Correlation between daily diffuse and global radiation for India

Energy Cora~era.Mgmt Vol. 24, No. 2, lap. 151-154, 1984

0196-8904/84$3.00+0.00 Copyright C) 1984PergamonPress Ltd

Printed in Great Britain.All rights rm~ervcd

CORRELATION BETWEEN DAILY DIFFUSE AND GLOBAL RADIATION FOR INDIA T. ~ E R mul M. M. HAWAS Mechanical Engineering Department, Faculty of Engineering, University of Garyounis, Benghazi, Libya (Received 7 March 1983)

Abstract--Solar radiation characteristics have been studied in various countries and many correlations developed. In the absence of such studies, the same correlations are applied in other countries. Since radiation records are now available in most developingcountries, it is possible to perform similar studies for these regions. The purpose of this study is to use daily global and diffuseradiation data for 13 stations in India to establish a correlation between the daily diffuse ratio and the clearness index. Plotting individual values of the daily diffuse ratio against the clearness index for all Indian Stations showed the existence of a definite relationship between them, confirming the validity of Liu and Jordan approach. It was found that a cubic equation provides a fairly accurate fit for this relationship. Comparison with other studies showed that no singlecorrelation is applicable to all regions, and that each region possesses its own characteristics. Although the stations considered had diverse latitude, climate and geographical variations, the study showed that none had any effect on the correlation. Solar energy

Solarradiation

Diffuseradiation

INTRODUCTION Solar radiation characteristics, based on measurements, have been studied in developed countries, and various correlations have been evolved. In the absence of such studies, these correlations are usually employed in other countries under the assumption that the radiation characteristics are the same. Solar radiation records are now available for a fairly large number of stations in most developing countries. Therefore, it is now possible and required to perform similar studies for these regions and to check the applicability of the forementioned correlations. One of the famous correlations in this field is that between daily diffuse and global radiation, originated by Liu and Jordan [1]. This type of correlation finds its use mainly in the estimation of the daily diffuse component from measured global radiation for simulation studies. In every country the number of stations recording global radiation exceeds those recording the diffuse component. The purpose of this study is to use daily global and diffuse radiation data available for 13 stations in India over a period of 3 years to establish a correlation between the daily diffuse and global radiation for this region.

PAST WORK

The idea of developing a relationship between diffuse and global radiation applicable for all degrees of cloud cover is due to the pioneering work of Liu and Jordan [1]. Their model relates the ratio of daily E.C.M. 24,'2--D

Daily insolation characteristics

diffuse to global radiation (herein called diffuse ratio) to the ratio of daily global to extraterrestrial radiation (clearness index). They suggested that their results could be applied for stations with similar dust content and surface albedo as the stations considered in their study. Choudhary [2] used rather limited (3 months) data for New Delhi and found a higher diffuse ratio, compared to Liu and Jordan's model. He attributed his differences to higher dust content over New Delhi and his small sample of data. Stanhill [3] studied the relationship using 3 year data for Gilat, a semi-arid location. He found a departure of the diffuse ratio from that suggested by Liu and Jordan, especially for lower values of clearness index. He attributed his and Choudhary's results to higher dust content of the stations situated in semi-arid regions. Tuller [4] used a 1 year record for four Canadian stations. He found an individual trend for each location. This, he attributed to a latitude effect. He also found that the regressed line for all combined data has a higher diffuse ratio than Liu and Jordan's and closer to Choudhary's results. Pereira and Rabl [5] used pyroheliometer data for five stations in the U.S.A. and found their results closer to those of Choudhary and Stanhill than the results of Liu and Jordan. They concluded that this discrepancy of Liu and Jordan is due to reliance on uncorrected measurements of diffuse radiation with a pyranometer plus shade ring. A summary of the work of the above mentioned researchers is presented in Fig. I. It can be seen that there is no single correlation which is applicable for all regions; each region has its own correlation. In the 151

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RESULTS AND DISCUSSION

present work, such a correlation is developed for India.

Individual values of D/H against Kr for the 13 stations in India, for all days considered, are shown in Fig. 2. It is quite clear that there exists a definite relationship between D/H and Kr. This confirms the validity of the Liu and Jordan's approach. Equations of various order have been tried to correlate D/H against Kr and it was found that a cubic equation provides a fairly accurate fit. The equation thus obtained is

METHODOLOGY Recently, 3 years of hourly, daily global and diffuse radiation data have been published by the India meteorological department for 13 stations in India [6]. These stations are listed in Table 1. They cover a wide range of latitude, altitude, climate and geographical conditions. We are analysing the daily global and diffuse radiation data of the forementioned stations in order to develop a correlation between the diffuse ratio and the clearness index. We have processed the data such that days for which the value of diffuse radiation (D) exceeds global radiation (H) and the days with either diffuse or global radiation data missing are not considered. For each city, the extraterrestrial horizontal radiation (He), dearness index (Kr = H/Ho) and diffuse ratio (D/H) were computed on a daily basis. The results were then fitted in a cubic equation and the corresponding R2-value calculated. The same procedure was adopted for all India as one region.

D/H = 0.98 (Kr< 0.2) D/H = 1.024 + 0.47Kr - 3.622K2r + 2K3 (0.2 ~ 0.77). The R2-value for this fit is found to be equal to 0.89. The effect of season on the correlation has been investigated and no such effect is noticed. Figure 3 shows the correlation for India developed in the present study in comparison with correlations developed for other countries. It is clear that India has its own correlation which is different than those

Table 1. Indianstationsconsideredin the study (years of observation: 1971, 1974, 1975) Latitude Longitude Altitude Station (deg) (rain) (deg) (rain) (m) Re-value Ahmedabad Bhavnagar Bombay Calcutta Goa Jodhpur Madras Nagpur New Delhi Poona Shillong Trivandrum Visakhapatnam

23 21 19 22 15 26 13 21 28 18 25 08 17

04 45 07 32 29 18 00 06 35 32 34 29 43

72 72 72 88 73 73 80 79 77 73 91 76 83

38 11 51 20 49 01 11 03 12 51 53 57 14

55 5 14 6 52 224 16 310 216 559 1600 64 3

0.945 0.949 0.893 0.731 0.925 0.898 0.949 0.935 0.910 0.912 0.892 0.938 0.923

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India far from the coast• Tuller [4] in his study based upon data of four Canadian stations reported the presence of a latitude effect on the said correlation. It is obvious from Fig. 4 that this effect is absent in the Indian region. Also, no effect of climate and geographical conditions is noticed. Figure 5 shows the individual points of D/H vs Kr for three stations. The order of scatter is the same for all stations. It is also noticeable that linear regression is not suitable• The R2-values for all individual stations based on the cubic equation fit are listed in Table 1. Choudhary [2] studied the correlation between the diffuse ratio and the clearness index for New Dehli. He used data for only 3 months. Figure 6 shows Choudhary's results in comparison with our findings for New Delhi, based on data for three complete years. The small discrepancy between the two results may be due to the use of limited data by Choudhary.

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CONCLUSIONS

A correlation between the diffuse ratio and the clearness index for India has been developed. This correlation is based on 3 years data for 13 stations. Comparison of the correlation obtained for India with work performed for other regions showed that. no single correlation is applicable to all regions; each region has its own characteristics. Neither latitude nor seasonal effects were noticed. REFERENCES l. B. Liu and R. C. Jordan, Solar Energy 4, l (1960). 2. N. K. O. Choudhary, Solar Energy 7, 44 (1963). 3. G. Stanhill, Solar Energy 10, 96 (1966).

4. S. E. Tuller, Solar Energy 18, 259 0976). 5. M. C. Pereira and A. Rabl, Solar Energy 22, 155 0979). 6. Radiation Data 1971, 74, 75, Meteorological Ofl~c¢, Pune, India 0980). Tr lvandrum

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