~ ) Pergamon Renewable Energy, Vol. 13, No. 3, pp. 355 362, 1998

@ 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain

PII : S0960-1481 (98)00009-3 0961~1481/98 $19.00 + 0.00

D A T A B A N K

Correlations between monthly average global solar radiation on horizontal surfaces and relative duration of sunshine in

Yunnan Province, China

W E N X I A N LIN* A N D E N R O N G LU Solar Energy Research Institute, Yunnan Normal University, Kunming 650092,

P.R. China

(Received 20 November 1997 ; accepted 2 January 1998)

Abstract--With measured data of global solar radiation and the relevant data of geographic and meteorological parameters at 7 meteorological stations in Yunnan Province, the correlations between monthly average global solar radiation on hori- zontal surfaces and relative duration of sunshine are developed in this special region which has significantly varying climates. It is believed that the two correlations developed in this work are applicable for estimating monthly global solar radiation on horizontal surfaces at any site in Yunnan Province, China. © 1998 Elsevier Science Ltd. All rights reserved.

1. INTRODUCTION

For the design of active and passive solar system, the knowledge of solar radiation on tilted surfaces is essential. Such data are often not available and are generally calculated from the corresponding values on horizontal surfaces, which in turn may be obtained from measured data. However, the network collecting solar radiation is still very scarce, therefore, the main method is to develop models based on the measured data of nearby sites to estimate solar radiation on horizontal surfaces at the considered site. In this objective, a very large number of models have been developed, especially sunshine-based models [1-24].

Situated on the well-known "Yunnan-Guizhou Plateau", Yunnan Province, China, covers the area of 380,000 km 2 (latitude: 21-29°N; longitude: 97.5-106°E), which is larger than that of Norway (324,000 km 2) or Finland (337,000 kin2). Within a tropical-subtropical area, the province has its unique "cubic climates". Its western part is the "Dianxi Lengthwise Valley Area" and the east is the main body of the "Yunnan-Guizhou Plateau". The entire region is with low latitudes, largely varied heights, and complex climatic and meteorological conditions. Due to the block of mountains to cold waves, most parts have high average daily temperatures and winter temperatures. The fresher and thinner plateau air, larger transmittance of sunlight, longer hours of bright sunshine, and better climatic and meteorological conditions in the province results in larger global solar radiation than those in the other regions in China. Yunnan Province has rich resources of solar energy and the application of solar water heaters are very popular. It is expected that other applications of solar energy engineering will also find their popular roles in this province in the near future. Nevertheless, there are only 7 meteorological stations in the province which have measured data of global solar radiation on horizontal surfaces, It is imperative to develop correlations to estimate the desired data

* Author to whom correspondence should be addressed : Wenxian Lin, Dept. of Mechanical and Mechatronic Engineering, University of Sydney, NSW 2006, Australia.

Fax: + 61-2-9351-7060; e-mail: wenxian@tiny.me.su.oz.au

355

356 Data Bank

of global solar radiation on horizontal surfaces at sites other than the seven stations in the province based on the measured data of the seven stations. Wang et al. developed a correlation to be applicable at any site in China [25] and Lin developed correlations to estimating monthly global solar radiation on horizontal surfaces at sites in Yunnan Province in the dry season (Nov.-Apr.) and in the wet season (May-Oct.), respectively [26, 27]. In this work, we develop correlations between monthly average global solar radiation on horizontal surfaces and relative duration of sunshine in Yunnan Province.

2. CALCULATION METHODOLOGY

Angstrom suggested a simple linear relationship between monthly average global solar radiation on horizontal surfaces and relative duration of sunshine which modified by Prescott [28] and others with the following form :

H/Ho = a+bn/Na (1)

where H and Ho are, respectively, the monthly average global solar radiation and extraterrestial radiation on horizontal surfaces, MJ/m2.month, n and Nd are, respectively, the monthly average daily hours of sunshine and maximum possible daily hours of sunshine, hour; a and b are constants obtained by the linear regression analysis.

Ho and Nd can be calculated with the formulae provided in [29, 30]. Hay suggested that Na in eqn (1) should be replaced by the modified N~ as the Campbell-Stokes sunshine recorders do not respond to the sunlight less than 5 ° of sun height [16]. In the past literatures, some researchers used Nd and the others used Nd. In this work, we also use the following form :

H/ Ho = a + bn/Nd. (2)

3. CORRELATIONS AND DISCUSSION

The general information about the seven meteorological stations in Yunnan Province, China, is listed in Table 1. In Figs 1 to 4, the relationships between 14/1to and n/Na and n/N'd are plotted for the seven stations in Yunnan Province. It is evident that very strong linear relationships exist between these parameters. With measured data of monthly average global solar radiation on horizontal surfaces and hours of sunshine at seven stations [31, 32], linear regression analyses are used to develop correlations between the monthly average global solar radiation on horizontal surfaces and the relative duration of sunshine in Yunnan Province at the following three cases :

Case 1 : all measured values of H and n in each month during the corresponding years of records for

Table 1. The general information of seven stations in Yunnan Province, China

Location Latitude Longitude Altitude Data record period

Kunming 25°01'N 102°41'E 1891.4 m 1971-1975, 1977 Tengchong 25°07'N 98°29'E 1647.8 m 1971-1975 Hekou 22°30'N 103°57'E 136.7 m 1971-1977 Jinhong 21°52'N 101°04'E 552.7 m 1971-1973, 1977 Zhaotong 27°20'N I03°45'E 1949.5 m 1971-1977 Lijiang 26°52'N 100°13'E 2393.2 m 1971-1973, 1977 Mengzi 23°23'N 103°23'E 1300.7 m 1971-1975

Data Bank 357

0.8

0.7

0.6

0.5

"g 0.4

0.3

0.2

0.1

0

~ , . ~ , , A ~ A axa

a A t,~ 4 t a a

~ z x z ~

i I I I

0.2 0.4 0.6 0.8 n/Nd

Fig. l. H/Ho vs n/Nd at case 1.

every stations are presented, but the average values of H and n in each month during the corresponding years of records for every stations are not presented (the number of observation is 456). Case 2 : all measured values of H and n in each month during the corresponding years of records for every stations are presented and the average values of H and n in each month during the corresponding years of records for every stations are also presented (the number o f observation is 540). Case 3 : only the average values of H and n in each month during the corresponding years of records for every stations are presented (the number of observation is 84).

The results are listed in Tables 2 and 3. With these two tables, the following points can be obtained :

1

0.9

0.8

0.7

=* o.6 -r"

0.5

0.4

0.3

0.2

0.1

0

O , o o

0

0

0

~oo

d I I

0.2 0.4

n/N d '

Fig. 2. H/Ho vs n/No at case 1.

0.6 0.8

358 Data Bank 0.7

0.65

0.6

0.55

0.5

0.45

0.4

0.35

0.3

0.25

0.2

~A

z~

2 ' 2 " .

~x

I I I I

0 . 2

A A

0.4 0.6

n/Na

Fig. 3. H/Ho vs n/Nd at case 3.

0.8

0.7

0.65

0.6

0.55

0.5

--..:° 0.45

0.4

0.35

0.3

0.25

0.2

0

q

0.1

I

0.2

IS

A A t A

& ~ Z$ &

a n ~ a a az x ~ ~ a

a ' ~ a a z~ zx

zx 6 A

I I t I I

0.3 0.4 0.5 0.6 0.7

n/N d' Fig. 4. H/Ho vs n/N~ at case 3.

~ A ~ a

~a

0.8

A

I

0.9

Data Bank

Table 2. The linear regression results with the correlations in the form ofeqn (1)

359

Number of Standard error Standard error Location Case a b r 2 observation of constant of coefficient

1 0.125 0.535 0.865 72 0.0362 0.0253 Kunming 2 0.127 0.534 0.875 84 0.0341 0.0223

3 0.146 0.514 0.967 12 0.0157 0.0299 1 0.225 0.530 0.959 60 0.0228 0.0145

Tengchong 2 0.223 0.529 0.957 72 0.0228 0.0133 3 0.208 0.529 0.975 12 0.0178 0.0268 I 0.185 0.480 0.810 84 0.0255 0.0256

Hekou 2 0.188 0.480 0.800 96 0.0255 0.0248 3 0.189 0.536 0.949 12 0.0102 0.0392 1 0.185 0,526 0.726 48 0.0412 0.0476

Jinhong 2 0.189 0.522 0.732 60 0.0384 0.0415 3 0.214 0.489 0.803 12 0.0252 0.0767 1 0.172 0.567 0.822 84 0.0357 0.0291

Zhaotong 2 0.173 0.567 0.821 96 0.0343 0.0273 3 0.186 0.546 0.790 12 0.0243 0.0891 1 0.207 0.545 0.886 48 0.0351 0.0288

L~iang 2 0.209 0.546 0.901 60 0.0321 0.0238 3 0.214 0.552 0.979 12 0.0150 0.0258 1 0.235 0.504 0.863 60 0.0301 0.0264

Mengzi 2 0.236 0.497 0.862 72 0.0287 0.0237 3 0.241 0.454 0.977 12 0,0088 0.0221 1 0.182 0.538 0.789 456 0.0462 0.0131

Stations* 2 0.184 0.536 0.797 540 0.0442 0.0117 3 0.199 0.519 0.864 84 0.0309 0.0227

* Seven stations together.

(a) the correlations in the form of eqn (2) have better regression results than the correlations in the form of eqn (1), that indicates the correlations in the form of eqn (2) should be used in Yunnan Province, China ;

(b) although all the correlations for each of the seven stations have good linear regression results, there are still differences among the seven stations, which reflects the effects of geographic and meteorological parameters at different stations ;

(c) the correlations based on the data of seven stations together have very good linear regression results which indicates these correlations are applicable for estimating the monthly average global solar radiation on horizontal surfaces at any site in Yunnan Province ;

(d) the correlations at case 2 are always better than those at case 1, therefore, the correlations at case 1 should be discarded ;

(e) the correlations at case 2 generally have smaller standard errors of constant but larger standard errors of coefficient than the correlations at case 3 and it is difficult to decide in which case the correlations have better linear regression results.

To further evaluate the performances of the correlations at case 2 and 3, we present in Table 4 the results of statistical comparisons between the measured and calculated values of monthly average global solar radiation by using the correlations of seven stations together at cases 1-3 and the overall performances of the correlations in different cases. From these results, it is found that the correlations at case 2 also have better performance than the correlations at case 1, which supports the above- stated point, and the correlations at case 3 have better performance than the correlations at case 2 but the improvement is very little. Therefore, we recommend that the correlations at case 2 and 3 are

360 Data Bank

Table 3. The linear regression results with the correlations in the form of eqn (2)

Number of Standard error Standard error Location Case a b r z observation of constant of coefficient

1 0.127 0.496 0.863 72 0.0364 0.0236 Kunming 2 0.129 0.495 0.873 84 0.0343 0.0209

3 0.148 0.477 0.966 12 0.0161 0.0285 1 0.228 0.490 0.960 60 0.0224 0.0131

Tengchong 2 0.225 0.489 0.959 72 0.0223 0.0121 3 0.211 0.488 0.978 12 0.0166 0.0231 1 0.183 0.456 0.815 84 0.0252 0.0240

Hekou 2 0.186 0.457 0.804 96 0.0252 0.0233 3 0.184 0.515 0.953 12 0.0098 0.0361 1 0.184 0.494 0.734 48 0.0406 0.0438

Jinhong 2 0.190 0.491 0.741 60 0.0378 0.0381 3 0.211 0.461 0.816 12 0.0244 0.0693 1 0.171 0.534 0.823 84 0,0356 0.0273

Zhaotong 2 0.172 0.533 0.820 96 0,0344 0.0257 3 0.188 0.506 0.758 12 0.0260 0.0903 1 0.215 0.495 0.886 48 0.0352 0.0262

LOiang 2 0.216 0.496 0.901 60 0.0321 0.0216 3 0.222 0.500 0.983 12 0.0132 0.0205 1 0.238 0.467 0.868 60 0.0295 0.0239

Mengzi 2 0.238 0.460 0.867 72 0.0282 0.0215 3 0.246 0.416 0.978 12 0.0085 0.0196 1 0.184 0.500 0.792 456 0.0458 0.0120

Stations* 2 0.186 0.498 0.800 540 0.0438 0.0107 3 0.201 0.479 0.868 84 0.0305 0.0206

* Seven stations together.

the general correlations to estimate the monthly average global solar radiation on horizontal surfaces at sites in Yunnan Province, China.

4. CONCLUSIONS

With the measured data of global solar radiation on horizontal surfaces and the hours of sunshine as well as the relevant data of geographic and meteorological parameters at seven meteorological stations in Yunnan Province, we develop various correlations between the monthly average global solar radiation on horizontal surfaces and the relative duration of sunshine and make a discussion about the linear regression results. We recommend the following two correlations to be used to estimate the monthly average global solar radiation on horizontal surfaces at any site in Yunnan Province, China :

H/Ho = 0.201 +0.479n/N~, (3)

and

H/Ho = 0.186 + 0.498n/Ng, (4)

Acknowledgements--The authors are grateful to Y u n n a n Provincia l Commi t t ee o f Science and Techno logy for the financial suppor t o f this work.

Data Bank

Table 4. The statistical comparisons of correlations in different cases

361

Case 1 Case 2 Case 3 Location MBE (%) RMSE (%) MBE (%) RMSE (%) MBE (%) RMSE (%)

Kunming 11.3 11.4 11.5 11.6 12.4 12.4 (7.4,19.6)* (7.4,19.6)* (7.5,19.8) (7.5,19.8) (7.4,20.4) (7.4,20.4)

Tengchong - 4.7 5.2 - 4.5 5.0 - 3.3 4.0 ( - 10.7,2.4) (1,10.6) ( - 10.5,2.6) (1.1,10.4) (-8.9,3.5) (1.5,8.8)

Hekou - 1.6 2.1 - 1.3 1.9 0.6 2.0 (-5.9,2.8) (0,5.8) (-5.7,3.1) (0,5.6) (-4.1,4.9) (0.2,4.9)

Jinhong - 1.5 4.3 - 1.3 4.2 - 0 . 2 4.1 ( - 8.3,6.6) (0.1,8.2) ( - 8.1,6.7) (0,8) ( - 7,7.2) (0.4,7.2)

Zhaotong - 1.5 5.0 - 1.3 4.8 0.2 4.5 (-7.8,13.6) (0.4,13.6) (-7.5,13.8) (0.1,13.8) (-5.7,15.4) (0.2,15.4)

Lijiang - 7.4 7.3 - 7.3 7.1 - 6.6 6.4 ( - 1 1 . 9 , - 3 . 5 ) (3.4,11.8) ( - 1 1 . 8 , - 3 . 5 ) (3.4,11.7) ( - 1 1 . 2 , - 3 . 4 ) (3.3,11.1)

Mengzi - 3.6 3.7 - 3.4 3.5 - 2.5 2.7 (-8.5,1.1) (0.3,8.4) (-8.2,1.2) (0.2,8.1) ( -6 .2 ,2) (0,6.1)

Stationst - 1.3 5.5 - 1.1 5.4 0 5.1

* Range of Bias Error or Root Square Error in 12 months. t Seven stations together.

REFERENCES

1. Akinoglu B. (3. and Ecevit, A., Constrution of a quadratic model using modified angstrom coefficients to estimate global solar radiation, Solar Energy, 1990, 45, 85-92.

2. Soler, A., Monthly specific Rietveld's correlations, Solar Wind Technol., 1990, 7, 305-308. 3. Jain, P. C., A model for diffuse and global irradiation on horizontal surfaces, Solar Energy, 1990,

45, 301 308. 4. Yeboah-Amankwah, D. and Agyeman, K., Differential angstrom model for predicting insolation

from hours of sunshine, Solar Energy, 1990, 41,371-377. 5. Gopinathan, K. K., Computing the monthly mean daily diffuse radiation from clearness index

and percent possible sunshine, Solar Energy, 1988, 41,379-385. 6. Benson, R. B., Paris, M. V., Sherry, J. E. and Justus, C. (3, Estimation of daily and monthly

direct, diffuse and global solar radiation from sunshine duration measurements, Solar Energy, 1984, 32, 523-535.

7. Catsoulis, B. D., A method for estimating monthly global solar radiation, Solar Energy, 1984, 33, 403407.

8. Dogniaux, R. and Lemoine, M., Classification of radiation sites in terms of different indices of atmospheric transparency, Solar Energy Research and Development in the European Community, Series F, Vol. 2, ed. D. Reidel, Dordrecht, the Netherlands, 1983.

9. Louche, A., Notton, G., Poggi, P. and Simommot, G., Correlation for direct normal and global horizontal irradiation on a French Mediterranean site, Solar Energy, 1991, 46, 261-266.

10. Hawas, M. M. and Muner, T., Correlation between global radiation and sunshine data for India, Solar Energy, 1983, 30, 28~290.

11. Luhanga, P. V. C. and Andringa, J., Characteristics of solar radiation at Sebele, Gaborone, Botswana, Solar Energy, 1990, 44, 77-81.

12. Ma, C. C. Y. and lqbal, M., Statistical comparison of solar radiation correlations--monthly average global and diffuse radiation on horizontal surfaces, Solar Energy, 1984, 33, 143-148.

13. Davies, J. A., McKay, D. C., Luciani, M. and Abdel-Wahab, M., Validation of models for

362 Data Bank

estimating solar radiation on horizontal surfaces, International Energy Agency, Vol. 1, Atmo- spheric Environment Service, Downsview, Ontario, Canada, 1988.

14. Gopinathan, K. K., A general formula for computing the coefficients of the correlations con- necting global solar radiation to sunshine duration, Solar Energy, 1988, 41,499-502.

15. Soler, A., Statistical comparison for 77 European stations of 7 sunshine-based models, Solar Energy, 1990, 45, 365 370.

16. Hay, J. E., Calculation of monthly mean solar radiation for horizontal and inclined surfaces, Solar Energy, 1979, 23, 301-307.

17. Iqbal, M., A study of Canadian diffuse and total solar radiation data, Solar Energy, 1979, 22, 81-86.

18. Iqbal, M., Correlation of average diffuse and beam radiation with hours of bright sunshine, Solar Energy, 1979, 23, 169-173.

19. Rietveld, M. R., A new method for estimating the regression coefficients in the formula relating solar radiation to sunshine, Agric. Meteorol., 1978, 19, 243-252.

20. Page, J. K., The estimation of monthly mean values of daily total short wave radiation on vertical and inclined surfaces from sunshine records for latitudes 40°N-40°S, Proceedings of U.N. Conference on New Sources of Energy, Paper No. $98, Vol. 4, 1961, 378 390.

21. Halouani, N., Nguyen, C. T. and Vo-Ngoc, D., Calculation of monthly average global solar radiation on horizontal surfaces using daily hours of bright sunshine, Solar Energy, 1993, 50, 247-258.

22. A1 Mahdi, N., A1 Baharna, N. S. and Zaki, F. F., Assessment of solar radiationmodels for the Gulf Arabian countries, Renewable Energy, 1992, 2, 65-71.

23. Jackson, E. A. and Akuffo, F. O., Correlations between monthly average daily global irradiation and relative duration of sunshine at Kumasi, Energy Convers. Mgmt., 1992, 33, 13-22.

24. Canada, J., Solar radiation prediction from sunshine in eastern Spain, Renewable Energy, 1992, 2, 305-310.

25. Binzhong, W., Fugao, Zh. and Lixian, L., The solar energy sources and calculations of China, Acta Energiae Solaris Sinica, 1980, 1, 1-9.

26. Lin, W., A general correlation for estimating the monthly average dialy direct radiation incident on a horizontal surface in Yunnan Province, China, Solar Energy, 1988, 41, 1-3.

27. Lin, W., General correlations for estimating the monthly total and direct radiation incident on horizontal surfaces in Yunnan, China, Int. J. Energy Research, 1989, 13, 589-593.

28. Prescott, J. A., Evaporation from a water surface in relation to solar radiation, Trans. R. Soc. S. Aust., 1940, 64, 114-118.

29. Iqbal, M., An Introduction to Solar Radiation, Academic Press, Toronto, Canada, 1983. 30. Duffle, J. A. and Beckman, W. A., Solar Engineerin 9 of Thermal Processes, (2rid Edition), John

Wiley and Sons, Inc., New York, USA, 1991. 31. State Meteorology Bureau of China, Solar Radiation Data of China (1961-1977), Weather Pub-

lishing House, Beijing, China, 1980. 32. Weather Service of Yunnan Province, Ground Climatic Data of 30 Years in Yunnan Province,

Kunming, China, 1982.