Estimation of Global Solar Radiation in Onitsha and Calabar Using Empirical Models
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1 Communitions in Applied Sienes ISS 0-77 Volume, umer, 0, 5-7 Estimtion of Glol Solr dition in Onitsh nd Clr Using Empiril Models M.. nuhi, J. E. Ekpe nd G. F Ieh Deprtment of Industril Physis, Eonyi Stte University, Akliki, igeri Corresponding uthor: G. F Ieh, Deprtment of Industril Physis, Eonyi Stte University, Akliki, igeri ABSAC Understnding solr rdition dt is essentil for modelling solr energy systems. he purpose of the present study ws to estimte glol solr rdition on horizontl surfe using meteorologil prmeters for period of eleven yers ( ). Monthly verge glol solr rdition, H hs een estimted for Onitsh nd Clr, igeri using prediting models generted y simple liner nd multiple regression nlyses. he models inluded one vrile model with reltive humidity s the independent vrile nd two three-vrile models orrelting H with reltive humidity nd eh of verge temperture, loudiness index nd numer of sunshine hours. he vlues of the glol solr rdition estimted y the models nd the mesured solr rdition were tested using the men is error (MBE), root men squre error (MSE) nd men perentge error (MPE) sttisl tehniques. he vlues of the orreltion oeffiient (CC) were lso determined for eh model. he model tht indite good greement etween the mesured nd estimted vlues for Onitsh nd Clr re nd respetively. he developed models n e used for estimting glol solr rdition in Onitsh nd Clr nd other lotions with similr limti ftors. Keywords: Sunshine, verge temperture, reltive humidity, loudiness, glol solr rdition Introdution Knowledge of the glol solr rdition is of fundmentl importne for ll solr energy onversion systems. Informtion on glol solr rdition reeived t ny site (preferly gined over long period) should e useful not only to the Copyright 0 the uthors. 5
2 Communitions in Applied Sienes 6 lolity where the rdition dt is olleted ut lso for the wider world ommunity (Mssquoi, 988). Prtilly, solr rdition dt re esily otined using the relevnt equipment. Pyrheliometer nd pyrnometer n e used redily to otin the diffused omponent of the rdition nd the glol solr rdition respetively. Wether sttions hve een used mostly for this purpose. However, there re few of suh sttions ross the gloe nd worse still in the developing ntions. In n effort to generte rdition dt, reserhers hd extrpolted vlues from one lotion for pplition in different lotion. Hene solr rdition predition from estimtion models hs een widely utilized glolly to generte solr rdition dtse for vrious lotions of the world. he development of the solr rdition dt se for vrious igeri lotions hs een n on-going tsk for reserhers in the field for mny yers now. With the very few meteorologil sttions, the option of using estimting models hs een widely dopted in igeri for prediting solr rdition t speifi lotion nd t regionl sle (Ago, et l 007). ESEACH MEHODOLOGY he dt suh s sunshine hours, verge tempertures, loud over, reltive humidity nd glol solr rdition dt for Onitsh nd Clr used for this study were otined from the igeri meteorologil Ageny, Federl ministry of Avition Oshodi, Lgos, igeri. he dt olleted overed period of eleven yers ( ) for Onitsh (Ltitude, Longitude, nd ltitude 56 metres ove se level) nd Clr (Ltitude, Longitude nd ltitude 58 metres ove se level). hese vlues were otined y the use of GPS (generl position stellite) equipment. DAA AALYSIS he monthly dt proessed in preprtion for the orreltion re presented in les nd for Onitsh nd Clr respetively.
3 7 Communitions in Applied Sienes le : Monthly men vlue of limti prmeters for Onitsh S/ MOH v( o C) % S/ /C H(MJ/m /dy) JA FEB MA AP MAY JU JULY AUG SEP OC OV DEC otl le : Monthly men vlues of limti prmeters for Clr ( ) S/ MOH v( o C) % S/ /C H(MJ/m /dy) JA FEB MA AP MAY JU JULY AUG SEP OC OV DEC otl
4 Communitions in Applied Sienes 8 v = monthly verge dily temperture (%) = eltive 9 hours H = vlue of mesured verge dily solr rdition on the horizontl surfe. = he loudiness index C S = he monthly verge dily reltive sunshine durtion. o develop the model, the glol solr rdition mesured using Gun-Bellini distillte were onverted to useful form (MJM /dy) using onversion ftor of.6 proposed y (Smo, 985). Professionl modellers hve proposed orreltion tht should e used to estimte the glol solr rdition. he first orreltion proposed for estimting the monthly men glol solr rdition on the horizontl surfe H (MJ/m /dy) using the sunshine durtion dt ws done y (Angstrom, 9). (Presott, 90) hs put the Angstrom orreltion in more onvenient form s: ( ) () Where H is the mesured monthly men dily glol solr rdition, Ho is the monthly men extrterrestril solr rdition on horizontl surfe, n is the monthly men dily right sunshine hours. is the mximum possile monthly men dily sunshine hour or the dy length, is the lerness index, is the frtion of sunshine hours, nd is regression onstnts. A numer of orreltions whih inlude more meteorologil prmeters suh s mient temperture, the totl preipittion, reltive nd speifi humidity, mount of totl loud over et. hve een developed y different workers (Attili nd Adll, 99). he ove eqution hs een found to e very onvenient to lrge numer of lotions nd most widely used orreltion. he extrterrestril solr rdition on horizontl surfe is given y (Igl, 98) s written elow: H o I s E o 80 s sin sin os os sin s ()
5 9 Communitions in Applied Sienes Where Is is the solr onstnt, Eo is the eentriity orretion ftor, = ltitude, =solr delintion, s = hour ngle.(igl,98) gve the expressions for Is,Eo,, s follows: s 67 x 600 I s E o 0.0 os s sin 65 os 5 os tn tn tn tn Where is the hrteristi dy numer for eh month where nd re onstnts whih n e determined, Y is eing repled s Hm nd it is dependent vrile nd is the independent vrile whih n reple ny of the meteorologil dt like verge temperte, v nd reltive humidity,. Equtions () nd () re equtions of lest squre line nd lest squre prol or first nd seond order regressions respetively (Murry, 96).o exeute the regression nlysis of the first order, oth sides of eqution () hs to e multiply y nd suessively nd summing oth sides to otin Y 5 Y 6 If we pply our vriles like (v nd ) s the independent vrile in eqn. (.), we hve these equtions: v H 7 H 8 At this point, pplying verge temperture, v s our independent vrile in equtions (5) nd (6) we hve:
6 Communitions in Applied Sienes v v v v H H Equtions (9) nd (0) will e used to evlute the regression onstnts nd he si eqution for seond order regression nlysis is known s lest squre prol. o otin these equtions we hve to multiply eqution (.) y, nd suessively, nd dding them to otin equtions (), () nd (). Y Y Y Applying these equtions to solve our prolem, tht is using our vriles, suh s verge temperture nd reltive humidity we hve 5 hen sustituting v s our independent vrile in equtions (), () nd (), we otin the eqution outlined elow: v v v v v v v v v v H H H 0 9 H H H o further uttress the nlysis, the multiple orreltion nlysis ws lso pplied to evlute for H5, H6, nd H7. In this se, the multiple vriles suh
7 Communitions in Applied Sienes s verge temperture, nd reltive humidity, re used whih led to the eqution written elow. Where nd re oeffiients. If we tke = H, = nd H = v, we n now employ regression eqution of on nd nd rry out orreltion nlysis on eqution () written elow s By multiplying oth sides of eqution () y, nd suessively nd dding them to otin the outlined equtions: 5 6 Sustituting our vriles in the lst two equtions we rrive s; 5 5 v H 7 5 v 5 v H v 8 Eqution 7 nd 8 were used to evlute for H5. Similrly, H6we e estimted y using -S omintion, tht is reltive humidity nd sunshine hours whih leds to: H6 = 6 + 6S 9 he sme proedure used in otining equtions 7 nd 8 were pplied to rrived t equtions 0 nd. 6 6 S H 0 6 S 6 S 6 HS
8 Communitions in Applied Sienes Under this we n lso estimte y using nd in omintion. Hene, in rrying out the orreltion nlysis in equtions (7) nd (8) we otin: 7 7 C H 7 C 7 C HC he ury of the predited vlues ws tested y lulting the Men Bis Error (MBE), the oot Men Squre Error (MSE), the Men Perentge Error (MPE) nd the oeffiient of orreltion CC. esults le : Mesured nd Predited Solr dition for Onitsh, ( ) S/ Month MJ/M /dy MJ/M / dy MJ/M / dy MJ/M / dy MJ/M / dy MJ/M / dy MJ/M / dy MJ/M / dy JA FEB MA AP MAY JU JULY AUG SEP OC OV DEC
9 Communitions in Applied Sienes le : Mesured nd Predited Solr dition for Clr, ( ) S/ MO H MJ/M / dy MJ/M / dy MJ/M / dy MJ/M / dy MJ/M / dy MJ/M / dy MJ/M / dy MJ/M / dy JA FEB MA AP MAY JU JULY AUG SEP OC OV DEC le nd show the omprison etween the mesured glol solr rdition nd the predited one. A plot of the mesured glol solr rdition with the predited vlues gve rise to figure s nd for Onitsh nd Clr respetively, whih sientifilly gree well with le nd grphilly.
10 Glol Solr dition (MJ/M /dy) Glol Solr dition (MJ/M /dy) Glol Solr dition (MJ/M /dy) Communitions in Applied Sienes GAPHICAL EPESEAIO OF HE MEASUED AD PEDICED VALUES OF SOLA ADIAIO When the mesured nd predited vlues of solr rdition otined from model equtions were plotted, they showed lmost the sme urve. his reveled tht the model equtions n e used to predit the solr rdition of ny prt of the world tht possessessimilr limtologil ftors like tht of Onitsh nd Clr. he following plotted grphs illustrted these points etter. Eqution. (Onitsh) Mesured S Months of the Yer Fig : Comprison etween the mesured nd predited vlues of orreltion eqution for Onitsh ( ) Eqution. (Onitsh) Months of the Yer Mesured S Eqution. (Onitsh) Months of the Yer Mesured S Fig : Comprison etween the mesured nd predited vlues of orreltion eqution for Onitsh ( ) Fig : Comprison etween the mesured nd predited vlues of orreltion eqution for Onitsh ( )
11 Glol Solr dition (MJ/M /dy) Glol Solr dition (MJ/M /dy) Glol Solr dition (MJ/M /dy) Glol Solr dition (MJ/M /dy) Glol Solr dition (MJ/M /dy) Glol Solr dition (MJ/M /dy) 5 Communitions in Applied Sienes Eqution.5 (Onitsh) Months of the Yer Mesured S Eqution. (Onitsh) Mesured S Months of the Yer Fig d: Comprison etween the mesured nd predited vlues of orreltion eqution for Onitsh ( ) Eqution. (Onitsh) Fig e: Comprison etween the mesured nd predited vlues of orreltion eqution for Onitsh ( ) Fig f: Comprison etween the mesured nd predited vlues of orreltion eqution for Onitsh ( ) Months of the Yer Months of the Yer Mesured S Eqution.8 (Onitsh) Mesured S Fig g: Comprison etween the mesured nd predited vlues of orreltion eqution for Onitsh ( ) Fig : Comprison etween the mesured nd predited vlues of orreltion eqution for Clr ( ) Fig : Comprison etween the mesured nd predited vlues of orreltion eqution for Clr ( ) Eqution. (Clr) Months of the Yer Eqution. (Clr) Months of the Yer Mesured S Mesured S
12 Glol Solr dition (MJ/M /dy) Glol Solr dition (MJ/M /dy) Glol Solr dition (MJ/M /dy) Glol Solr dition (MJ/M /dy) Glol Solr dition (MJ/M /dy) Communitions in Applied Sienes 6 Fig : Comprison etween the mesured nd predited vlues of orreltion eqution for Clr ( ) Fig d: Comprison etween the mesured nd predited vlues of orreltion eqution for Clr ( ) Fig e: Comprison etween the mesured nd predited vlues of orreltion eqution for Clr ( ) Eqution. (Clr) Months of the Yer Eqution.5 (Clr) Months of the Yer Mesured S Eqution. (Clr) Months of the Yer Mesured S Mesured S Fig f: Comprison etween the mesured nd predited vlues of orreltion eqution for Clr ( ) Fig g: Comprison etween the mesured nd predited vlues of orreltion eqution for Clr ( ) COCLUSIO Eqution.8 (Clr) Months of the Yer Eqution. (Clr) Months of the Yer Mesured S Mesured S he proposed model equtions for Onitsh nd Clr n e used for estimting the monthly verge solr rdition on horizontl surfe for ny lotion in the ountry with solute vlues of the MPE less thn 8%
13 7 Communitions in Applied Sienes nd other ples outside the ountry whih hve the sme vlues of the mximum lerness index. herefore, from the ove results, it n e onluded tht the following simple first order Angstrom type orreltion n e used for the estimtion of glol solr rdition H on horizontl surfe t the lotions under study rn. So. S. Austr. Vol. 6, pp. - 8 Smo A. S, (985). Solr rdition with meteorologil dt.igeri Journl of Solr Energy Vol.. pp 59-6 EFEECES Angstrom, A.S. 9 Solr nd terrestril rdition meteorologil soiety. Vol. 50. Pp. -7 Ago, S., F.I. Ezem, nd P.E. ugwoke 007 Solr dition estimtes from eltive humidity-bsed D-model igeri Journl of solr Energy. vol. 8,pp. -8 Attili, P. nd Adll, A. (99).Sttistil omprison of glol nd diffuse solr rdition orreltion. Meteorologil Soiety, Vol 50, pp.. Iql, M. 98 An Introdution to solr rdition Ademy press.ew York. Murry, B. 96 Correltion of solr rdition with louds Solr Energy, Vol. () pp. 07. Presott, J.A 90 Evportion from wter surfe in reltion to solr rdition
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