Estimation of Solar Radiation at Ibadan, Nigeria

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1 Journal of Emerging Trends in Engineering and Applied Sciences (JETEAS) 2 (4): Scholarlink Research Institute Journals, 2011 (ISSN: ) jeteas.scholarlinkresearch.org Journal of Emerging Trends in Engineering and Applied Sciences (JETEAS) 2 (4): (ISSN: ) Estimation of Solar Radiation at Ibadan, Nigeria 1 Sanusi Yekinni K and 2 Abisoye Segun G 1 Department of Applied Physics, Ladoke Akintola University of Technology P.M.B 4000, Ogbomoso, Oyo State, Nigeria. 2 Physical Science Department, Yaba College of Technology P.M.B 2011, Sabo-Yaba, Lagos, Nigeria Corresponding Author: Sanusi Yekinni K Abstract This study presents and evaluates the behaviour of three empirical models based on the difference between maximum and minimum temperatures at Ibadan (7 o 22, 3 o 53 E). This was done by using monthly data on solar radiation and minimum and maximum temperature for a period of 6 years, ( ). The corresponding monthly value of extraterrestrial solar radiation (R a ) was calculated for each data. Forecasting performance parameters such as coefficient of determination (r 2 ), root mean square error (RMSE), mean bias error (MBE) and mean absolute percentage error (MPE) are presented as analyzed for the models. The model with linear regression has the highest r 2 value of 0.72 and lowest RMSE, MBE, and MPE values of 1.59 MJm -2 day -1, 0.82 MJm -2 day -1 and -7.36% respectively. The best performance for the present data set was found at model with linear regression, and followed by model with power regression and original model. The present result suggested the model with linear regression reasonably predictable global solar radiation and the expected solar radiation behaviour in the area of study. Keywords: solar energy, solar radiation, temperature, empirical models, extraterrestrial radiation I TRODUCTIO Solar radiation at the earth s surface is essential for the development and utilization of solar energy. It is needed for designing collectors for solar heaters and other photovoltaic equipment that depend on solar energy. Incoming solar radiation has a significant role in hydrological and crop growth modelling. For instance, it is a key input for estimating potential evapotranspiration which play a major role in the design of water supply storage reservoirs and irrigation systems. In spite of the importance of global solar radiation data, its measurements are not frequently available especially in developing countries. Akpabio et al. (2004) observed that the meteorological stations measuring solar radiation data in the developing countries are few. This situation can be solved by using empirical models, which estimate global solar radiation based on the relationships with frequently measured climatic variables. Many studies have been calculated to estimate incoming solar radiation in Nigeria (Bamiro, 1983; Akpabio et al., 2004;). Angstom (1924) was the first scientist known to suggest a simple linear relationship to estimate global solar radiation. Later on Prescott (1940) put the correlation in a convenient form as 701 where Rs the global solar radiation (MJm -2 day -1 ), S the real sunshine (h), So the day s length (h), Ra the extraterrestrial duration (MJm-2day-1), a and b are coefficients of Angstrom s formula. Different models use different approaches for estimating the coefficient a and b (Rietveld, 1978; Neuwirth, 1980). and Samani (1982) correlated solar radiation (Rs) with temperature and extraterrestrial radiation. Allen (1997), calculated mean global solar radiation following the work of and Samani (1982), as where T max and T min are the mean daily maximum and the minimum air temperature ( o C) respectively, and k r is the regional coefficient = 0.16 for interior regions and 0.19 for coastal regions. In this work, k r = 0.16 is adopted for original -Samani model. Bamiro (1983) investigated various empirical models from the viewpoint of obtaining appropriate empirical model to determine solar radiation in Ibadan. Akpabio et al. (2004) developed a multiple linear regression model with ten variables to estimate monthly average daily global solar radiation for Onne, Nigeria. However, accurate modelling depends on the quality and quantity of the measured data used and is a better tool for estimating the global solar radiation of

2 location where measurements are not available. Therefore, the objective of the present study is to develop models using set of data obtained from IITA Ibadan, Nigeria and investigating suite of models that can be used to relate global solar radiation and temperature for the study area and other locations having similar solar characteristics. This is important for the development and the applications of solar energy technology. MATERIAL A D METHODS The data used in this study was obtained from IITA (International Institute of Tropical Agriculture) station of Ibadan, located within the rainforest climatic zone of western Nigeria. The data obtained, covered a period of 6yrs ( ). The monthly averages data processed in preparation for the models are presented in Table 1. Extraterrestrial Solar Radiation Extraterrestrial radiation is the maximum amount of solar radiation available to the earth at the top of the atmosphere. The extraterrestrial solar radiation was calculated using latitude and day of the year, and by the following equations (Duffie et al., 1994). where a and b are the empirical coefficients for model with power regression. Model Testing and Assessment The performance of the present models was assessed in term of estimation accuracy. The estimation accuracy was evaluated by calculating mean bias error (MBE), root mean square error (RMSE), and mean percentage error (MPE). The RMSE is a measure of the variation of predicted values around the measured values, while the MBE is an indication of the average deviation of the predicted values from the measured values. The MPE test gives long term performance of the examined regression equations, a positive MPE values provide the averages amount of overestimation in the calculated values, while the negative values gives underestimation. The expressions for the MBE (MJm -2 day -1 ), RMSE (MJm - 2 day -1 ), and MPE (%) are expressed as follows: where I sc is the solar constant (1367Wm -2 ), J is the Julian day number, Ø is the latitude of the location, δ is the solar declination angle given as and ω is the sunset hour angle given as In this paper, we used Microsoft Excel to calculate R a based on the Equation (3). -Samani Model We used -Samani model expressed in Equation (2) to estimate global solar radiation. Nominal value of 0.16 for k r was used in our evaluation. Model with Linear Regression Instead of using the nominal k r value of 0.16, linear regression is applied to improve model. That is, here a and b are the empirical coefficients for model with linear regression. Model with Power Regression In the present study, model taking the form of a power regression is applied to improve model performance. Namely, RESULT A D DISCUSSIO The values of the daily extraterrestrial solar radiation (R a ) on a horizontal surface calculated for a year, at latitude 07 o 22 N and longitude 03 o 53 E outside the earth s atmosphere at Ibadan, Nigeria is as shown in Figure 1. The highest extraterrestrial solar radiation value of 40.21MJm -2 day -1 was obtained on the 217 th day, while the lowest value MJm -2 day -1 was obtained on the 355 th day. Figure 2 shows that in the overall average years ( ), there were two maxima (major and minor). The major maximum occurred between February April during the dry season and the minor maximum occurred between November December. In the rainy season, we have the minima in the months July August. Figure 2 also indicates the trend of global solar radiation at Ibadan, with high values during the dry season while minimum global solar radiation during the rainy season, as a result of the rain bearing clouds pervade. The best month, March, with R s of MJm -2 day -1 contributed 9.98% and the worst month, August, with R s of 10.62MJm -2 day -1 contributed 6.27% of the annual total. The result also shows that global solar 702

3 radiation value for Ibadan is between and MJm -2 day -1. Based on the measurements of incoming solar radiation together with monthly temperature range, three empirical models were developed. All the calibrated equations are as follows. -Samani model model with linear regression model with power regression model with linear regression has the best coefficient of determination of r 2 = 0.72 followed by model with power regression r 2 = 0.70; and the lowest coefficient of determination r 2 = 0.50 is from -Samani model. Figures 3, 4, and 5 show the comparison of the estimated global solar radiation given by Equations (11), (12), and (13) and the monthly average daily global solar radiation measured for six years. Equation (12) gives the best fit to the global solar radiation data, while Equation (11) does not fit the measured data very well, with a very big overestimation. The model performance of three empirical models was compared based on MBE, RMSE, and MPE as shown in Table 2. Based on the RMSE, model with linear regression produces the best coefficient of determination, while the - Samani model gives the worst with larger value of RMSE. It was observed that the lower the RMSE, the more accurate the equation used. For MBE, the result shows that the model with linear regression is the best while the -Samani is the worst. With respect to MPE, model linear regression offers best correlation while the -Samani model gives the worst. The best performance for the present data set was found at model with linear regression (Eq. 12), and followed by model with power regression (Eq. 13). The estimation using -Samani model resulted in worst in all the criteria of MBE, RSME, and MPE. The applicability of model with linear regression approach was supported by all the criteria applied in this study. A model such as this could be used to backfill missing data when radiation data were not available but temperature data were available. This equation could also be used for global solar radiation estimation within a limited radius of where the equation was developed, assuming similar topography, elevation, and geographical features for the additional site. Table 1. The monthly average solar radiation (MJm -2 day -1 ) data for Ibadan. Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec (Obtained from IITA Ibadan, Nigeria) Table 2. Comparison of error values for the estimated monthly average global solar radiation from different models. Models Original Model with Linear Regression Model with Power Regression RMSE (MJm - 2 day -1 ) MBE (MJm - 2 day -1 ) MPE (%) Figure 1. Extraterrestrial Solar Radiation at Ibadan 703

4 Average Daily Global Solar Radiation (MJm -2 day -1 ) Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month Figure 4. Comparison of the measured and predicted values of model with linear regression Figure 2. Monthly average daily global solar radiation ( ). Figure 5. Comparison of the measured and predicted values of model with power regression Figure 3. Comparison of the measured and predicted values of -Samani Model CO CLUSIO From the monthly average solar radiation measurements, three empirical models have been developed for use in estimating global solar radiation at Ibadan, southwest, Nigeria. The first one was originally formulated by -Samani while the other two were modified by the authors to make it fit Ibadan meteorological station. The models require only the maximum and minimum temperatures. The performance of the models was evaluated and analyzed using statistical indicators that is RMSE, MBE and MPE. It was observed that the model with linear regression has the highest values of coefficient of determination (r 2 ) and the lowest values of MBE, RMSE and MPE. Hence, the model could be employed in estimating global solar radiation of location that has the geographical location information as Ibadan. 704

5 ACK OWLEDGEME TS The authors are grateful to IITA for providing all the necessary data. REFERE CES Akpabio, L.E., UDO, S.O., Etuk, S.E., Empirical correlations of global solar radiation with meteorological data for Onne, Nigeria. Turk. J. Physics 28, (2004), Allen, R.G., Self-calibrating method for estimating solar radiation from air temperature. ASCE J. Hydrol. Eng. 2, Angstrom, A., Solar and terrestrial radiation. Quart. Jour. Roy. Meteorol. Soc. 50, Bamiro, O.A., Empirical relations for the determination of solar radiation in Ibadan. Nigeria Sol. Energy 31, Duffie, J.A. and Beckman, W.A., Solar engineering of thermal processes. 2 nd Ed. John Wiley, New York., G.H., Samani, Z.A., Estimating potential evaporation. J. Irrig. Drain. Eng. 108, Neuwirth, F., The estimation of global and sky radiation in Austria. Sol. Energy 24, Prescott, J.A., Evaporation from a water surface in relation to solar radiation. Trans. R. Soc. Sci. Austrialia 64, Rietveld, M.R., A new method for estimating the regression coefficients in the formula relating solar radiation to sunshine. Agric. Meteorol. 19,

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