Investigation of the Dependence of Global Solar Radiation on Some Atmospheric Parameters Over Kano and Oyo-Nigeria

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1 Radiatin cience and Technlgy 2017; 3(1): di: /j.rst Invigatin f the Dependence f Glbal lar Radiatin n me Atmspheric Parameters Over Kan and Oy-Nigeria Inalegwu Emmanuel Ogwuche, mb T. Department f Physics, Federal University f Agriculture, Makurdi, Nigeria address: inalegwu4free@yah.cm (Inalegwu E. O.), jtsmb@gmail.cm (mb T.) T cite this article: Inalegwu Emmanuel Ogwuche, mb T. Invigatin f the Dependence f Glbal lar Radiatin n me Atmspheric Parameters Over Kan and Oy-Nigeria. Radiatin cience and Technlgy. Vl. 3, N. 1, 2017, pp di: /j.rst Received: January 29, 2017; Accepted: February 24, 2017; Published: March 6, 2017 Abstract: me multi-linear regressin equatins were develped t invigate the dependence f glbal slar radiatin n a cmbinatin f the fllwing parameters: relative humidity, mean f daily temperature, rati f maximum t minimum daily temperature, relative sunshine hur, rainfall, and the difference f mnthly daily maximum and minimum temperature fr Kan and Oy-Nigeria fr a span f 30 years ( ). Using the Angstrm mdel as the base, ten (10) ther regressin equatins were develped by mdifying Angstrm equatin. The results f statistical indicatrs: Cefficient f Determinatin (R 2 ), Mean Bias Errr (MBE), Rt Mean quare Errr (RME) and Mean Percentage Errr (MPE); perfrmed n the mdel alng with practical cmparisn f the imated and bserved data validate the excellent perfrmance accuracy f the prpsed mdel. The equatins with the high value f cefficient f determinatin R 2 and least value f RME, MBE, and MPE are given as: / = (/ ) 0.268(R/100) and / = (/ ) (R/100) fr Kan and Oy respectively, where / is the relative sunshine duratin and R is the relative humidity. The mdels can be used fr imating glbal slar radiatin n hrizntal surfaces fr places with similar latitudes where radiatin data are unavailable. Based n verall results, it was cncluded that unshine duratin and relative humidity are the mst apprpriate cmbinatin f climatic variables suitable fr the imatin f glbal slar radiatin in the study areas. Keywrds: lar Radiatin, Meterlgical Parameters, Relative umidity, Temperature, Relative unshine Duratin, tatistical Indicatr 1. Intrductin lar radiatin hlds ne f the relevant places amng the diverse pssible ptins f energy surces. It is the energy prvided by the un. Nigeria receives ample slar energy that can be usefully explited with an annual average daily slar radiatin f abut 5250Wm -2 day -1 [1]. This alternates between 3500Wm -2 day -1 at the castal hrizn and 7000 Wm -2 day -1 at the nrthern periphery. The average amunt f daily sunshine hurs all-ver the cuntry is abut 6.5hurs [1] and it has been fund that there is an imated 3,000 hurs f annual sunshine [2] lar radiatin data are fundamental fr fabricating slar energy equipments. wever, the instrument fr measuring slar radiatin is nt easily available due t the expense and instrumentatin invlved [3]. Technlgy fr measuring glbal slar radiatin is unecnmical and has instrumental risk [4]. The pr cverage f the measurement shws that there is a need t practice theretical methds fr imating slar radiatin. Amng the methds develped, are thse based n empirical crrelatin using cmmnly measured meterlgical elements. This methd has attracted great attentin wing t lwer data requirement and cmputatin cst [5]. The cmmnly used crrelatins fr imating slar radiatin are majrly based n sunshine duratin. But, sunshine duratin is nt as available as air temperature data at standard meterlgical statins [6]. it is meaningful t elabrate mdels that imate slar radiatin based n air temperature. me studies were based n hurly slar radiatin predictin using different meterlgical parameters and the methds are claimed t perfrm well. Obviusly, measured data is the b frm f this knwledge. Unfrtunately, there are very few meterlgical statins that

2 2 Inalegwu Emmanuel Ogwuche and mb T.: Invigatin f the Dependence f Glbal lar Radiatin n me Atmspheric Parameters Over Kan and Oy-Nigeria measure glbal slar radiatin, especially in develping cuntries. Fr such statins where n measured data are available, the cmmn practice is t imate glbal slar radiatin frm ther measured meterlgical parameters like relative sunshine duratin and temperature. The quantity f slar radiatin the Earth receives n its surface varies drastically as a functin f changing atmspheric cnditins as well as the changing psitin f the sun thrugh the day [7]. The slar radiatin reaching the earth s surface depends n the climatic cnditin f the specific site lcatin, and this is essential fr accurate predictin and design f a slar energy system [2]. Meterlgical parameters such as relative humidity, rainfall, relative sunshine duratin, mean temperature, sil temperature play an essential rle in the radiative energy budget f the Earth and in the transfer f energy between the surface and atmsphere. Infrmatin n glbal slar radiatin received at any site (preferably gained ver a lng perid) shuld be useful nt nly t the lcality where the radiatin data is cllected but als fr the wider wrld cmmunity [8]. Glbal slar radiatin is an imprtant parameter necessary fr mst eclgical mdels and serves as input fr different phtvltaic cnversin systems; hence, it is f ecnmic imprtance t renewable energy alternative. A glbal study f the wrld distributin f glbal slar radiatin requires knwledge f the radiatin data in varius cuntries and fr the purpse f wrldwide marketing, the designers and manufacturers f slar equipment will need t knw the average glbal slar radiatin available in different and specific regins [9]. When glbal slar radiatin is used t generate electrical energy fr any specific site lcatin, a prvisin shuld be made t frecast slar energy which will cnvert t electrical energy t recver the lad demand, that is, the amunt f slar energy fr that place ught t be knwn. The slar radiatin received at a particular lcatin n the earth s surface must be knwn in rder t evaluate the perfrmance f any slar system at a given lcatin. This energy depends n tw main factrs, namely the extraterrrial slar radiatin and the state f the atmsphere. The extraterrrial slar radiatin is the rate at which slar energy arrives n a hrizntal surface at the tp f the atmsphere. It varies accrding t the latitude f the lcatin, the distance f the Earth frm the sun, and the time f the year. On any particular day, it varies frm zer at sunrise t a maximum at nn and back at zer at sunset [10]. 2. Methdlgy The glbal slar radiatin, sunshine hur, rainfall, relative humidity, minimum and maximum air temperature data fr Oy (8.11 N, 3.42 E, and 304m) and Kan (12.2 N, 8.30 E, 488m) were btained frm the Internatinal Institute fr Trpical Agriculture (IITA), Ibadan. The data spanned fr a perid f thirty years ( ). The extraterrrial slar radiatin ( ), relative sunshine duratin (/ ), rati f Tmin minimum t maximum temperature ( ), relative Tmax humidity (R), rainfall (RF), mnthly mean daily temperature (T mean ), and the difference between maximum and minimum daily temperature (T max T min ) were used as input parameters fr the imatin f glbal slar radiatin are recrded in Table 1 fr Kan while that f Oy is recrded in Tables Data Analysis A lt f climatic parameters have been used in develping empirical relatins fr predicting the mnthly average glbal slar radiatin. Amng the existing crrelatins, the fllwing relatin is the generally accepted mdified frm f the Angstrm-type regressin equatin, relating the mnthly average daily glbal radiatin t the average daily sunshine hurs and is given as [11] m 0 =a+b (1) where m is the mnthly average daily glbal radiatin n a hrizntal surface (MJm -2 day -1 ). 0 is the mnthly average daily extraterrrial radiatin n a hrizntal surface (MJm - 2 day -1 ). is the mnthly average daily number f hurs f bright sunshine. 0 is the mnthly average daily maximum number f hurs f pssible sunshine (r day length) and a and b are regressin cnstants t be determined. The extraterrrial slar radiatin n a hrizntal surface is given by [12] as: = x 3.6 x 10-3 x I sc { cs D )}csфcsδsinω+ ωsinфsinδ (2) ( where, D is the Julian day number, I sc is the slar cnstant in MJm -2 day -1. The value f I sc t be used in this wrk is 1367wm -2, ɸ is the latitude f the lcatin, δ is the declinatin angle. The value f declinatin can be fund frm the equatin f [13] as: δ = 23.45sin ( D 365 ) (3) The maximum pssible daily, als called the length f day is given by [14] as sunshine duratin 0 is given by 0 = ( ) ω s (4) Where ω s is the sunset hur angle given by [15] as: ω s = cs -1 (-tanфtanδ) (5)

3 Radiatin cience and Technlgy 2017; 3(1): Equatins 1 5 were used in the analyses f the meterlgical data in this wrk Tw Variable Equatins fr Kan The mnthly mean daily glbal slar radiatin calculated using equatins (6)-(10) were recrded as mdel 1-5 is shwn in Table 1 while variatins f the measured and imated glbal slar radiatin are presented in Figures 1-5. The crrelatins t which the measured data were fitted are as fllws: ( T T ) ( R ) = (6) ( T T ) ( R ) = + (7) = ( R ) = ( Tmean ) T min = T 2.3. Tw Variable Equatins fr Oy max (8) (9) (10) The mnthly mean daily glbal slar radiatin calculated using equatins (11)-(15) were recrded as mdel 6-10 in Table 2 while variatins f the measured and imated glbal slar radiatin are presented in Figures The crrelatins t which the measured data were fitted are as fllws: ( T T ) ( R ) = (11) ( T T ) ( R ) = + + (12) 3. Results = ( R ) (13) = ( Tmean ) T min = T max (14) (15) where T mean is the mean temperature ( C),T max is the mnthly maximum daily temperature ( C), T min is the mnthly minimum daily temperature ( C), is imated glbal slar radiatin n a hrizntal Plane (MJm -2 day -1 ), RF is rainfall (mm), R is Relative umidity (%), is extraterrrial slar radiatin (MJm -2 day -1 ), (/ ) is the relative sunshine duratin (hr) 2.4. tatistical Analysis The accuracy f the imated values was ted by calculating the RME (Rt Mean quare Errr), MBE (Mean Bias Errr) and MPE (Mean Percentage Errr). The expressins fr RME (MJ/m 2 ), MBE (MJ/m 2 ) and MPE (%) as stated accrding t [16] are given as fllws; {( ( pred bs ) )/ } RME = n (16) ( ) pred bs / MBE = n (17) MPE = bs bs pred ( 100 ) / n (18) where pred and bs are the predicted (imated) and bserved (measured) values respectively and n is the ttal number f bservatins. RME and MBE statistical indicatrs are frequently used in cmparing the mdels f slar radiatin predictins. The t RME prvides infrmatin n the shrt-term perfrmance f the studied mdels as it allws a term-by-term cmparisn f the actual deviatin between the calculated value and the measured value. [14], [17] and [18] have recmmended that a zer value fr MBE is ideal and lw RME is desirable. The use f RME and MBE statistical indicatr is nt adequate fr the evaluatin f mdels perfrmance thus decisins were made that MPE be used in additin t RME and MBE t give mre reliable result. Table 1. MONTLY MEan input parameters and measured glbal slar radiatin fr Kan. Mnth T max-t min ( C) Tmin ( C) T mean ( C) m (MJ -2 mday -1 ) 0 (MJ -2 mday -1 ) T (hurs) max (hurs) R mean (%) Jan Feb Mar Apr May Jun Jul

4 4 Inalegwu Emmanuel Ogwuche and mb T.: Invigatin f the Dependence f Glbal lar Radiatin n me Atmspheric Parameters Over Kan and Oy-Nigeria Mnth T max-t min ( C) Tmin ( C) T T mean ( C) m (MJ -2 mday -1 ) 0 (MJ -2 mday -1 ) (hurs) max (hurs) R mean (%) Aug ep Oct Nv Dec Table 2. Mnthlymean input parameters and measured glbal slar radiatin fr Oy. Mnth T max-t min T min T mean ( C) m (MJ -2 mday -1 ) 0 (MJ -2 mday -1 ) (hurs) (hurs) RMean (%) T max Jan Feb Mar Apr May Jun Jul Aug ep Oct Nv Dec Table 3. Observed and predicted glbal slar radiatin fr mdels cmprising f tw variables fr Kan statin. Mnths M (MJm -2 day -1 ) Mdel 1 (MJm -2 day -1 ) Mdel 2 (MJm -2 day -1 ) Mdel 3 (MJm -2 day -1 ) Mdel 4 (MJm -2 day 1 ) Mdel 5 (MJm -2 day -1 ) Jan Feb Mar Apr May June July Aug ep Oct Nv Dec Figure 1. Cmparisn between measured and predicted glbal slar radiatin using mdel 1.

5 Radiatin cience and Technlgy 2017; 3(1): Figure 2. Cmparisn between measured and predicted glbal slar radiatin using mdel 2. Figure 4. Cmparisn between measured and predicted glbal slar radiatin using mdel 4. Figure 3. Cmparisn between measured and predicted glbal slar radiatin using mdel 3. Figure 5. Cmparisn between measured and predicted glbal slar radiatin using mdel 5. Table 4. Observed and predicted glbal slar radiatin fr mdels cmprising f tw variables fr Oy statin. Mnths M (MJm -2 day -1 ) Mdel 6 (MJm -2 day -1 ) Mdel 7 (MJm -2 day -1 ) Mdel 8 (MJm -2 day -1 ) Mdel 9 (MJm -2 day -1 ) Mdel 10 (MJm -2 day -1 ) Jan Feb Mar April May June July Aug ept Oct Nv Dec Figure 6. Cmparisn between measured and predicted glbal slar radiatin using mdel 6. Figure 7. Cmparisn between measured and predicted glbal slar radiatin using mdel 7.

6 6 Inalegwu Emmanuel Ogwuche and mb T.: Invigatin f the Dependence f Glbal lar Radiatin n me Atmspheric Parameters Over Kan and Oy-Nigeria 4. Discussin 4.1. Estimatin f lar Radiatin fr Kan Using Tw Variables Figure 8. Cmparisn between measured and predicted glbal slar radiatin using mdel 8. Figure 9. Cmparisn between measured and predicted glbal slar radiatin using mdel 9. Figure 10. Cmparisn between measured and predicted glbal slar radiatin using mdel 10. Table 5. Mdels and tatistical indicatrs fr Kan. Mdel R R 2 MBE RME MPE Table 6. Mdels and tatistical Indicatrs fr Oy. Mdel R R 2 MBE RME MPE Figure 1 shws that in the rainy seasn, the lw slar radiatin was btained in Octber while the lw values fr glbal slar radiatin (Fig. 2 5) was btained in August fr bth the measured and imated glbal slar radiatin (prbably due t cluds which permeated the sky). In the dry seasn, the high value f slar radiatin was measured in March fr the measured and imated value fr mdel 1 and April fr mdels 2-5. The lw value fr bth measured and imated slar radiatin fell between December and January (prbably due t harmattan dust which perturbed slar radiatin at the time). Of the five mdels, mdel 3 had the b cefficient f determinatin (R 2 ) f 90.9% sugging a gd crrelatin and reliable imate f the regressin cnstants. Overall, mdel 3 prduced mre accurate imates than the existing 4 mdels. This can be seen frm the fact that Figure 3 (mdel 3) has smaller values fr MBE, RME and MPE cmpared with the ther mdels. This is in agreement with [17], [18] that a zer value f MBE is ideal and lw RME and MPE is desirable Estimatin f lar Radiatin fr Oy Using Tw Variables Table 6 cntains summaries f the mdels under cnsideratin. It is clear that the statistical indicatr f cefficient f determinatin R 2, MBE, RME and MPE vary frm ne mdel t anther. In general, mdel 6, 8, 9 and mdel 10 having a crrelatin cefficient ( ) are high fr these mdels. This implies that, there are statistically significant relatinships between the measured and the imated values. This is further demnstrated by high value f cefficient f determinatin R 2 ( ) acrss the variables. The lw RME value f shwed that mdel 8 has the b crrelatin between imated and measured glbal slar radiatin. 5. Cnclusin and Recmmendatin Multiple regressin techniques have been emplyed in this study t develp several crrelatin equatins t describe the dependence f glbal slar radiatin n sme atmspheric data fr Kan and Oy, Nigeria. The values f statistical indices (MBE, RME, and MPE) btained in this research wrk shw that the difference between the imated and the measured glbal slar radiatin is nt much, implying that the mdels used in this research t imate the glbal slar radiatin in these cities are validated. The result shws that mdel 3 and 8 which are the equatins with the high R 2 give the b result fr Kan and Oy respectively when cnsidering the errr terms (MBE, RME, and MPE). ence the multiple regressin

7 Radiatin cience and Technlgy 2017; 3(1): equatin can be emplyed fr the purpse f imating glbal slar radiatin fr Kan and Oy-Nigeria and fr lcatins that have the same climate and latitude as bth lcatins. The mdel fr Kan is: = imilarly, the mdel fr Oy is = R R 100 (19) (20) The maximum and minimum values f mnthly average glbal slar radiatin fr Kan-Nigeria are fund t be 19.66MJm -2 day -1 and 16.35MJm -2 day -1 respectively while that f Oy-Nigeria is fund t be MJm -2 days- 1 and MJm -2 days- 1 respectively. ince facilities fr recrding glbal slar radiatin data are nt easily available prbably because f pr maintenance culture r lack f trained persnnel t take measurements r delay in repair in case f instrument failure r malfunctin, these equatins can be used t imate glbal slar radiatin in these areas and their envirns with similar climatic cnditins. References [1] Chineke, T. C. and Igwir, E. C. (2008): Urban and rural electrificatin-enhancing the energy sectr in Nigeria using phtvltaic technlgy. African jurnal science and tech. Vl. 9, Pp [2] Burari and amb (2001). Mdel fr the predictin f glbal slar radiatin fr Bauchi using meterlgical data. Nigeria jurnal f renewable energy Vl. 91 Pp [3] El-ebaii, A. A, Al-azmi, F.. Al-Ghamdi, A. A. Yaghmur,. J.(2010). Glbal, direct and diffuse slar radiatin n hrizntal and tilted surfaces in Jeddah, audi Arabia. Applied Energy.87 (2): [4] Alam M.. aha,. K. Chwdhury, M. A. aifuzzaman, M. and Rahman, M. (2005). imulatin f slar radiatin systems. American Jurnal f Applied ciences. 2 (4): [5] Liu, X. Mei, X. and Li, Y. (2009). Evaluatin f temperature based mdels in China. Agricultural and Fr Meterlgy. 149 (9): [6] Rahimikhb, A. (2010). Estimating glbal slar radiatin using artificial neural netwrk and air temperature data in a semi-arid envirnment. Renewable Energy. 35 (9): [7] Falayi, E. O. (2013). The Impact f Clud Cver, Relative umidity, Temperature and Rainfall n lar Radiatin in Nigeria. [8] Massaqui, J. G. M. (1988). Glbal slar radiatin in ierra Lene (W Africa). lar Wind Technlgy.5, 281 (283). [9] Ibrahim. M. A (1985). Nigeria Jurnal n lar Energy 35 (2): [10] Liu, (1980); Intrductin t Atmspheric Radiatin. Academy press New Yrk. [11] Angstrm, A. J. (1924). lar and terrrial radiatin. Q. J Ry Met. c. 50: [12] Duffie J. A.; Beckmann W. A. (2013). lar engineering f thermal prcesses 3 rd Editin, Jhn Wiley, New Jersey. [13] Cper, P. I. (1969). The absrptin f slar radiatin in slar stills. lar energy, 12 (3): 31. [14] Igbal, M. (1983). An intrductin t slar radiatin. Academy press, New Yrk. [15] Fayadh, M. A. and Ghazi, A. (1983). Estimatin f glbal slar radiatin in hrizntal surfaces ver Egypt. J. slids, 28: [16] El-sebaii, A. A. and Trabea, A. A. (2005). Estimatin f glbal slar radiatin n hrizntal surfaces ver Egypt. J. lids, 28: [17] Almrx, J. (2005). Estimating glbal slar radiatin frm cmmn meterlgical data in Aranjuez, pain [18] Che,. Z. hi, G. Y. Zhang, X. Y. Zha, J. Q. and Li, Y. (2007). Analysis f sky cnditin using 40 years recrd f slar radiatin data in china. Theretical and applied climatlgy. 89: