Solar radiation: Correlation between measured and predicted values in Mubi, Nigeria

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1 Internatinal Jurnal f cience and Technlgy Educatin Research Vl. 4(1), pp , January 2013 Available nline at DOI: /IJTER IN Academic Jurnals Full Length Research Paper lar radiatin: Crrelatin between measured and predicted values in Mubi, Nigeria Medugu D. W. 1, Adisa A. B. 2, Burari F. W. 3 and Abdul Azeez M. A. 3 1 Department f Pure and Applied Physics, Adamawa tate University, Mubi, Adamawa tate, Nigeria. 2 Department f Mechanical Engineering, Abubakar Tafawa Balewa University, Bauchi tate, Nigeria. 3 Department f Physics, Abubakar Tafawa Balewa University, Bauchi tate, Nigeria. Accepted 14 December, 2011 In this study, the crrelatin between measured and predicted values f slar radiatin was made. A series f daily measurements f the glbal slar radiatin n a hrizntal surface was recrded in Mubi with the aid f a cnstructed pyranmeter. The mnthly average value was determined. The mnthly average daily slar radiatin n hrizntal surface was als determined using sunshine duratin. These parameters were input in sme radiatin mdels t cmpute the slar radiatin. Finally, a predictin f the glbal slar radiatin frm climatlgical data has been attempted. The predicted values have been cmpared with the crrespnding measured values. Predictins and measurements were fund t be in rather gd agreement. These results indicate that the pyranmeter develped may be used satisfactrily fr the measurement f slar radiatin in the wrld. Key wrds: lar radiatin, pyranmeter, sunshine duratin, climatlgical data. INTRODUCTION The grwing ppulatins f the wrld, the fast depleting reserves f fssil fuels, and the awareness f envirnmental impact have led the researchers t think f alternate surces f energy fr a safer life n this earth. Therefre, the whle wrld is lking fr nn-exhaustible energy surces fr their future. Amng all the nncnventinal energies, slar energy is the best ptin if it can be used in a cst effective manner because the technlgy is als envirnmentally sund. As the slar energy intercepted by the earth in ne year is ten times greater than the ttal fssil resurces including undiscvered and unexplred nn-recverable reserves (Palz, 1977), it is expected that the present wrldwide research and develpment prgram n slar energy will help t slve the future energy crisis f the wrld. lar radiatin is the radiant energy that is emitted by the sun frm a nuclear fusin reactin that creates electrmagnetic energy. The glbal radiatin is an imprtant parameter necessary fr mst eclgical *Crrespnding authr. dalemedugu@yah.cm, dalemedugu23@gmail.cm. mdels and an input fr different slar systems. It is the ultimate energy fr all ecsystems. lar radiatin data are very imprtant t architects, engineers and scientists fr energy-efficient building designs; the develpment f active and passive slar energy applicatins; and climatlgy and pllutin studies. The best way f knwing the amunt f glbal slar radiatin at a site is t install pyranmeters at different lcatins in the given regin and lk after their day-t day maintenance and recrding but this methd is very expensive. An alternative apprach is t crrelate the glbal slar radiatin with the meterlgical parameters at the place where the data is cllected. The resultant crrelatin may then be used fr lcatins f similar meterlgical and gegraphical characteristics at which slar data are nt available. In many applicatins f slar energy, the mst imprtant parameters that are ften needed are the average glbal slar irradiatin and its cmpnents. Unfrtunately, the measurements f this parameter are dne nly at a few places. Fr this reasn, there have been attempts at estimating them frm theretical mdels. uch mdels include that f amb (1985), Awachie and Okeke (1990), Akpabi and Etuk (2004),

2 12 Int. J. ci. Technl. Educ. Res. Badmus and Mmh (2005), ussaini et al. (2005), Ihenu (2001), Arinze and Obi (1983), Falayi and Rabiu (2005), El-ebaii and Trabea (2005), Babatunde and Ar (1990), and Burari and amb (2001) t mentin but a few. This crrelatins estimate the amunts f mnthly average slar radiatin frm mre readily available meterlgical parameters such as the sunshine duratin and extraterrestrial radiatin. Althugh slar radiatin data are available at mst meterlgical statins, there are still statins in many regins in Nigeria - especially Mubi, in Adamawa tate - that suffers frm a shrtage cncerning the slar radiatin recrds; therefre, we present the measurement f slar radiatin frm a develped reliable mdel pyranmeter and crrelated the values with ne f the famus predicted mdel. In the present wrk, slar radiatin measurement and estimatin have been dne fr the first time fr Mubi, t utilize slar energy fr useful purpse. The Mubi twn has an area f km 2. It is lcated at latitude and lngitude It is ne f the largest twns in Adamawa tate, Nigeria. This wrk will help the energy strategist and planners t utilize slar energy ptential t slve the energy deficit in this twn f abundant sunshine, thrughut the year. METOD OF PREDICTION Varius climatic parameters have been used in develping empirical relatins fr predicting the mnthly average glbal radiatin (Nguyen and Pryr, 1997). Amng the existing crrelatins, the data f sunshine duratin are widely available in many cuntries; varius frmulas based n them have been prpsed t determine slar radiatin frm sunshine duratin. The mst generally used methd was develped by Angstrőm, and later mdified by Presctt. The mdified versin f Angstrőm Presctt has been the mst cnvenient and widely used crrelatin fr estimating the glbal radiatin. The frmula is (Duffie and Beckman, 1994): 0 = a b where, and 0 are, respectively, the glbal radiatin (MJm -2 day -1 ) and the extraterrestrial slar radiatin n a hrizntal surface (MJm - 2 day -1 ); and 0 are, respectively, number f hurs measured by the sunshine recrder and the maximum daily sunshine duratin (r day length); and a, b are regressin cnstants t be determined. Regressin equatin (1) has been fund t accurately predict glbal slar radiatin in several lcatins (Akpabi, 1992). Fr mnthly average, this frmula hlds (Duffie and Beckman, 1994): 0 = a b ere, is the mnthly average daily glbal radiatin n a hrizntal surface (MJm -2 day -1 ), is the mnthly average daily (1) (2) extraterrestrial radiatin n a hrizntal surface (MJm -2 day -1 ), is the mnthly average daily number f hurs f bright sunshine, is the mnthly average daily maximum number f hurs f pssible sunshine. Regressin cefficient a and b have been btained frm the relatinship given by Tiwari and angeeta (1977) and als cnfirmed by Frere (1980): a = b = cs φ ( / cs φ ( / ) There are als different methds in evaluating these cnstants. The extraterrestrial slar radiatin n a hrizntal surface can be calculated frm the fllwing equatin (Duffie and Beckman, 1994): 24 x3600 π ) (3) dn 2πω s cs 360 sinφ sinδ csφ csδ sinω (4) = Isc s The value f 1367 Wm -2 has been recmmended fr slar cnstant I sc (Frlich and Brusca, 1981). The hur angle ω s fr hrizntal surface is given as (Duffie and Becman, 1994): ω = cs ( tan φ tan δ ) 1 s (5) Declinatin is calculated as (Cper, 1969): 284 dn = sin δ (6) Where dn is the day f the year frm January 1 t December 31. The day length 0 is the number f hurs f sunshine r darkness within the 24 h in a given day. Fr a hrizntal surface, it is given by (Duffie and Becman, 1994): 2 2 = cs 1 ( tan φ tan δ ) = ω (7) s (Frm Equatin (5)) Instrumentatin design fr the measurement The instrument used fr the measurement f slar radiatin is a reliable mdel pyranmeter (RMP001) which we develped. The pyranmeter is shwn in Figure 1 as an utline in its husing and as a circuit diagram in Figure 2. The sensr element is a silicn dide, munted n a plastic base, cvered with a Tefln diffuser. The whle unit is placed n a base with a level cntrl t ensure hrizntality. The best detectr was chsen based n the characteristics in the datasheets supplied by the manufacturers. The mst suitable phtdide fr this applicatin was BPW21 with respnsivity, sensitive area and nise equivalent pwer f 0.34 A/W, m 2 and W/z 1/2 respectively. Cnstructin f slar cell based pyranmeters are cnceptually very simple and cheap. wever, they require care design based n an understanding f the underlying physical principles. The

3 Medugu et al. 13 Figure 1. Picture f the cnstructed reliable mdel pyranmeter (RMP001). C r 68 pf R f 1 K 9 V Op. Amp C c R c 68 pf 1K V - Figure 2. Pyranmeter circuit diagram.

4 14 Int. J. ci. Technl. Educ. Res. C r R f I p V cc C - V = I p R f Cc R c V cc Figure 3. Transimpedance amplifier circuitry. develped pyranmeter generates an electrical signal prprtinal t the irradiance received and cnverts the small current received frm the detectr t a vltage and amplifies it t a vltmeter. The transimpedance amplifier shwn in Figure 3 is cnfigured arund the LTC1051 peratinal amplifier (OPAM) in rder t cnditin signal frm the phtdide as shwn in Figure 2. In this circuit, I p is the phtcurrent frm the dide and C its parasitic capacitr. C c, R c Cr are cmpensatin capacitr, crrectin resistr and stabilizatin capacitr respectively. The feedback resistr R f fixes the DC gain in the circuit in rder t btain an utput frmv 0 = I p R f. An irradiance f 1,200 W/m 2 btained frm a 200-W quartz tungsten halgen lamp is used t calculate the value f R f. Fr this, the BPW21 phtdide prduces the phtcurrent Ip = A (that is, Ip.= irradiance sensitive area respnsivity). In rder t carry ut precise adjustment fr maximum analgue-t-digital cnverter f 3 V, the value f Rf implemented is 1 KΩ (frm R f = V /I p).rc with value f 1 KΩ is cnnected t the nn-inverting input f the OPAM fr crrecting the DC errr due t plarizatin currents. This resistr has a detrimental effect in terms f nise which is amplified (Graeme, 1996); hence, a 68 pf cmpensatin capacitr Cc is cnnected in parallel with it. The parasitic capacitr n the phtdide BPW21, C, is 580 pf which influence the stability f the assembly. Finally, a 68 pf capacitr Cr is cnnected in parallel with the feedback resistr R f t perfect the stability f the amplifier (Figure 2). The reliable mdel pyranmeter (RMP001) was then calibrated against a reference high quality pyranmeter, Kipp and Znen CMP 3 whse calibratin was trusted (14.71± 0.36 µv -1 Wm -2 ). The cnversin f the utput frm RMP001 frm vlts t Wm -2 was dne t btain a calibratin cnstant f 5230±0.02 Wm -2 (Figure 4). Materials and measurement prcedures The daily sunshine hur data were cllected fr a perid f ne year (frm 1 st Nvember, 2008 t 31 st Octber, 2009) frm Adamawa tate University s meterlgical statin at Mubi. The relevant meterlgical and slar radiatin data like,, /,ω,δ, a and b calculated frm equatins (1) t (7) are presented. The measurement f slar radiatin at 1 min intervals with the aid f the reliable mdel pyranmeter was recrded fr Mubi, Adamawa tate, Nigeria, using a data lgger. The lgger has a UB interface with prprietary sftware fr cmmunicating with a cmputer. The data was stred in a prpriety binary frmat and later saved as a text file that was imprted int excel. Daily average value f slar radiatin was then determined in Wm -2. The glbal slar radiatin data measured in (MJm -2 day -1 ) was cnverted t (Wm -2 ) using a factr f 11.6 Wm -2 ( This is presented in Table 1. The cmparisn methds In this study, tw statistical tests, mean bias errr (MBE) and rt mean bias errr (RME), and t-statistic were used t evaluate the accuracy f the cnstructed reliable mdel pyranmeter. Mean bias errr The mean bias errr is defined as: 1 MBE = n n d i i= 1 where n is the number f data pairs and d i is the difference between the measured and predicted values. This test prvides infrmatin n the lng-term perfrmance. A lw MBE is desired. A psitive value gives the average amunt f ver-inslatin in the measured value and vice-versa. A drawback f this test is that ver-inslatin f an individual bservatin will cancel under-inslatin in a (8)

5 Medugu et al. 15 Figure 4. Graph f slar radiatin measured with CMP3 and RMP001verses time n 30 th Octber, Table 1. Crrelatin between predicted and measured values f mnthly average daily glbal radiatin. Mnth / a b MJm -2 d -1 Predicted Measured MJm -2 d -1 Wm -2 Wm -2 Nv Dec Jan Feb Mar Apr May Jun Jul Aug ept, Oct, separate bservatin. Rt mean square errr The rt mean square errr is defined as: 1/ 2 n 1 2 RME = d (9) i n i= 1 This test prvides infrmatin n the shrt-term perfrmance f the crrelatins by allwing a term-by-term cmparisn f the actual

6 16 Int. J. ci. Technl. Educ. Res. Figure 5. The predicted and measured values f slar radiatin. deviatin between the measured value and the predicted value; the smaller the value, the better the pyranmeter s perfrmance. wever, a few large errrs in the sum can prduce a significant increase in RME. It is bvius that each test by itself may nt be an adequate indicatr f a pyranmeter s perfrmance. It is pssible t have a large RME value and at the same time a small MBE (a large scatter abut the line f perfect measurement).it is als pssible t have a relatively small RME and a relatively large MBE (cnsistently small ver- r under measurement). Althugh these statistical indictrs generally prvide a reasnable prcedure t cmpare mdels, they d nt bjectively indicate whether a mdel s measures are statistically significant, that is, nt significantly different frm their predicted cunterparts. In this article, an additinal statistical indicatr, the t-statistic, was used. The statistical indicatr allws mdels t be cmpared and at the same time, indicate whether r nt a mdel s measures are statistically significant at a particular cnfidence level (tne, 1993). It was seen that the t-statistic used in additin t the RME and MBE gave mre reliable and explanatry results (Tgrul, 1998). t-statistic t-statistic is defined as (Walple and Myers, 1989): ( n 1) 1/ 2 2 MBE t = (10) 2 2 RME MBE The smaller the value f t, the better is the mdel s perfrmance. T determine whether a mdel s predicts are statistically significant, ne simply has t determine a critical t value btainable frm standard statistical tables, that is, tα / 2 at theα level f significance and (n-1) degrees- f- freedm. Fr the mdel s predicts t be judged statistically significant at the 1 α cnfidence level, the calculated t value must be less than the critical t value. REULT AND DICUION Table 1 shws the values f pssible fractin f sunshine /, mnthly average daily extraterrestrial radiatin n a hrizntal surface, predicted and measured mnthly average daily glbal radiatin n a hrizntal surface. The regressin cefficient a and b are als presented in Table 1. A clse examinatin f Figure 5 shws that the maximum predicted and measured values are and Wm -2, respectively, ccurred in the mnth f March during winter. The minimum values predicted and measured are and Wm -2 respectively. They ccurred in August during summer perid. It is pssible t bserve that the regressin cefficients shw variatins during the curse f the year as shwn in Table 1. Variatins in a andb values are explained as a cnsequence f peridic climatlgical variatins in the atmsphere. The a estimates varies frm 0.34 t 0.25

7 Medugu et al. 17 Table 2. tatistical test results. MBE Wm -2 RME Wm -2 t which is maximum in March and minimum in August; while theb cefficient ranges frm 0.44 t 0.63, being highest in August and lwest in March. It is clearly bserved that a is inversely prprtinal tb. Accrding t the statistical test results, the values f RME and MBE are in the acceptable ranges. As shwn in Table 2, the values f RME and MBE are and Wm -2, respectively. The cmparisn between the measurement and estimatin was carried ut accrding t the t value, because this statistic is mre effective fr determining the statistical prperties. Fr all the whle perid, the calculated t value is 1.0 which is less than the critical t value (1.96). Cnclusin The crrelatins between measured and predicted values f slar radiatin at Mubi were carried ut in this wrk. The average RME and MBE fr the cmparisn between measured and predicted glbal radiatin are and Wm -2, respectively. These values are in the acceptable ranges. The t-statistic depends n bth, the RME and MBE, and it was recmmended that it shuld be used in cnjunctin with these indicatrs in rder t help t assess a mdel s perfrmance mre reliably. These results indicate that the pyranmeter develped in this paper may be used satisfactrily fr the measurement f slar radiatin in the wrld. ACKNOWLEDGEMENT REFERENCE Akpabi LE (1992). Cmparisn between lar radiatin Energy and the Characteristic f Wind Pwer Calculatins in uth Eastern Nigeria. Nig. J. Phys. 4: Akpabi LE, Etuk E (2004). Relatinship Between lar Radiatin and unshine Duratin fr Onne. Nigeria. Turk. J. Phys. 27: Arinze EA, Obi E (1983). lar Energy Availability and Predictin in Nrthern Nigeria. Nig. J. l. Energy 3:3-10. Awachie IRN, Okeke CE (1990). New Empirical lar Mdel and its use in Predicting lar Irradiatin. Nig. J. l. Energy 9: Babatunde EB, Ar TO (1990). Characteristic Variatin f Ttal (Glbal) lar Radiatin at IIrin, Nigeria. Nig. J. l. Energy 9: Badmus IB, Mmh M (2005). Cmparisn f Mdels fr Estimating Mnthly Average Daily Inslatin n a rizntal urface. 41st cience Assc. Nig. Cnf., kt Nig April. Burari FW, amb A (2001). Mdel fr the Predictin f Glbal lar fr Bauchi using Meterlgical Data. Nig. J. Renew. Energy 91: Cper PI (1969). The Absrptin f lar Radiatin in lar till. l. Energy 12(3): Duffie JA, Beckman WA (1994). lar Engineering f Thermal Prcesses. Jhn Wiley, New Yrk, U..A. 2 nd Edn. pp El-ebaii AA, Trabea AA (2005). Estimatin f Glbal lar Radiatin n rizntal urfaces Over Egypt. Egypt. J. lids pp Falayi EO, Rabiu AB (2005). Mdelling Glbal lar Radiatin Using unshine Duratin Data. Nig. J. Phys. 17: Frere EA (1980). Graphs given in A.A Flcas paper Estimatin and predictin f Glbal lar Radiatin ver Greece. l. Energy 24: Frlich C, Brusca RW (1981). lar Radiatin and its Variatin in Time. lar Phys. pp ussaini AM, Maina M, Onyewuenyi EC (2005). Crrelatin f lar Radiatin with sme Meterlgical Parameters fr Maiduguri, Brn tate, Nigeria. Nig. J. l. Energy 15: Ihenu EE (2001). Mdel fr the Predictin f Average Mnthly Glbal lar Radiatin n a rizntal urface fr sme Lcatins in the Trpics using Temperature Data. Nig. J. lar Energy 9: Palz W (1977). lar electricity. amb A. (2005). lar Radiatin in Kan. A Crrelatin with Meterlgical Data. Nig. J. l. Energy 4: tne RJ (1993). Imprved statistical prcedure fr the evaluatin f slar radiatin estimatin mdels. l. Energy 51: Tiwari GN, angeeta (1977). lar ThermalEngineering ystem, Narsa Publishing use, New Dehli, India. Tgrul IT (1998). Cmparisn f statistical perfrmancef seven sunshine- based mdels fr Elazığ, Turkey, Chimica Acta Turcica. pp Walple RE, Myers R (1989). Prbability and statistics fr engineers and scientists. 4th ed. New Yrk: Macmillan. The authrs wuld like t thank Dr. David Brks frm the Institute fr Earth cience Research and Educatin Energy Research Institute, Nrristwn, PA UA, fr his great help in prviding us the necessary materials.

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