the sunshine durat ion data of six locations has been performed using the least squares technique. All the above mentioned data have been used in Angs t r6m's correlation to find the monthly average daily global solar radiation. Results obtained are useful for any solar energy system application in P.D.R. Yemen.

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

Solar energy occupies one o f the most important places among the various possible alternative energy sources. The information on the solar radiation characteristics and the relevant meteorological parameters at any place is of vital importance to solar engineers, designers and architects for providing them with an estimate of the available solar energy.

Many models have been devised for the prediction of the amoun t of solar energy incident on a horizontal plane at the Earth's surface. The most important radiation data, which is often needed, is the long term average daily global radiation on a horizontal surface. One of the simplest, which also gives the smallest percentage error, for the estimation of the monthly average global radiation is the well-known/~ngstr6m correlation [1]

H = Ho(a+b~/N). (1)

However, the main problem in employing the ,~ngstr6m type correlation for predicting global radiation, is in obtain- ing the proper values for the regression coefficients a and b of eq. (1) for a given location. The coefficients a and b are found to vary not only in different parts of the world but even for nearby locations in the same region having similar geographical and climatological conditions.

Among the recommended correlations which are based mainly on parameters such as latitude angle and altitude is Hottel 's correlation. ,~ngstr6m's and Hottel 's correlations have been used in this study to compare the measured results and correlated results,

2. M E T H O D OF C A L C U L A T I O N

The relationship between global radiation on a horizontal surface and the relative durat ion of sunshine can be estimated in the usually accepted way, using regression equations of the /~ngs t r6m type

I71- Ho(a+b~/N)

where :

/1 is the monthly average of daily global radiation on a horizontal surface,

H0 is the extraterrestrial solar radiation on a horizontal surface on an average day of each month, is the monthly daily number of hours of bright sun- shine per day,

N is the mean daily number of hours of daylight in a given month between sunrise and sunset, and

a and b are regression constants.

Where N is calculated from Cooper 's formula :

N - 2/15 cos ~ ( - tan q~ tan 3) (2)

and

H0 = 241~c [1 +0.033 cos (360~/365)]

[cos(pcos6sinw~+27cws/360sind?sin6] (3)

w, = cos t [ - tan ~b tan 6]. (4)

Regression analysis is carried out to determine the con- stants a and b. Since eq. (1) forms a straight line having an intercept of value a and a slope of value b, the regression analysis is carried out between the computed ITI/Ho and ~/N, by using computer programming and then tT1/Ho and ~/N for each mon th are calculated. The values 171/Ho are plotted against the corresponding values ofr~/Nas shown in Fig. 1 for Aden and hence a and b constants are obtained as follows : a = 0.329 and b = 0.46. Using the same method the con- stants a and b for six places in P.D.R. Yemen (Fig. 2) are obtained and given in Table I.

The second method which we find useful for the estimation of global solar irradiance as suggested by Hottel [2] is

In = l,c[1 +0.033 cos (360~'/365)]

[a0 + a l exp ( - K(cos (0~))] cos (0~) (5)

cos 0h = cos q~ cos 3 cos w + sin 4~ sin 3 (6)

t5 = 23.45 sin (360(284 + N)/365) (7)

109

110 Data Bank

i v " i v "

1.0

0.8

0.6

0.4

0.2 • RR = 0.329 + 0.46 PP Aden

1958 to 1964 I 1 I I I

0.2 0.4 0.6 0.8 1.0 PP

Fig. 1. Finding constants a and b for Aden.

global solar radiation in M J / m 2 - d a y using eqs (1) and (9) for Seiyun and Aden.

Figure 3(a) to (f) shows the variation of measured and computed average daily total global solar radiations for Seiyun, Aden, Lahej, Fiyush, A1-Sufal and Mukiras, respec- tively.

The variation of the measured and the computed average daily total global solar radiation in Seiyun is shown in Fig. 3(a) which shows that the maximum is obtained during the month of May which is equal to 26.9 M J / m 2 - d a y by using eq. (9) and 23.19 by using eq. (1).

Figure 3(b) shows the variation of the measured value of global solar radiation for Aden from Sayigh [3] and com- puted values of global solar radiation in MJ/m 2 - day using eqs (1) and (9).

i From Fig. 3(b) the difference between the measured values from Aden Airport Meteorological Department and com- puted values using eqs (1) and (9) is small, but between the measured values from Sayig~a [3] and computed values using eqs (1) and (9) it is found to be high.

42

18

~6 .~

14

42

44 46 48 50 52

I ~,"~ l - ~ / f tO ~

V I : ' I LJ

A l s u f a l / ~ - - .~.~ Y !~ o ~,Ix ~'~' ~ M u k i r a s + .,X'

.~ Lahe, j Fiyush ~'~

44 46 48 50 52 Longitude

Fig. 2. Six studied locations in Yemen.

I d = [0.0271~(1 + 0.033 cos (360.N/365)) - 0.29391b] cos (0z)

where :

ao = r0 × a'0,

al = rl x a't,

K = r k × k ' ,

l~=Ib+Id

a'o = 0.4237-0.00821 ( 6 - A ) 2

a'l = 0.5055+0.001 (6--A) 2

k' = 0.2711 +0.01858 ( 2 . 5 - A) 2

r0, rl and rk are the climate corrections which equal 0.95, 0.98 and 1.02, respectively.

Table 2 shows the measured and the computed values of

3. RESULTS AND DISCUSSION

18 Prediction o f H by eq, (I) Table 3 gives the estimated values of monthly average of

17 daily global solar radiation in six towns in P.D.R. Yemen. 16 ~ These estimates are obtained by means of the ~ngstr6m

correlation eq. (1) and are based on sunshine records for "~ periods ranging from 1 to 7 years in these towns. Comparison

1 5 25 is made between computed and measured values when these 14 are available.

It is seen that for the first five towns (Aden, Seiyun, Lahej, 13 Fiyush and AI-Sufal) the per cent difference between com-

puted and measured values is less than 13.8% and in most cases it is much less, but for Mukiras the per cent difference between computed and measured values is so high this may be due to the availability of measured data being limited.

The variation of the measured and computed average daily of total global solar radiation using eq. (I) for Seiyun, Aden, Lahej, Fiyush, A1-Sufal and Mukiras is shown in Fig. 3.

(8) Figure 3 shows that the maximum is obtained during the months of April, May and June. January and December

(9) represent the months for minimum solar radiation. Figure 4 shows the mean monthly totals of global

solar radiation for six places. The pattern of fluctuations of radiation is the same for all locations. Peak solar radiation occurs in April and May. Among the six places, it appears that Aden has the highest total o f global radiation of 26.37 MJ /mZ-day . In general the daily global solar radiation for the six places lie between 13.7 and 25.37 MJ /m2-day . It can be seen from Table 2 and Fig. 3(b) that using Hottel's method is found to be in good agreement with an error of

Table 1. Geographical coordinates and regression parameters for six towns in P.D.R. Yemen

Town

Regression Correlation Geographical coordinates coefficients coefficients

Alt. (m) Lat. °N Long. °E a b a + b r

Aden 5 12.83 45.0 0.329 0.46 0.789 0.78 Seiyun 700 15.56 49.0 0.359 0.278 0.637 0.71 Lahej 30 13.10 45.0 0.12 0.534 0.654 0.73 Fiyush - - 12.58 44.6 0.50 0.20 0.7 0.63 A1-Sufal - - 14.19 - - 0.403 0.163 0.566 0.75 Mukiras 2040 13.52 45.41 0.24 0.30 0.54 0.62

Data Bank 111

Table 2. The measured and computed values of global solar radiation in MJ /m2-day using eqs (1) and (9) for Seiyun in 1988 and Aden in 1964 (these two years give a complete data record)

Station Month : J F M A M J J A S O N D

Aden H,, 17.60 19.70 24.40 24.90 24.90 22.00 19.90 21.20 22.20 22.70 20.90 18.4 H~ 19.60 21.90 25.70 26.10 26.80 22.30 22.00 23.80 24.80 24.30 22.50 20.5 H2 19.20 21.20 23.60 24.80 24.90 24.50 24.60 24.70 23.90 21.90 19.60 18.4 H 3 14.04 15.01 18.70 18.70 19.40 19.20 20.00 18.22 19.20 18.50 16.40 13.1 E' 09.10 07.60 --3.30 --0.04 00.00 11.00 24.00 17.00 7.70 3.5 --6.2 0.0

Hm 15.50 17.80 20.50 22.50 23.20 23.20 19.50 20.10 21.30 19.60 17.60 16.80 H~ 16.80 18.30 20.00 21.70 22.80 22.10 21.90 21.10 20.30 19.10 17.50 16.80 H2 18.60 21.20 24.20 26.30 26.90 26.80 26.70 26.40 24.90 22.20 19.30 17.80

Seiyun

Hm, measured monthly/average daily global radiation (MJ/m 2 - day). H,, computed monthly/average daily global radiation (M J /m2-day) by using eq. (1). H2, computed monthly/average daily global radiation (M j /m2-day) by using eq. (9). H3, measured monthly/average daily global radiation (MJ/mZ-day) from Sayigh [3]. E', per cent different between estimated values using eq. (9) and the measured data (Hm).

24

~20 .= E 516

12

3O > .

2O

I I t I I I I I I I I 2 3 4 5 6 7 8 9 10 11 12

(a) Seiyun

--x-- eq. (1) --o--- Measured

• e q . (9) I Ref. [5]

2 3 4 5 6 7 8 9 10 11 12 (b)Aden

25

24

~ 2 3

. 22 -~ 21

20

19

24

> 2O

f I I I 1 I J I I I I

20t

t I I I I 2 3 4 5 6 7 8 9 10 11 12 Month 1 2 3 4 5 6 7 8 9 10 11 12 Month

(c) Lahej (d) Fiyush

I >20

:2 :3 4 ; ; "I 8 ; 110 1ll l l2Month 1 2 3 4 5 6 7 8 9 10 111 ll2Month (e) AI-Sufal (f) Mukiras

Fig. 3. Variation of measured and computed average daily of the total global solar irradiance.

112 Data Bank

Table 3. Compar ison of measured and estimated daily global radiation using eq. (1)

Station Month : J F M A M J J A S O N D

Aden H m 17.6 19.7 24.4 24.9 24.9 22.0 19.9 21.2 22.2 22.7 20.9 18.4 H 19.6 21.9 25.7 26.1 26.8 22.3 22.0 23.8 24.8 24.3 22.5 20.5 E 11.4 11.2 5.3 4.4 7.6 1.3 10.5 12.0 11.7 7.0 7.3 11.4

Hm 15.5 17.8 20.5 22.5 23.2 23.2 19.9 20.1 21.3 19.6 17.6 16.8 H 16.8 18.3 20.0 21.7 22.8 22.1 21.9 21.1 20.3 19.1 17.5 16.8 E 8.7 2.7 --2.4 - 3 . 4 - 1 . 7 - 4 . 7 0.12 4.9 - 4 . 8 - 2 . 2 0.77 0.0

nm 16.8 15.8 21.2 21,8 19.3 19.0 18.5 19.9 15.4 20.3 16.5 13.7 H 12.3 16.7 19.5 20.2 19.3 17.5 16.9 18.7 15.9 19.7 17.8 15.4 E 13.8 5.6 - 8 . 7 - 7 , 9 0.0 --8.5 - 9 . 5 6.4 --3.2 - 3 . 0 7.9 12.4

Hm 18.8 19.9 23.2 22.7 24.4 24.1 20.8 20.3 21.9 22.4 22.5 24.1 H 18.9 20.5 21.0 24.0 25.0 24.0 22.4 22.7 23.7 22.6 20.9 20.7 E 0.53 3.0 --1.0 5.7 2.5 - 0 . 4 7.7 11.8 8.2 0.89 - 7 . 7 - 1 2 . 4

Seiyun

Lahej

Fiyush

AI-Sufal

Mukiras

Hm 15.5 17.8 19.5 18.0 16.2 14.4 13.0 13.8 15.2 15.7 15.8 16.0 H 13.7 17.8 21.0 16.2 15.1 13.5 15.0 13.9 14.0 15.5 14.5 15.0 E -13 .1 0.0 7.7 --11.1 - 7 . 3 - 6 . 6 15.4 0.72 - 8 . 6 --1.3 - 8 . 9 6.7.0

Hm 9.25 10.72 24.5 24.0 18.9 9.1 8.2 13.0 15.1 H 14.2 14.0 19.7 20.1 18.8 15.0 12.3 28.8 17.2 E 53.0 30.5 - 2 4 . 0 --19.4 0.54 64.0 50.0 25.0 14.0

_ _ m

Hm, measured month ly average daily global radiation (MJ/m 2 - day). H, computed monthly average daily global radiation (MJ/m 2 - day). E, per cent difference between estimated and measured values.

27

25

23

>.

-~21

~ 1 9 ~

17~

I l I I I I I I I I I

2 3 4 5 6 7 8 9 1011 12

Fig. 4. Monthly variation of total global solar irradiance in P.D.R. Yemen.

l 1%. Hottel 's method will be useful to calculate the solar radiation when no measured data are available. The data required for applying this method are angle of latitude and altitude above sea level.

Compar ing the results of Sayigh [3] and other results of solar radiation estimation it is seen that the difference is large. However, no reference has been mentioned by Sayigh regarding the source of measured solar radiation data.

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

It is possible to compute monthly mean daily global radi- ation on a horizontal surface from A.ngstr6m's correlation for different locations in P.D.R. Yemen, which have been proved the most simple and accurate correlation provided that the meteorological parameters (measured solar radi- ation and sunshine duration) are available.

The main problem in employing Angst rSm's correlation is in obtaining the proper values for the regression coefficients a and b for a given location. The coefficients a and b are found to vary not only in different parts of the world but even for nearby locations in the same region having similar geographical and climatological conditions.

Among the six locations in P.D.R. Yemen, it appears that Aden has the highest total global solar radiation per annum. For other locations where no measurements of solar radi- ation are available Hottel 's correlation can be used to some extent.

It can be concluded from this work that for the first time information is available about accurate solar radiation data for P.D.R. Yemen.

N O M E N C L A T U R E

A distance above sea level, km lb direct radiation, M J / m 2 - d a y I~ diffuse radiation, M J / m 2 - d a y Is° solar constant, W / m z IT total radiation M J / m 2 - d a y N mean daily numbers of hours of daylight in a given

mon th between sunrise and sunset in hr the day of the year

w~ sunset hour angle in degrees

Data Bank 113

6 solar declination in degrees ~b latitude of the location in degrees

REFERENCES

1. J. F. Kreider and F. Kreith, Solar Energy Handbook, McGraw-Hill, New York (1981).

2. H. C. Hottel, Solar Energy 18, 129 134 (1976). 3. A. A. M. Sayigh, The iso-radiation map for the Arab

region. Solar Wind TechnoL 4, 163 177 (1987). 4. S. Jain and P. C. Jain, Solar Energy 40, 93 (1988). 5. J. F. Kreider and F. Kreith, Principles of Solar Engin-

eering, McGraw-Hill , New York (1978).