PROJECTING THE SOLAR RADIATION IN NASARAWA-NIGERIA USING REITVELD EQUATION

PROJECTING THE SOLAR RADIATION IN NASARAWA-NIGERIA USING REITVELD EQUATION * Benedicta C. Njoku 1, Musibau A. Adesina 2, Eshipemi W. Lukman 3 and Bankole Omojola 4 1,2,3 Mechanical Engineering Department, Federal Polytechnic Nasarawa, Nasarawa State, Nigeria. 4 Electrical/Electronics Engineering Department, Federal Polytechnic Nasarawa, Nasarawa State, Nigeria. Abstract-A model to project the solar radiation of Nasarawa (Latitude of 8 31' 45" N, Longitude of 7 43' 27" E) was developed using Reitveld equation. The parameters measured were solar radiation intensity (W/m 2 ) and hours of bright sunshine from 6. H to 18. H daily for the months of January to December, 213. Other data collected were maximum and minimum temperatures values and relative humidity of the study area on daily basis for a year. The regression constants a and b were obtained to be.28 and.49 respectively. The performance of a and b was tested using Root mean square error (RMSE), Normalized root mean square error (NRMSE) and Nash-Sutcliffe coefficient (E).The developed empirical model for determining the solar radiation for Nasarawa was * ( )+ with a coefficient of correlation of.55. The measured solar radiation (H m ) was compared to the solar radiation predicted by the model using F-LSD at p.64. The low Normalized Root Mean Square Error (NRMSE) of.9 % showed a good agreement between the measured and predicted global solar radiation. The model therefore, can also be used to predict the solar radiation of Nasarawa. Keywords- Solar Radiation, Modeling, Reitveld Equation, Clearness index and Nasarawa. I. INTRODUCTION The SUN being one of the powerful sources of energy emits this energy at a rate equivalent to the energy coming from a furnace at a temperature of about 6, K. Therefore, if we could harvest the energy coming from just 11,171 m 2 (1 hectares) of the surface of the sun, we would have enough to supply the current energy demand of the world (William and Michael 21). However, the above statement cannot be possible due to the following reasons: First, the earth is displaced from the sun, and since the sun s energy spreads out non-uniformly, not all the sun energy from an area of the sun touch an equal area on the earth. Secondly, the earth rotates about its polar axis, so that any collection device located on the earth s surface can receive the sun s radiant energy for only about one-half of each day. The third and least predictable factor is the condition of the thin shell of atmosphere that surrounds the earth s surface. At best, the earth s atmosphere accounts for another 3 percent reduction in the sun s energy. The most reliable data is that obtained from direct measurement of the quantity at the time needed, this is equally applicable to measurement of global solar radiation data of Nasarawa as well. Global solar radiation is the computed solar radiation from the extraterrestrial direct and diffuse components of solar radiation putting into consideration the sunshine duration data, temperature and humidity (Katiyar and Pandey 213). Regularly, researchers, students, solar energy designers, desire to have information data on solar irradiance of a particular location for use, but in most cases, this information is not readily available. In view of this, the need to research to have this information data is very essential. This work will expose researchers, students, designers, and so on, to the information of solar radiation of Nasarawa in Nasarawa state Nigeria. DOI:1.21884/IJMTER.218.516.D8PR3 91

There are various models for estimating solar radiation using relative sunshine durations and other meteorological data. The commonly used model which relates the global solar radiation to sunshine duration was first developed by Angstrom (Isikwue et al., 212), (Angstrom, 1924). This work is aimed at developing a Reitveld-type of empirical model for the estimation of solar radiation for Nasarawa and locations with similar weather-related conditions. Reitveld here, is chosen due to its simplicity in determining the values of constants a and b which refer to the fraction of the extraterrestrial radiation that is diffused (scattered), and fraction of the extraterrestrial radiation that is direct (beam) respectively. The determination of these constants will enable the determination of the global solar radiation for that location whose solar radiation information is required. Nasarawa is located in Nasarawa state-nigeria at latitude of 8 31' 45" N and longitude of 7 43' 27" E. The town is characterized by a tropical sub-humid climate with two distinct seasons. The wet season begins around May and ends in October and the dry season is between November and April. Most of the rain fall between May and September, with the wettest month being July and August. Here, the rain comes with thunder storms of high intensity especially at the beginning and end of the rainy season. Temperatures are generally high at day time especially between the month of March and April. (www.onlinenigeria.com 11/4/214), (www.newstrackindia.com). II. METHODS AND PROCEDURES Rietveld, (1978) examined the published values of a and b and observed that 'a' is related linearly and 'b' hyperbolically to the mean values of and suggested the following relationship to evaluate these constants (Ahmad, 1989) as thus: Where * ( )+ (1) ( ) ( ) (2) (3) ( ) (4) ( ) (5) (6) ( ) (7) ( ) (8) (NRM & E Department, 1998), (Ahmad, 1989). Where = monthly mean of the daily global radiation on a horizontal surface (MJ/m 2 ) H = extraterrestrial solar radiation on the 15th of month (MJ/m 2 ) = number of monthly mean of the daily hours of bright sunshine = the maximum daily hours of sunshine (or day length) G sc = solar constant =.82 (MJ/m 2 /min) d r = inverse relative distance earth-sun = solar declination (rad) = latitude of the place (rad) = sunset hour angle (rad) = day number from January 1st @IJMTER-218, All rights Reserved 92

= fraction of maximum possible numbers of bright sunshine hours = atmospheric transmission coefficient, commonly known as clearness index Measurement of solar radiation was taken on hourly basis from January to December 213. That of sunshine duration (n) was directly taken from the measurement of solar radiation taken for the twelve months. The estimation of monthly average of daily global solar radiation on horizontal surface was made, using the Reitveld Equation. The analysis of this equation was made using Correlation coefficient (r), significant level at 1%, and Normalized root mean square error (NRMSE). Also collected were data for daily maximum and minimum temperature values and daily average relative humidity of Nasarawa for the whole of 213. III. RESULTS AND DISCUSSION Most parameters used in this analysis are as shown in the table below: - Table 1:Summary of the measured and calculated solar radiation parameters from January to December 213 for Nasarawa Nigeria Month MEASURED PARAMETERS Total Bright (W/m 2 sunshine ) (hrs) hours (hrs) CALCULATED PARAMETERS N (hrs) (W/m 2 ) H cal (W/m 2 ) January 281.9 298 9.61 11.56.83.75 378.8 259.63 February 242.29 269 9.25 11.71.71.54 4.95 251.76 March 281.2 274 9.81 11.95.82.65 428.75 292.32 April 288.64 297 9.87 12.18.81.66 435.6 294.86 May 264.38 284 9.45 12.39.76.61 43.29 28.72 June 258.83 245 9.14 12.46.69.61 421.72 26.67 July 169.96 183 6.71 12.44.54.4 424.67 231.28 August 164.95 2 6.74 12.25.55.39 43.14 236.36 September 172.3 27 6.97 12.3.58.4 427.69 241.3 October 28.62 269 8.68 11.8.74.51 49.3 263.2 November 236.83 227 9.87 11.6.63.46 382.64 225.26 December 299.74 259 9.96 11.51.73.68 367.91 234.62 Mean 239.14 251 8.84 11.99.7.56 411.48 256.35 The following graphs were plotted from the solar parameters that were measured. @IJMTER-218, All rights Reserved 93

AVERAGE DAY LENGTH (n) RADIATION 35 3 25 2 15 1 5 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec MONTH Figure 1:Summary of the Measured Solar Radiation Parameters from January to December for Nasarawa 12 1 8 6 4 2 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec MONTH Figure. 2:Monthly Average Hours of Bright Sunshine per Day for Nasarawa Figure 1 shows the measured solar radiation for the months of January to December for Nasarawa where the highest global solar radiation value of 288.64 W/m 2 was observed in April while the lowest value of 164.95 W/m 2 was obtained in August. All or part of the following reasons are responsible for these observed values at these periods of the year: - i. The movement of the earth around the sun is such that the sun faces the Northern hemisphere in the months of April and this brings the earth closer to the sun in this period (Itodo et al 24), (Ejeh 28). ii. July to October recorded the lowest values of solar radiation in Nasarawa, the low solar radiation here is directly attributed to this season being the wettest period of the rainy season. December to June had good solar radiation distribution with April being the peak of the dry season. @IJMTER-218, All rights Reserved 94

Hm/Ho and n/n iii. Another reason can be attributed to the fact observed in the Monthly Total and Monthly Average Hours of Bright Sunshine per Day for Nasarawa in Table 1 and Figure 2 where the brightest day was in April with a day length of 9.9 hours while the cloudiest day was in August with a day length of 6.67 hours. iv. The consistency of the solar radiation across the year is also based on the monthly average range from Table 1. Radiation was mostly steady in the months of November and December where the range value was the lowest. While in the months of April and May which had high range values of 239 and 341 respectively showed that the solar radiation in these months were not steady. The high range values of solar radiation in April and May can be so because clouds had begun to form in these months and the period being the peak of dry season with high day temperatures. 3.1 Sky conditions of Nasarawa It is to be noted that the variation of cloudiness is primarily responsible for the day to day variation of the daily total radiation during the whole month (Ahmad, 1989). The average clearness index K T over the years is shown in Fig. 3. The index has a minimum value of.37 corresponding to lowest solar radiation value of 164.95 W/m 2 in the month of August, indicating the presence of thick cloud cover. In the top dry season months, April, the sky is very clear with K T of.66 which corresponds to the highest value of solar radiation recorded value of 288.64 W/m 2 which allows on the average nearly 6 percent of the extraterrestrial radiation to reach the earth's surface. 1.8.6.4.2 Figure 3:Sky condition (K T ) of Nasarawa Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec MONTH Hm/Ho n/n Figure 4: Comparison of Clearness Index to Relative Sunshine duration of Nasarawa in 213 @IJMTER-218, All rights Reserved 95

3.2 Maximum and Minimum Temperatures Table 2:Monthly Average Maximum and Minimum Temperatures ( C) for Nasarawa (213) Month Maximum Temperature (C) Minimum Temperature (C) Total Average Total Average Jan 199 35.45 531 17.12 Feb 145 37.31 698 24.93 Mar 1145 36.93 785 25.33 Apr 1118 37.27 785 26.15 May 162 34.26 788 25.42 Jun 94 31.35 72 24 Jul 979 31.59 738 23.79 Aug 924 29.79 726 23.41 Sep 929 3.96 694 23.13 Oct 988 31.86 716 23.8 Nov 138 34.6 645 21.5 Dec 119 35.78 524 16.91 The monthly average maximum and minimum temperatures of Nasarawa in 213 were presented in Table 2 and represented diagrammatically in Figure 5. From these charts, February, March and April have the higher values of average maximum temperatures of 37.31 C, 36.93 C and 37.27 C respectively. The lowest minimum monthly average temperature was recorded in November, December and January, which were respectively 21.5 C, 16.91 C and 17.12 C. The lowest minimum temperature readings here is because; in Nasarawa, harmattan is mostly from November to early February which marks the coldest period of the year. The monthly average maximum and minimum temperatures of Nasarawa in 213 were presented in Table 2 and represented diagrammatically in Figure 5. From these charts, February, March and April have the higher values of average maximum temperatures of 37.31 C, 36.93 C and 37.27 C respectively. The lowest minimum monthly average temperature was recorded in November, December and January, which were respectively 21.5 C, 16.91 C and 17.12 C. The lowest minimum temperature readings here is because; in Nasarawa, harmattan is mostly from November to early February which marks the coldest period of the year. @IJMTER-218, All rights Reserved 96

Relative Humidity (%) Temperature ( C) 4 35 3 25 2 15 1 5 Month Max. Mean Temp. (C) Min. Mean Temp. (C) Figure 5: Monthly Average Maximum and Minimum Temperatures ( C) for Nasarawa (213) 3.3 Relative humidity Table 3: Monthly Average Relative Humidity of Nasarawa (%) Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Relative humidity (%) 23.86 22.42 24.91 62.34 66.73 73.18 84.6 83.14 77.39 59.69 31.39 17.45 9 8 7 6 5 4 3 2 1 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month Figure 6: Monthly Average Relative Humidity of Nasarawa (%) The solar radiation intensity arriving at the earth's surface is mostly affected by the existence of carbon dioxide and other gases, water vapour, dust particles, ozone, etc, in the atmosphere (Ahmad 1989). Nasarawa being characterized by a tropical sub-humid climate has an average of about 52 % humidity for the whole of the year (213), reaching up to a maximum of 83 84 % during the months of July and August respectively. This is as shown in Table 3 and diagrammatically represented in Figure 6. In this period the percentage of sunshine hours is the least as the sky is mostly heavily clouded. @IJMTER-218, All rights Reserved 97

Radiation (W/m 2 ) 3.4 Comparative Analysis of Measured (Measured) and Predicted (Calculated) Solar Radiation Using the Determined Model Statistical tests were conducted to ascertain the degree of accuracy for the measured (H m ) and the predicted (H cal ) solar radiation in table 1 obtained from the developed model equation. From the tests, the measured solar radiation (H m ) was compared to the solar radiation predicted by the model using F- LSD at p.6. The low Normalized Root Mean Square Error (NRMSE) of.9 % showed a good agreement between the measured and predicted global solar radiation. 35 3 25 2 15 1 5 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month Hm (Measured) Hcal (Predicted) Figure 7: Comparative Analysis of Measured (Measured) and Predicted (Calculated) Solar Radiation Using the Determined Model The measured and the predicted solar radiation obtained in the model were comparatively analysed and there was no significant difference between them using F SLD at P.5 as shown in table 1, Figure 7, which is the graphical representation of the measured and calculated solar radiation also confirms the agreement between the measured and predicted solar radiation of Nasarawa. IV. CONCLUSION Solar radiation of Nasarawa, Nasarawa state, Nigeria was acquired for a full year (213) on hourly basis. Also collected were daily maximum and minimum temperatures and relative humidity values of Nasarawa for a period of one year. A model was developed from this data to predict the solar radiation of Nasarawa. The model was developed using Reitveld equation type. The constants a and b were.28 and.49 respectively specifically for Nasarawa and other locations with related weather conditions. The model equation developed is as stated below: - H m H * ( )+ @IJMTER-218, All rights Reserved 98

The following discussions compare this work to previous work done on solar radiation models: - Turton, (1986) developed a model of Angstrom type regression equation for humid tropical countries with its model being ( ) The values of a and b were respectively.3 and.4 and a + b =.7. The disparity in the respective values of a and b could be attributed to the fact that Turton model did not pick a particular location to carry out his research. It was a general model for the humid tropical countries. However, there is strong agreement between the values of the summation of the constants since that obtained from Turton was.7 and that for Nasarawa.77. The agreement can be as a result of Nasarawa being located in a sub-humid climate region. Also, Sambo, (1986) used various meteorological parameters from Northern Nigeria to predict the global solar radiation for the region as follows: ( ) ( ) ( ) Where θ is the temperature ratio. From the model above, the values a obtained from Nasarawa model and that of Sambo did not agree with each other; the values being.1 and.14 respectively. This can be because of the differences in the modelled equation used because that of Sambo s model has temperature ratio as part of its equation parameters. Isikwue et al (212) developed an empirical model using relative sunshine duration and measured global solar radiation data for Makurdi as: ( ) From the model above, the values of a and b are respectively.138 and.488 for Makurdi and the values of a and b for Nasarawa model using Reitveld equation are.28 and.48 respectively. There is strong agreement between the values of the constants of these models which can be as a result of Nasarawa and Makurdi having similar climatic conditions. Adesina et al (215) developed a model of Angstrom type regression equation for predicting solar radiation of Nasarawa, Nigeria with its model being ( ) The values of a and b were respectively.1 and.75 and a + b =.76. The disparity in the respective values of a and b could be attributed to the fact that Angstrom model type uses regression analysis to obtain values of the constants while it is not so in Rietveld equation type which uses simple formulas to calculate these constants. However, there is strong agreement between the values of the summation of the constants since that obtained from Angstrom was.76 and that from Reitveld was.77. From the study of global solar radiation on horizontal surface in Nasarawa the prospects of application and efficient utilization of solar energy seems to be very bright. The sun shines for about 3 hours per year and this abundance of sunshine is an indication of clear sky condition in Nasarawa. This is also confirmed from the high clearness index (K T ) throughout the year. V. RECOMMENDATIONS Further work can be done on this research to cover not less than three years to ten give a more accurate result. With the availability of high percentage of direct radiation, the solar cookers, ovens for household applications and solar driers for agricultural applications should be designed based on these @IJMTER-218, All rights Reserved 99

data with sophistication and improved efficiency for the rural areas. The economic feasibility and costbenefit ratio is also an important factor to be considered. REFERENCES [1] Adesina, M. A., Ibrahim, J. S., Ponzi, U. D. (215). A Model for Predicting Solar Radiation for Nasarawa, Nigeria. International Journal of Modern Engineering Sciences, 215, 4(1): 22-3. Florida USA [2] Ahmed F. (1989). Solar radiation studies at Karashi Pakistan. A. Ph.D. thesis submitted to the department of Physics, University of Karashi Karashi. [3] Angstrom, A. (1924). Solar and terrestrial radiation. Q. J. R. Meteorol. Soc., 5: 121 125. Bechini, L., G. Ducco, M. Donatelli [4] Ejeh A. C. (28). A model for determining solar radiation for Makurdi, Nigeria. Unpublished M. Eng. thesis submitted to the Mechanical Engineering Department, University of Agriculture, Makurdi. [5] http://www.newstrackindia.com/information/worldinfo/latitudelongitude/countrycities/nigeria/city-nasarawa- 1644755.htm 11-4- 214 [6] Isikwue, B.C. Amah, A.N. and Agada, P.O. Empirical Model for Estimation of Global Solar Radiation in Makurdi, Nigeria. Global Journal of Science Frontier Research Physics and Space Science, vol. 12, no. 1, pp 59-61, 212 [7] Itodo, I.N. and A. U. Fulani. (24). Development of a passive solar dryer with an air pre-heater unit. Proceedings Nigerian Institution of Agricultural Engineers. [8] National Resources Management & Environmental (NRM & E) Department (1998). Crop evapotranspiration guidelines for computing crop water requirements. FAO Irrigation and Drainage papers. Version 56. Retrieved from (www.onlinenigeria.com/links/nasarawaadv.asp?blurb=324 on 11/4/214. [9] Rietveld, M.R. (1978). A New Method for Determining the Regression Coefficients in the formula relating Solar Radiation to Sunshine. Agric Meteorol. vol. 19, pp 243 252. [1] Sambo, A. S. (1986). Empirical models for the correlation of global solar radiation with meteorological data for northern Nigeria. Solar and wind Technology. 3(2). p. 89 [11] Turton, S. M. (1986). The Relationship between Total Irradiation and Sunshine Duration in the Humid Tropics. Solar Energy. Vol. 38: pp 353-354, 1986. [12] Wiliam B. S. and Michael G. (21). Power from the sun. retrieved from http://www.powerfromthesun.net/book/chapter2/chapter2.html on 11-1 212 @IJMTER-218, All rights Reserved 1