Solar radiation in Onitsha: A correlation with average temperature

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1 Scholarly Journals of Biotechnology Vol. 1(5), pp , December 2012 Available online at ISSN Scholarly-Journals Full Length Research Paper Solar radiation in Onitsha: A correlation with average temperature Ekpe J. Elom and Nnabuchi M. Nnamdi Department of Industrial Physics, Ebonyi State University, Abakaliki, Nigeria. Accepted 17 December, 2012 Measurement of global solar radiation and average temperature during the period of eleven years (1996 to 2006) at Onitsha was used to establish a model equation. The equations are and. The Correlation Coefficient (CC) of the model equations are and 0.017, respectively. The accuracy of the model was tested by applying the Mean Bias Error (MBE), Root Mean Square Error (RMSE) and the Mean percentage Error (MPE) statistical techniques. The results show that the developed models can be used for estimating global solar radiation in Onitsha and other locations with similar climatic characteristics. Key words: Average temperature, clearness index, global solar radiation, regression. INTRODUCTION Without the sun, the earth would be no more than a frozen rock stranded in space. The sun warms the earth and makes life possible. Its energy generates clouds, cleanses our water, produces plants, keeps animals and humans warm and drives ocean currents and thunderstorms. Despite the sun s importance, scientists have only begun to study it with high precision in recent decades (Sofia, 2008). Energy is the motive force behind the sustained technological development of any nation and Nigeria is blessed with reasonably high quantities of various energy resources. These include the non-renewable such as crude oil, natural gas, coal, uranium and the renewable such as biomass, solar, wind and hydro energy. Currently, the dominant energy source used in Nigeria is oil and its derivatives, accounting for over 85% of the total energy consumption except in the rural areas where biomass in the form of fuel, wood dominates (UNIDO, 2003). Solar radiation passing through the atmosphere to the ground surface is known to be depleted through scattering, reflection and absorption by the atmospheric constituents like air molecules, aerosols, water vapour, ozone and the clouds. The reflection of solar radiation is mainly by clouds and this plays an overriding part in reducing the energy density of solar radiation reaching *Corresponding author. ibehgabriel@ymail.com the surface of the earth (Exeil, 2000). The radiation arriving on the ground directly in line with the solar disks is called direct or beam radiation. A portion of the scattered and reflected radiation goes back to space and a portion reaches the ground from the sky hemisphere as diffuse radiation. Practically, solar radiation data are easily obtained using the relevant equipment. Pyrheliometer and pyranometer can be readily used to obtain the diffused component of the radiation and the global solar radiation respectively. Weather stations have been used mostly for this purpose. In an effort to generate radiation data, researchers had extrapolated values from one location for application in a different location. Hence, solar radiation prediction from estimation models has been widely utilized globally to generate solar radiation database from various locations of the world. These meteorological variables are easy to measure and have been readily employed for the estimation of H by means of simple and multiple regression analyses. The development of the solar radiation database for various Nigeria locations has been an on-going task for researchers in the field for many years now. With the few meteorological stations, the option of using estimating models has been widely adopted in Nigeria for predicting solar radiation at specific location and at a regional scale (Agboet et al., 2007). The amount of total (global) solar radiation, H, eventually obtained on the ground surface is found to be a fraction of the extra-terrestrial radiation,

2 Scholarly J. Biotechnol. 102 Table 1. Monthly mean values of climatic parameters for Onitsha 1996 to S/N MONTH Tav ( C) R (%) S/N C/c HMJ/M 2 /day 1 January February March April May June July August September October November December Total T av = Monthly average daily temperature; R (%) = Relative humidity at 9 h; H = Value of measured average daily radiation on the horizontal surface; C /c = The cloudiness index; S /N = The monthly relative sunshine duration. at the top of the atmosphere of the site. Extra-terrestrial radiation is the maximum amount of solar radiation eventually available at the ground surface after scattering, reflection and absorption in the atmosphere. The ratio is used to define the coefficient of transmission or the transmittance of the atmosphere (Babatunde et al., 1990). This paper aims at proposing models using average temperature data to estimate the solar radiation of Onitsha in Nigeria. MATERIALS AND METHODS The monthly mean daily data for average temperature for Onitsha were obtained from the Archives of Nigeria Meteorological Agency, Oshodi, Lagos. The monthly mean global solar radiations were obtained from renewable energy for rural industrialization and development in Nigeria. The data obtained covered a period of eleven years (1996 to 2006) for Onitsha (Latitude 5 45 N longitude 6 45 E and altitude 56 m above sea level. Data analysis The monthly mean daily data processed in preparation for the correlation are presented in table 1. To develop the model, the global solar radiation data measured in were converted to using conversion factor of 3.6 as proposed by Iqbal (1983). The first correlation proposed for estimating the monthly mean daily global solar radiation on a horizontal surface using the sunshine duration data is according to Angstrom (1924) and Prescott (1940) have put the Austrom correlation in a more convenient form as: Where a and b are regression constants, measured monthly mean daily global radiation, monthly mean daily bright sun shine hours, (1) is the is the is the maximum possible monthly mean daily sunshine hours or the day length, is the fraction of sunshine hours, is the monthly mean extra-terrestrial solar radiation on horizontal surface, given by Iqbal (1983) as outlined: Where the solar is constant, is the eccentricity correction factor, is the latitude, is the solar declination and (2) is the hour angle. The expression for,, and are given by Iqbal (1983): (3) (4)

3 Ekpe and Nnamdi 103 At this point, it is worthy to note that (5) (6) is the day number ranging from on 1 st January to on 31 st December. To analyze these data further, the first and second order regressions of normal equations were employed as written: Equations 13 and 14 will be used to evaluate the regression constants a and b. In second order regression analysis, Equation 8 is multiplied by, and successively and summed to obtain Equations 15, 16 and 17 as outlined: (15) (16) (7) Where and is as earlier explained, stands for and it is a dependent variable and (8) is the independent variable which can replace any of the meteorological data such as average temperature and relatively humidity etc. Equations 7 and 8 are equations of least square line and least square parabola or first and second order regression respectively (Murray, 1961). To execute the regression analysis of the first order, both sides of Equation 7 have to be multiplied by 1 and successively and summing both sides to obtain: (17) In solving the problem, the aforementioned equations have to be substituted with the variable to obtain the following equations: (18) (19) In the same principle, taking the stand of our independent variable in Equations 15, 16 and 17 we arrived as follows: (9) (20) (10) If our variables like are applied as an independent variable in Equation (7), then we have: (11) (12) In the same vein, applying in Equations 9 and 10 leads to Equations 13 and 14 given as: (13) (14) (21) (22) The accuracy of the predicted values were tested by calculating the Mean Bias Error (MBE), the Root Mean Square Error (RMSE), the Mean Percentage Error (MPE) and the coefficient of correlation CC. Iqbal (1983), Almorox et al. (2005) and Chandel et al. (2005) have recommended that a zero value for MBE is ideal and a low value of RMSE is desirable. The RMSE test provides information on the short-term performance of the developed model as it allows a term-by-term comparison of the actual deviation between the predicted values and the measured values. The MPE test gives long term performance of the examined regression equations, a positive MPE values provide the average amount of overestimation in the predicted values, while the negative values gives underestimation. A low value of MPE is desirable by Akpabio et al. (2002).

4 Global Solar Radiation Temperature ( C) Temperature Scholarly J. Biotechnol. 104 Table 2. Measured and predicted solar radiation for Onitsha, 1996 to S/no Month 1 January February March April May June July August September October November December Figure 1. Monthly variation of temperature Figure 2. Monthly variation of solar radiation.

5 (MJ Global / (MJ/M M 2 /day) 2 Solar Radiation (MJ Global / (MJ/M M 2 /day) 2 Solar Radiation Global Solar Radiation Ekpe and Nnamdi Figure 2. Monthly variation of solar radiation Predicted SR for H 2 H1 Figure 3. Comparison between measured and predicted solar radiation for H Predicted SR for H 2 H1 Figure 3. Comparison between measured and predicted solar radiation for H 1.

6 (MJ/M / M 2 2 /day) Global Solar Radiation Global Solar Radiation Global solar Solar radiation Radiation Scholarly J. Biotechnol Predicted SR for H2 Predicted SR for H 2 Figure 4. Comparison between measured and predicted solar radiation for H Predicted SR for H3 Predicted SR for H 3 Figure 5. Comparison between measured and predicted solar radiation for H Predicted SR for H4 Predicted SR for H 4 Figure 6. Comparison between measured and predicted solar radiation for H 4.

7 Ekpe and Nnamdi 107 Table 3. Model equations and statistical indicators for Onitsha, 1996 to Model equations MBE RMSE MPE CC C /c = The cloudiness index RESULTS AND DISCUSSION From the scientific point of view, and looking closely at table 2, it shows that the maximum values of the monthly mean daily global solar radiation on a horizontal surface occurs in the month of November. At the tropical site, this value is within what is expected (Okogbue et al., 2005). Though the months of occurrence is not expected because of the harmattan season where aerosol mass loading greatly reduces the intensity of solar radiation (Babatunde, 2001). Hence, during the month of November, a very high daily mean sunshine hour is obtained because it has a high clearness index. It is also pertinent to note that the minimum values of the monthly mean daily global radiation on a horizontal surface occur in the month of August. In a similar way, the value is within what is expected of a tropical site (Okogbue et al., 2005). Heavy rainfalls characterize this month. It is also important to note that from the record of temperature made during the same period, August has the lowest monthly mean daily, temperature of C. A close examination of table 1 shows that the month of February has the highest temperature of C. This is because the month of occurrence is characterized by heavy sunshine. Least solar radiation is observed in Table 1 and it shows that the month of July and August has the highest cloud cover with a corresponding solar radiation of MJ/M 2 /day and MJ/M 2 /day respectively. This is expected because a heavy rainfall characterizes the months of occurrence during the period; the total solar radiation recorded is quite low because of the wet atmosphere and the presence of heavy clouds. A close examination of figure 1 shows that maximum value of temperature occurs in the month of February with a value of C, which is in good agreement with table 1, while figure 2 reveals that the month of November has the highest value of global solar radiation of MJ/M 2 /day. This is because during the month of November, a very high mean daily sunshine hour is obtained due to high clearness index. Figure 3 to 6 shows the comparison between the measured and predicted solar radiation for H 1, H 2, H 3 and H 4. From the regression analysis, the following correlation was found to be adequately fit for the radiation data presented in table 1. CONCLUSION The monthly mean daily global solar radiation and average temperature have been employed statistically to obtain the model equations such as: and. It was found that these model equations gave very good results when considering statistical indicators, that is, MBE, RMSE MPE and CC. In this work, a cross examination of table 3, shows that the model equation gives a better prediction of which indicates that 87.1% of variation in the monthly mean daily solar radiation on a horizontal surface can be explained by the model REFERENCES Agbo, SN, Ezema, FI, Ugwoke, PE (2007). Solar Radiation estimates from Relative humidity-based D-model. Nig. J. of solar Energy. 18: Akpabio, LE, Etuk, SE (2002). Relationship between solar radiation and sunshine duration for Onne Nigeria Turkiah J. Physics. 27: Angstrom, AS (1924). Solar and terrestrial radiation meteorological society. 50: Babatunde, EB (2001). Determination of total wavelength turbidity and optical depth of the harmattan dust atmosphere using total wavelength transmittance Nig. J. of physics. 13: Babatunde, EB, Aro, TO (1990). Characteristics variation of total solar radiation at Ilorin, Nigeria Nig. J. of solar energy. 9: Chandel, SS, Aggarwal, RK, Pandey, AN (2005). New correlation to estimation global solar radiation on horizontal surface using sunshine duration and temperature data for Indian site. J. Solar Engine. 127(3): Iqbal, M (1983). An Introduction to solar radiation Academy press. New York. Murray, B (1961). Correlation of solar radiation with clouds Solar Energy, 12(1): Okogbue, EC, Adedokun, JA (2005). The solar radiation at a tropical site, Ile Ife in southwestern Nigeria Conference paper 28 th Annual conference of NIP, Ile- Ife August Prescott, JA (1940). Evaporation from a water surface in relation to solar radiation Tran. R Soc. S. Austr. 64: Sofia, J (2008). The Relationship between global solar radiation and sunshine duration Renewable energy.12: UNIDO (2000). United Nations Industrial Development Organization