International Journal of Scientific & Engineering Research, Volume 5, Issue 2, February-2014 161

ISSN 2229-5518

**Abstract – **An attempt has been made to evaluate the daily average clearness index (H g /H 0 ) and cloudiness index (H d /H g ) and to find the relation between them for three tropical locations in South India (Chennai, Trivandrum and Visakapatnam). Long range 15 years (1993 – 2007) measured data of daily average global and diffuse solar radiation have been utilized for this study. Two simple mathematical models have been proposed for each location for estimating H d /H g in terms of H g /H 0 and found its validity for the prediction of diffuse radiation.

The availability of solar radiation is indispensable to harness solar energy for different applications. Design of any solar energy system is influenced by the daily average global and diffuse solar radiation on a horizontal surface. Extensive solar radiation measuring devices are installed only in selected locations due to cost**, **maintenance and calibration requirements of the devices. Researchers have made sincere efforts to develop empirical models by using measured radiation to calculate global and diffuse solar radiation by incorporating various climatic parameters where measured data are not available. Angstrom [1] and Prescott [2] have proposed a correlation to estimate the monthly average daily global solar radiation on a horizontal surface using sunshine duration as

𝐻 𝑆

= 𝑎 + 𝑏

Babatunde and Aro [3] have studied the characteristics of clearness and cloudiness index by expressing the cloudiness index in terms of clearness index. It has been found that they are opposite in characteristics and higher the clearness index more the transparency of the atmosphere and higher the cloudiness index more the turbidity or cloudiness of the atmosphere. Correlations have been developed for the estimation of monthly average daily diffuse solar radiation as a function of sunshine hours and clearness index at Karachi, Pakistan by Firoz Ahmad *et al*., [4]. It has been found that the established relations, Iqbal and Stanhill overestimate and Liu and Jordan underestimate the radiation value. Empirical correlations for beam and diffuse fraction of the global radiation to clearness index have been developed by Lanetz and Kudish [5] for semi-arid southern region of Israel. It has been concluded that the approach is

intended to correct the multiplicity of possible cloud conditions

𝐻0

𝑆0

Followed by them, empirical correlations have been developed by the researchers by incorporating different meteorological parameters viz., latitude, ambient temperature, humidity, the elevation, water vapor pressure etc.

R. K. Aruna is currently pursuing Ph.D in Physics in Department of

Physics, Karpagam University, Coimbatore – 641021, India, PH- +91-422-

2611146. E-mail: rkaruna691@yahoo.com

B. Janarthanan is currently working as an Assistant Professor in Department of Physics, Karpagam University, Coimbatore – 641021, India, PH-+91-422-2611146. E-mail: bjanarthanan2002@yahoo.co.in

that can give the same value for the cloudiness index. Coppolino

[6] has developed a new correlation between clearness index and relative sunshine for computing the monthly mean daily global radiation at Italian locations and found that it is suitable to predict monthly mean global solar radiation with a high degree of accuracy.

Elagib *et al*., [7] have expressed the clearness index of

16 meteorological stations in Sudan in terms of the fraction of bright sunshine duration. The established relationships are statistically significant at 99.9% accuracy level. Udo [8] has

characterized the sky conditions at Illorin, Nigeria by

IJSER © 2014 http://www.ijser.org

International Journal of Scientific & Engineering Research, Volume 5, Issue 2, February-2014 162

ISSN 2229-5518

incorporating clearness index and relative sunshine duration and revealed that results were comparable with frequency distribution of global solar radiation at Ibdan and Kumasi. Paliatsos *et al*., [9] have correlated experimental values with modeled values of global and diffuse clearness index in Athens, Greece. The modeled linear regression has shown better fit with

the experimental data. Further an attempt has been made by

Trivandrum and Visakapatnam for the period of 15 years are collected from Indian meteorological Department, Pune. These data are used to find daily average clearness and cloudiness index for the corresponding location. The daily amount of extra- terrestrial radiation for the locations have been found by using the expression

𝐻0 =

Saima Munawwar and Tariq Muneer [10] to explore the

24×3600 𝐼

�1 + 0.033 𝐶𝑜𝑠 �360 𝑛�� × �𝐶𝑜𝑠 𝜙 𝐶𝑜𝑠 𝛿 𝑆𝑖𝑛 𝜔 +

prospects of using sunshine duration and cloud cover in the

𝜋

2𝜋𝜔𝑠

𝑠𝑐

365 𝑠

estimation of daily diffuse irradiation besides the conventional

use of global irradiation. It has been shown that estimation of daily diffuse irradiation by incorporating effective variables along with global radiation for local and independent sites. Koray Ulgan and Arif Hepbasli [11] have developed empirical correlation to establish relationship between cloudiness index, clearness index and sunshine fraction for three big cities in Turkey. The new model for cloudiness index and diffuse coefficient as a function of clearness index and sunshine fraction has shown better result than other available models.

Moreover Marco Bortolini *et al*., [12] have proposed a multi-locations model to estimate the horizontal diffuse component of solar radiation by using European geographical area comprising of 44 weather stations in all countries. It has proved the effectiveness of multi-location approach to estimate solar radiation components instead of several single location models.

In the present study, long range 15 years measured data of dail y average global and diffuse solar radiation of three tropical l ocati ons in South India (Chennai, Tri vandrum and Visakapatnam) have been used to find the relationship between clearness and cloudiness index. Moreover two sets of equation for each l ocation i.e., cloudiness index in terms of cl earness index (linear and pol ynomial) have been devel oped. The equations have been validated with measured data of global and diffuse solar radiation to predict the best fit with least error (linear or pol ynomial).

Measured data of daily average global and diffuse solar radiation of three South Indian locations viz., Chennai,

𝑆𝑖𝑛 𝜙 𝑆𝑖𝑛 𝛿� (1)

360

Where, Isc - solar constant

n - day of the year

φ - latitude of the location

δ - solar declination

ωs - hour angle

The latitude and longitude of the locations have been presented in Table . 1.

Location | Latitude | Longitude |

Chennai | 13°N | 80°E |

Trivandrum | 8°28’N | 76°57’E |

Visakapatnam | 17°N | 83°E |

For the three locations, 15 year data of daily average global and diffuse radiation has been averaged to find the daily average global and diffuse radiation for all the days in the year. Daily extra-terrestrial radiation for the three locations (Chennai, Visakapatnam and Trivandrum) has been evaluated by using the Eq. (1) and it has been used to find the daily average clearness index for all the days in the year. The daily average cloudiness index is evaluated by utilizing the average global and diffuse radiation.

The daily average clearness and cloudiness index for the three locations have been plotted with respect to the day of

the year and depicted in Figs. 1-12.

IJSER © 2014 http://www.ijser.org

International Journal of Scientific & Engineering Research, Volume 5, Issue 2, February-2014 163

ISSN 2229-5518

Fig. 1 Variation of Clearness and Cloudiness index with respect to day of the year

Fig. 4 Variation of Clearness and Cloudiness index with respect to day of the year

Fig. 2 Variation of Clearness and Cloudiness index with respect to day of the year

Fig. 5 Variation of Clearness and Cloudiness index with respect to day of the year

Fig. 3 Variation of Clearness and Cloudiness index with respect to day of the year

Fig. 6 Variation of Clearness and Cloudiness index with respect to day of the year

IJSER © 2014 http://www.ijser.org

International Journal of Scientific & Engineering Research, Volume 5, Issue 2, February-2014 164

ISSN 2229-5518

Fig. 10 Variation of Clearness and Cloudiness index

Fig. 7 Variation of Clearness and Cloudiness index

with respect to day of the year

with respect to day of the year

Fig. 8 Variation of Clearness and Cloudiness index with respect to day of the year

Fig. 11 Variation of Clearness and Cloudiness index with respect to day of the year

Fig. 12 Variation of Clearness and Cloudiness index

Fig. 9 Variation of Clearness and Cloudiness index

with respect to day of the year

with respect to day of the year

IJSER © 2014 http://www.ijser.org

International Journal of Scientific & Engineering Research, Volume 5, Issue 2, February-2014 164

ISSN 2229-5518

Figs. 1-3 represent the variation of clearness and cloudiness

index during the month from January to March for Chennai, Trivandrum and Visakapatnam. From the figures it is understood that the clearness index for the locations is higher than the cloudiness index due to the absence of cloud or little and the atmosphere is almost clean. Figs. 4-6 represents the clearness and cloudiness index of the locations during the month from April to June. For Chennai (Fig. 4), it is seen that in April and May the clearness index exceeds the cloudiness index due to the clear sky. From Fig. 5 for Trivandrum, the clearness and cloudiness index in the month of April and May have comparable values due to the turbidity in the atmosphere. In Visakapatnam, the clearness index is higher than the cloudiness index in the month of April and May due to clear sunny days. Figs. 7-12 represents the variation of both the index during the month from July to December. It is clear that for all the three locations, the cloudiness index is almost higher than the clearness index. This is due to the fact that the atmosphere is occupied by the sufficient amount of clouds and dust. Hence the variations are due to the atmospheric conditions as mentioned by Babutunde and Aro [3].

With these comparisons, it is concluded that the two ratios are

antiphase with each other throughout the year for the considered

Though the ratios are not linearly related, it has shown a

significant agreement of the relations given by Eq. 2. It has been found that the sum of Hd /Hg and Hg /H0 for the three locations is equal or approximately equal to unity during most of the days in the year. The validation of the Eq. 2 can be established inspite of slight differences in few days of the year. Hence it can be found that, the diffuse radiation ratio can be derived in terms of clearness index for all the three locations as

Hd /Hg = 1 - Hg /H0

(3)

From Eq.3, it is clear that the maximum value of cloudiness index is 1 if the clearness index Hg /H0 is 0. This means that the atmosphere is not clear and solar radiation entering the atmosphere gets scattered due to dust particles, clouds and turbidity of the atmosphere before reaching the ground surface of the earth. In the other way, it is also seen that the maximum value of clearness index is 1 leading to the absence of diffuse radiation. The atmosphere is clear and clean without dust particles and clouds providing the clear path way for solar radiation to reach the surface of the earth. Thus the ratio Hd /Hg can be expressed in terms of Hg/H0.

locations. It is also confirmed that the clearness index is higher in clear sunny days as the cloudiness index has low value and vice- versa in cloudy days.

The graph of daily average Hd /Hg against the corresponding values of Hg /H0 for the three locations has been plotted and shown in the Figs. 13-15 by using the data from 1993-2007. Linear and polynomial regressions of Hd /Hg on Hg/H0 have been found and presented. The linear and polynomial equations for Hd /Hg for the

three locations have been used to find the values of cloudiness

index for all the days in the year. Graphs have been drawn for measured and calculated cloudiness index by using the linear and polynomial equations for all the days in a year and depicted in Figs.

16-18.

Results have shown that, both the ratios lead to a simple mathematical relation

Hd /Hg + Hg /H0 = 1

(2)

Fig. 13 Variation of Hd /Hg with respect to Hg/H0 for Chennai

IJSER © 2014 http://www.ijser.org

International Journal of Scientific & Engineering Research, Volume 5, Issue 2, February-2014 165

ISSN 2229-5518

0.9 __ __

0.7

Hd/Hg (Measured) Hd/Hg (Linear) Hd/Hg (Polynomial)

0.5

0.3

0.1

0 50 100 150 200 250 300 350

Fig. 14 Variation of Hd /Hg with respect to Hg/H0 for

Trivandrum

Fig. 17 Variation of cloudiness index in Trivandrum

0.9

Hd/Hg (Measured) Hd/Hg (Linear)

0.7 __ __ Hd/Hg (Polynomial)

0.5

0.3

0.1

0 50 100 150 200 250 300 350

Fig. 15 Variation of Hd /Hg with respect to Hg/H0 for

Visakapatnam

0.9

Fig. 18 Variation of cloudiness index in Visakapatnam

The linear and polynomial equations derived for the cloudiness index in terms of clearness index for the three locations and are For Chennai

0.7

0.5

0.3

0.1

Hd/Hg (Measured)

Hd/Hg (Linear) Hd/Hg (Polynomial)

Linear

Hd /Hg = -0.202 Hg/H0 + 0.405

Polynomial

Hd /Hg = -0.481 (Hg/H0 )2 + 0.223 (Hg/H0 ) + 0.314

For Trivandrum

Linear

Hd /Hg = -0.760 Hg/H0 + 0.824

Polynomial

0 50 100 150 200 250 300 350

Fig. 16 Variation of cloudiness index in Chennai

Hd /Hg = -2.801 (Hg/H0 )2 + 1.920 (Hg/H0 ) + 0.196

For Visakapatnam

Linear

Hd /Hg = -0.826 Hg /H0 + 0.710

Polynomial

IJSER © 2014 http://www.ijser.org

International Journal of Scientific & Engineering Research, Volume 5, Issue 2, February-2014 166

ISSN 2229-5518

Hd /Hg = 2.097 (Hg/H0 )2 – 2.582 (Hg /H0 ) + 1.061

Comparisons between measured and calculated values of cloudiness index in terms of clearness index have been made for the three locations viz., Chennai, Trivandrum and Visakapatnam by finding the percentage average standard deviation between them for both linear and polynomial equations. From the results it has been found that the percentage average standard deviation for both the linear and polynomial equations between the measure and calculated values for the three locations is less than 10% on average. Results have been presented in Table. 2

Table. 2

Location | Linear Average Standard Deviation (%) | Polynomial Average Standard deviation (%) |

Chennai | 9.15 | 7.44 |

Trivandrum | 6.71 | 5.59 |

Visakapatnam | 10.39 | 8.69 |

Thus the percentage deviation of the calculated values from the measured ones made an optimistic hope to use the equations when measured radiation are not available in that locations and in other places having similar climatic conditions.

The linear and polynomial equations for cloudiness index in terms of clearness index for the three locations viz., Chennai, Trivandrum and Visakapatnam are found to be easy and reliable to predict when diffuse radiations are not available in the locations. Moreover the equations can also be used for the locations having similar climatic conditions with least error. The two ratios clearness and cloudiness index can be used to identify the different atmospheric conditions i.e., the cleanliness of the atmosphere in summer gives higher value of clearness index than the cloudiness index and in winter due to clouds and dust particles, the cloudiness index has higher value when compared to the clearness index. The two parameters are inversely proportional in all the locations and thus diffuse radiation can be estimated when measured global radiation alone is available.

[1] A. Angstrom, “Solar and Terrestrial Radiation,” Quar-terly

Journal of the Royal Meteorological Society, Vol. 50, no. 210, pp.

121-125, 1924.

[2] J. A. Prescott, “Evaporation from a water surface in relation to solar radiation”, Trans Roy Soc Aust, Vol. 64, pp. 114-48, 1940. [3] E.B. Babatunde and T.O. Aro, “Relationship between clearness index and cloudiness index at a tropical station (Ilorin, Nigeria)”, Renewable Energy, Vol. 6, no. 7, pp. 801-805, October

1995.

[4] Firoz Ahmad, S.M. Aqil Burney and S.A. Husain, “Diffuse solar radiation estimates from sunshine hours and clearness index for Karachi, Pakistan”, Energy Conversion and Management, Vol.

30, no. 4, pp. 439–447, 1990.

[5] A. Ianetz and A.I. Kudish, “Correlations between values of daily beam, diffuse and global radiation for Beer Sheva, Israel”, Energy, Vol. 17, no. 6, pp.523–533, June 1992.

[6] S. Coppolino, “A new correlation between clearness index and relative sunshine”, Renewable Energy, Vol. 4, no. 4, pp. 417–

423, June 1994.

[7] N.a. Elagib, S.H. Alvi and M.G. Mansell, “Correlationships between clearness index and relative sunshine duration for Sudan”, Renewable Energy, Vol. 17, no. 4, pp. 473–498, August 1999.

[8] S.O. Udo, “Sky conditions at Ilorin as characterized by clearness index and relative sunshine”, Solar Energy, Vol. 69, no.

1, pp. 45–53, 2000.

[9] A.G. Paliatsos, H.D. Kambezidis and A. Antoniou, “Diffuse solar irradiation at a location in the Balkan Peninsula”, Renewable Energy, Vol. 28, no. 13, pp. 2147–2156, October 2003.

[10] Saima Munawwar and Tariq Muneer, “Statistical approach to the proposition and validation of daily diffuse irradiation models”, Applied Energy, Vol. 84, no. 4, pp. 455–475, April 2007. [11] Koray Ulgen and Arif Hepbasli, “Diffuse solar radiation estimation models for Turkey’s big cities”, Energy Conversion and Management, Vol. 50, no. 1, pp. 149–156, January 2009.

[12] Marco Bortolini, Mauro Gamberi, Alessandro Graziani, Riccardo Manzini and Cristina Mora, “Multi-location model for the estimation of the horizontal daily diffuse fraction of solar radiation in Europe”, Energy Conversion and Management, Vol. 67, pp.

208–216, March 2013.

IJSER © 2014 http://www.ijser.org