Solar Energy Vol. 50, No. 5, pp. 441~.46, 1993 0038-092X/93 $6.00 + .00 Printed in the U.S.A. Copyright © 1993 Pergamon Press Ltd.

ESTIMATING DIRECT, DIFFUSE, AND GLOBAL SOLAR RADIATION FOR VARIOUS CITIES IN IRAN BY

TWO METHODS AND THEIR COMPARISON WITH THE MEASURED DATA

M. ASHJAEE, M. R. ROOMINA, and R. GHAFOURI-AZAR Department of Mechanical Engineering, University of Tehran, Tehran, Iran

Abstract--Two computational methods for calculating hourly, daily, and monthly average values of direct, diffuse, and global solar radiation on horizontal collectors have been presented in this article for location with different latitude, altitude, and atmospheric conditions in Iran. These methods were developed using two different independent sets of measured data from the Iranian Meteorological Organization (IMO) for two cities in Iran (Tehran and Isfahan) during 14 years of measurement for Tehran and 4 years of measurement for Isfahan. Comparison of calculated monthly average global solar radiation, using the two models for Tehran and Isfahan with measured data from the IMO, has indicated a good agreement between them. Then these developed methods were extended to another location (city of Bandar-Abbas), where measured data are not available. But the work of Daneshyar [1] predicts its monthly global radiation. The maximum discrepancy of 7% between the developed models and the work of Daneshyar [1]was observed.

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

In locations where solar radiation measurements are sparse, like Iran, theoretical estimations have to be used. Thus, various methods have been devised to pre- dict available solar radiation from other existing data. Both direct and diffuse components of solar radiation have to be estimated for all systems, especially the nonfocusing ones. For this purpose, the presence of clouds, which have a major effect and may cover some or all parts of the sky, must be taken into account.

There are many parameters that change the amount of direct and diffuse solar radiation such as time, date, local latitude, altitude, declination angle, zenith angle, atmospheric transmissivity, water vapor, regional al- bedo, cloud condition, sunshine hours, maximum air temperature, relative humidity, etc. It is very difficult to obtain a general formula in order to estimate direct and diffuse solar radiation by considering all of these parameters simultaneously. On the other hand, some of the above mentioned parameters have little effect on solar radiation and can be neglected, and only im- portant factors may be taken into account. In this ar- ticle, two different methods are presented for estimating the direct, diffuse, and global solar radiation.

2. M E T H O D I

2.1. Diffuse irradiance Diffuse solar radiation for engineering applications

may be considered isotropic and primarily a function of zenith angle 0 in clear sky. The proposed equation for diffuse solar radiation will also be applicable in cloudy conditions, and it has been assumed that diffuse solar radiat ion/De is not only a function of O but also a function of cloud factor CF, which is defined in sec- tion 2.3. The proposed model for the diffuse compo- nent was obtained from Daneshyar [ 1 ]. Daneshyar used

the same model for diffuse radiation that was proposed for the United States[2]. However, in his work, com- parison of the predictions with the experimental data of Tehran indicated that values in the diffuse equation should be multiplied by the factor 0.604, and the fol- lowing equation for the prediction of diffuse solar ra- diation was proposed by h im[l ] .

IDF(O, CF) = 0.132 + 9.75(7r/2 -- 0) + 10.45CF. ( 1 )

The mean daily value of diffuse solar radiation IDF is calculated by

~s sunset IDF = IDF(O, CF)dt.

unrise (2)

2.2 Direct beam radiation As previously stated, for better and easier estimation

of solar radiation, it is necessary to choose dominant and major parameters. It is known that variation of solar radiation due to the amount of water vapor, re- gional albedo, and atmospheric aerosols is relatively small ( 5-10% ) [ 3 ]. Therefore, in this method, for sim- plicity the most important parameter, zenith angle 0 and cloud factor CF, has been chosen and considered in corresponding equations.

The creation of a single empirical curve that relates direct radiation and zenith angle based on the above mentioned assumptions, is the work of Paltridge and Proctor [ 3 ] :

IB(O) = 950{1 - e x p I - 0 . 0 7 5 ( T r / 2 - 0)]}. (3)

Since Is is directly altered from one location to an- other by the exponential term, a new coefficient is sub- stituted for 0.075 in eqn (3) in such a way to obtain a

441

442 M. ASHJAEE, M. R. ROOMINA, and R. GHAFOURI-AZAR

fit between the computed values and the measured global radiat ion data from the IMO. This is done for each monthly value throughout 14 years ( 1974-1987 ). The new obtained equat ion for direct c o m p o n e n t is:

IB(O) = 950{1 - e x p [ - 3 . 4 5 ( T r / 2 - 0)]} (4)

where 18 is in W m -2 and 0 must be calculated for the specified location and time. The new coefficient in the direct eqn (4) was basically obtained by applying two independent sets of data as input in a compute r pro- gram. Then a series of computa t ion and compar isons with measured values were done for all mon ths dur ing 1974-1987 until the least discrepancy was observed. Then the modified equat ion (direct) extended to an- other city (Bandar -Abbas) and checked with the avail- able source Daneshyar [I] and only 7% discrepancy was observed.

Since for corresponding location, 0 is funct ion of time, by integrating IB(O) from sunrise to sunset time, direct beam energy over a day is calculated. In this article integrat ion was done by using the Romberg in- tegral method. Presence of clouds causes the solar beam radiat ion to reduce to zero. Thus, a cloud factor CF must be considered, and by considering these aspects, an appropriate formula for mean daily direct solar en- ergy IB is

-~u unset

IB = (1 - CF) Is(O)cosidt. (5) nrise

2.3. Cloud factor In order to account for the cloud on solar radiation,

a cloud factor parameter CF has been int roduced [ 3 ]. This factor was a true month ly average calculated by using the measured month ly hours of sunshine during the last ten years. It is t rue that an individual cloud report may have some degree of inaccuracy. However, the t ime and spatial averaging used in the calculations of CF involves so many observat ions which reduce the r a n d o m error. Cloud factors are obtained based on the ratio of measured sunny hours ( reported by meteo- rological centers) to the potent ial as t ronomical sun- shine hours (calculated theoretically) in one month . The lati tude angle and the month ly averaged values of the CF, obtained by using meteorological data, for three cities in Iran, are presented in Table 1 [1].

IG = 16.(0)COS i + IDF(O)( 1 + COS /~)/2

q- rg(IB q- IDF)( 1 -- COS 3)/2. (6)

3. M E T H O D 2

The presented me thod in this section is based on a proposed model by Bird and Hu l s t rom[4 ] fo r esti- mat ing global irradiance in clear sky. But some mod- ifications in precipitable water Uw and a m o u n t of con- t r ibut ion of transmissivity, due to Rayleigh scattering TR for calculation of diffuse componen t of solar ra- diation, have been done. On the other hand Uw effects a,. in direct component . Then Barbaro 's et al.[ 5 ] work was used to account for cloudiness effect in this method by considering the IMO observations.

3.1. Direct and diffuse radiation The direct and diffuse components of solar radiation

that have been formulated by Bird and Hul- s trom[ 4 ] are:

IB = 0.9662Io( TM -- aw) TA; (7)

IDF = (IoCOS O)0.79ToT,,TuMTA,[0.5( 1 - TR)

+ Ba( l - TAS)]/[I -- m + m1°2]. (8)

TA is funct ion of turbidity, while the others are funct ions of P, Uw, and m. The percentage of diffuse radiat ion scattered by particles to the ground B, is con- sidered to be 0.84. Uw depends on relative humidi ty , temperature, and alt i tude and varies from 0.5-5 through the different seasons of the year [6] . In this work, an average precipitable water for the seasons of a year has been considered as follows:

For spring Uw = 1, summer Uw = 4.5, autumn Uw = 3, and winter Uw = 0.5. We have taken the range of the value of Uw from[6]for the latitude between 30-40 ° Noah. Then a trial and error method has been used to select a proper value for Uw from the range in order to fit the model respect to the measured data by the IMO for the cities of Tehran and Isfahan. A similar trial and error method has been also used to obtain coefficient of TR in the corresponding equation.

Also r~ could be approximated b y [ 4 ] :

rA = 0.2758rA(0.38 urn) + 0.35ZA(05 t~m) (9)

2.4. Global solar radiation The global solar radiat ion is the sum of diffuse and

direct components and is calculated from the following equation:

where rA(0 38 tam) and 7"A(0. 5 #m) are turbidity values mea- sured at 0.38/~m and 0.5 #m, respectively. The visibility range that has to be utilized in selecting the rA has been proved to be difficult to specify, because of geographic

Table 1. Latitude and cloud factor

Location Latitude January February March April May June July August September October November December

Tehran 35.68 0.429 0.391 0.456 0.400 0.325 0.209 0.216 0.186 0.180 0.242 0.316 0.423 lsfahan 32.61 0 . 3 0 4 0 . 3 2 4 0.299 0.349 0.320 0.162 0.206 0.168 0.149 0.159 0.277 0.330 Bandar-Abbas 27.21 0.325 0.304 0.353 0.354 0.212 0.254 0.357 0.299 0.251 0.176 0.195 0.246

Direct, diffuse, and global solar radiation in Iran

Table 2. The coefficient of K* values for different latitudes

443

Latitude 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0

K* 0.35 0.34 0.34 0.33 0.33 0.32 0.32 0.32 0.33 0.34 0.36 0.38 0.40

features of the area and the wide spread of the values which may be due to the different ability of the ob- servers.

Pisimanis and Notaridou [ 7 ] have presented tur- bidity coefficients for warm and cold periods. The val- ues of turbidity coefficients for the cold period (Oc- tober-March) and warm period (April-September) have been obtained by interpolation of Bird and Hul- strom's tables [ 8 ]. Using only turbidity values of cold period throughout the year for Iran caused closer agreement between computed results and the measured data. These values are as follows:

7"A(0.38 #m) = 0.35, ZA<0.5 ,m) = 0.27. (10)

In order to achieve a fit between the estimated global radiation and the measured data by the IMO, a new value is substituted for 0.5 in eqn (8). The new equa- tion is:

IDF = (/oCOS O)0.79ToTwTcM TAA[ 0.7 ( 1 -- TR)

+ O a ( 1 - - T A s ) ] / [ I - - m + m L ° 2 ] . (11)

3.2. Cloudiness effect The above relations are for clear sky. The inclusion

of the cloudiness effect is accounted for by the ratio of measured to potential astronomical sunshine duration

n / N . Thus, the actual average daily direct I, and diffuse Dn radiation including cloudiness can be calculated by the following expressions [ 5 ]:

In = n / N IB, (12)

D, = n / N IDF + K*( 1 - n /N) ( IB + IDF), and (13)

G, = (I~cos 0 + D, ) / ( 1 - rgrs). (14)

The K* depends on local latitude and is given by Table 2[5]. The value of n / N can be calculated by dividing the hours of sunshine n, given by the IMO, to hours of shining sun in a day from sunrise to sunset, N. To account for cloudiness, 10,/Dr, and I~ are re- placed by In, Dn, and Gn, respectively in eqn (6). De- tailed relations for all parameters which have been ap- plied in the equations are given in Appendix A.

4. COMPARISON OF GLOBAL SOLAR RADIATION CALCULATED BY THE MENTIONED METHODS

WITH MEASURED DATA

A numerical model was developed in order to cal- culate hourly, daily, direct, diffuse, and global solar radiations for every location by two methods which were described before. Sunrise and sunset times, zenith angle, declination angle, and atmospheric transmissiv-

M J

P E R

8 0

/i E T E R

P E R

D A Y

6 0

60

40

30

20

10 JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC

MONTH

Fig. 1. Average monthly global solar radiation for Tehran.

444 M. ASHJAEE, M. R. ROOMINA, and R. GHAFOUR1-AZAR

60 M J

P E 50 R

S O 40

E T E 30 R

P E R 20

D A Y

10 JAN

/

method 1 method 2 measured

I I I l l I I 1 I I J

FEB MAR APR MAY JUN JUL AUG 8EP OCT NOV DEC MONTH

Fig. 2. Average monthly global solar radiation for Isfahan.

ity are calculated according to input data which are local latitude, date, altitude, and inclination by the mentioned computer program. Then, by using Rom- berg integral method, from sunrise to sunset time, the amount of solar energy that is reached at the surface during one day is obtained. The mean value of solar radiation through a month could be approximated by values on the 15th day of each month. However, monthly average values can be obtained by averaging daily values during one month.

Mean values of global solar radiation for Tehran and Isfahan which have been collected by the IMO have been used for comparison with estimated values. Global solar radiation estimated by the above men- tioned methods, and the mean value of measured global solar radiation for Tehran, are shown in Fig. 1. The maximum discrepancy between measured data and calculation by method i is 11.9% (for March) and in other months varies from 0.1-7.2% (April to De- cember). On the other hand, method 2 is closer to the

M 6O

50 R -

40

R 80

P E R

D A Y

20

10 JAN

method 1 - ~ - method 2 ~ ref.ll| 1

m

I I I I I I I I I I

FEB MAR APFI MAY JUN JUL AUG 8EP OCT NOV DEC MONTH

Fig. 3. Average monthly global solar radiation for Bandar-Abbas.

Direct, diffuse, and global solar radiation in Iran 445

measured data as expected, since atmospheric trans- missivity has been taken into account. The max imum aw discrepancy in this method with measured data is less i than 5%. Comparat ive results for Isfahan are shown" m in Fig. 2. The max imum discrepancies of method 1 n

rs and 2 for the months January and February are 18% re and 15%, respectively. But in other months a good Xo degree of accuracy has been obtained for both methods B~ with respect to measured data (discrepancies were less

CF than 10% by both methods). D,

The main purpose of this article is to present meth- G. ods for estimating solar radiation in Iran. Since solar Is measurements through Iran are sparse, devising a /De method for accurate prediction of available solar energy la

I. in every location is worthwhile. Therefore, the men- Io tioned methods were extended to locations where no N measured data are available. A similar estimation has P been carried out for the city of Bandar-Abbas. Com- P0 parison of the results of methods 1 and 2 for the city TA

of Bandar-Abbas and the work of Daneshyar [ 1 ] is pre- TAA sented in Fig. 3. Method 1 shows 5% and method 2 To shows 7% difference with Daneshyar[1]. It is notable TM that the assumptions of method 1 and [ 1 ] are nearly TR

TvM the same. Tw

The device that measures the global solar radiation Uw in the IMO is a CM5 model with solarimeter integrator CCI by Kipp and Zonen, Holland. Since 1973 it has 0 been calibrated each year and has an accuracy within TA 2%. It was first calibrated in 1973 in the Regional Ra-. diation Center[2]in Puna, India. From 1974, and each year after, it has been calibrated by the IMO, and in 1988, was calibrated in Tokyo, Japan based on the International Angstrom System.

5. CONCLUSIONS

This article has presented two computational methods for calculating hourly, daily, and monthly average values of direct, diffuse, and global solar ra- diation for Iran. Comparison of calculated monthly average global solar radiation by the above mentioned methods with measured data for Tehran and Isfahan during 1981-1985, indicates a good degree of accuracy, especially by method 2, as would be expected. This is due to taking atmospheric conditions into account. By considering the crude and irregular nature of obser- vations, obtaining such accuracy is quite remarkable. Obtaining satisfactory results from a comparison of measured and calculated values indicates that the above methods are a viable tool for those locations in Iran where no measured data are available.

NOMENCLATURE

the percentage is absorbed by water vapor incidence angle air mass hours of measured sunshine sky albedo ground albedo the amount of ozone times the air mass the percentage of diffuse radiation to the ground due to particles cloud factor diffuse radiation including cloudiness global radiation including cloudiness direct beam radiation diffuse radiation global radiation direct beam radiation including cloudiness solar constant potential astronomical sunshine hours local absolute pressure reference pressure at sea level transmissivity due to absorption and scattering by par- ticles transmissivlty due to absorption by particles transmissivlty due to ozone transmissiv~ty of atmospheric gases except water vapor transmissiv]ty due to Rayleigh scattering transmissivlty due to oxygen and carbon dioxide transmissivlty of water vapor percipitable of water tilt angle zenith angle turbidity coefficient

REFERENCES

1. M. Daneshyar, A theoretical method for the prediction of monthly mean solar radiation parameters, Presented at the 13th Intersociety Energy Conversion Engineering Conference ( 1978 ).

2. J. F. Kreider and F. Kreith, Solar heating and cooling, engineering practical design and economics, McGraw Hill Book Company, New York (1975).

3. G. W. Paltridge and D. Proctor, Monthly mean solar ra- diation statistic for Australia, Solar Energy 18, 235-243 (1976).

4. R. Bird and R. L. Hulstrom, A simplified clear sky model for direct and diffuse insolation on horizontal surface, U.S. Solar Energy Research Institute (SERI), Technical Report TR-642-761, Golden Co ( 1981 ).

5. S. Barbaro, S. Coppolino, C. Leone, and E. Sinagra, An atmospheric model for computing direct and diffuse solar radiation, Solar Energy 22, 225-228 ( 1979 ).

6. W.C. Drickinson and P. N. Cheremisinoff, Solar energy technology handbook, Part A: Engineering fundamental, Sec. 4.2, Selection of Typical Atmospheric Condition, The International Solar Energy Society (1980).

7. D. Pisimanis and V. Notaridou, Estimating direct, diffuse and global solar radiation on an arbitrarily inclined plane in Greece, Solar Energy 39, 159-172 (1987).

8. R. Bird and R. L. Hulstrom, Review evaluation and im- provement of direct irradiance model, J. Solar Energy Eng. 103, 183 (1981).

APPENDIX A

TM = 1.041 -O.15[m(9.368*lO-4p+o.051)] 1/2. (AI)

P/Po = exp[h/1000.(-0.174 - 0.0000017h)]. (A2)

T A = exp[-'r°'S73(i. 0 + 7" A - "r°7°SS)m°91°s]. (A3)

aw = 2.4959Uwm[( 1.0 + 79.03Uwm) °'6s24

+ 6.385Uwm] -~.

Tw = 1 - aw.

(A4)

(A5)

446 M. ASHJAEE, M. R. ROOMINA, and R. GHAFOURI-AZAR

m = I / [ c o s 0 + 0 .15(93.885 - 0)-L253]. (A6)

"l" A : 0 .2758TA(0 .38 ) -~- 0 . 3 5 T A ( 0 . S ) . (A7)

TuM = e x p [ - 0 . 1 2 7 m ° 2 6 ] . (A8)

Taa = 1 - 0.1(1 - TA)(I -- m + m1°6). ( A 9 )

TR = e x p [ - 0 . 0 9 3 m ° S 4 ] . (A10)

TAs = TA/TAA. ( A l l )

To = 1 - 0 . 1 6 1 x o ( l + 139.48xo) -°'3°35

- 0 .00271Xo/( 1.0 + 0.044xo + 0.0003xo2). (A12)

rs = 0.0685 + ( 1 - B~)( 1 - Tas). (A13)

Tas = 10 -O'045t(P/e°)mlO'7. (A14)

Ba = 0.84. (A15)

rg = 0.2. ( A I 6 )

6 = 23.45 s i n [ 3 6 0 ( 2 8 4 + n ) / 3 6 5 ] . (A17)