Estimation of Global Solar Radiation on Horizontal Surfaces Over Egypt

Transcription

1 Egypt. J. Slids, Vl. (28), N. (1), (05) 163 Estimatin f Glbal Slar Radiatin n rizntal Surfaces Over Egypt A. A. El-Sebaii 1 and A. A. Trabea 2 1 Physics Department, Faculty f Science, Tanta University, Tanta, Egypt 2 Physics Department, Faculty f Educatin, Suez Canal University, Al-Arish Branch, Egypt The ured data f the mnthly average glbal slar radiatin n a hrizntal surface and the number f bright sunshine hurs n fr five lcatins in Egypt are analyzed. The selected lcatins represent the varius weather cnditins f Egypt. Matruh, Rafah and Al-Arish are in the nrth, Tanta in the middle and Aswan in the suth. The regressin cnstants fr the first, secnd and third rder Angström type crrelatins fr each lcatin have been ulated using the methd f regressin analysis. Cmparisns between ured and ulated values f are perfrmed fr the present lcatins. The values btained fr the RMSE, MBE and the MPE indicated that the secnd and third rder Angström type crrelatins d nt imprve the accuracy f estimatin f glbal radiatin. Therefre, the ured data available fr the selected lcatins are cmbined and a first rder crrelatin has been prpsed fr all Egypt. Mrever, all Egypt crrelatin is extended t ther Egyptian lcatins which are nt included in the regressin analysis. Cmparisns between ured and ulated glbal radiatin indicated that all Egypt crrelatin is applicable fr any lcatin f Egypt and may be extended utside Egypt fr places which have the same values f the maximum clearness index (a + b). 1. Intrductin: In any slar energy cnversin system, the knwledge f glbal slar radiatin is extremely imprtant fr the ptimal design and the predictin f the system perfrmance. The best way f knwing the amunt f glbal slar radiatin at a site is t install pyranmeters at many lcatins in the given regin and lk after their day-t day maintenance and recrding, which is a very cstly exercise. The alternative apprach is t crrelate the glbal slar Authr fr crrespndence: Fax: ; aasebaii@yah.cm

2 A.A. El-Sebaii and A.A. Trabea 164 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. The first crrelatin prpsed fr estimating the mnthly average daily glbal slar radiatin n a hrizntal surface (MJ/m 2 day) using the sunshine duratin data is due t Angström [1]. Presctt [2] has put the Angström crrelatin in mre cnvenient frm as / = a + b( n / N ), (1) where is the mnthly average daily extraterrestrial radiatin (MJ/m 2 day), n is the mnthly average daily bright sunshine hurs, N is the maximum pssible mnthly average daily sunshine hurs r the day length and a and b are cnstants. A number f crrelatins which include mre meterlgical parameters such as latitude, ambient temperature, the ttal precipitatin, relative and specific humidity, the elevatin, amunt f clud cver.etc have been develped by different wrkers [3-]. Equatin (1) has been fund t be very cnvenient t a large number f lcatins and the mst widely used crrelatin [3, 6, 9]. A new methd has been prpsed by Karsten [11] t evaluate the cefficients f Eq. (1) a and b. e assumed that a has the physical meaning f the mnthly average daily diffuse radiatin transmittance d / 0 and b has the meaning f the mnthly average daily beam radiatin transmittance b / 0. Singh et al [12], Fagbenle [13], Shaltut [14] and Ulgen and epbasli [] have estimated a new set f cnstants fr the secnd and third rder Angström type crrelatins. It has been cncluded that the secnd r the third rder crrelatins give the best verall estimate f glbal slar radiatin n a hrizntal surface. Recently, Ulgen and epbasli [16] have crrelated the glbal and diffuse radiatin with respect t the ambient temperature in the fifth rder plynmial frm fr Izmir in Turkey. They have utlined that their mdel predicts the glbal and diffuse slar radiatin n hrizntal surfaces reasnably well with crrelatin cefficients ver The bjective f the present study is t present and analyze the glbal slar radiatin and sunshine duratin data recrded at five cities (Matruh, Rafah, Al-Arish, Tanta and Aswan) in Egypt, and t develp new cnstants fr the first, secnd and third rder Angström type crrelatins which may be used

3 Egypt. J. Slids, Vl. (28), N. (1), (05) 165 fr estimating at any lcatin f Egypt. Perfrmance f the new cnstants is checked by cmparing the estimated and ured values f glbal slar radiatin. Statistical cmparisns between ured and estimated glbal slar radiatin indicated that the secnd and third rder Angström type crrelatins d nt imprve the accuracy f estimatin f glbal slar radiatin. Therefre, first rder r linear crrelatins between the mnthly average daily clearness index / and the relative pssible sunshine duratin n / N fr the selected lcatins and als fr all Egypt have been prpsed. All Egypt crrelatin is then extended t ther fur Egyptian lcatins nt included in the regressin analysis. It is cncluded that the crrelatin prpsed fr all Egypt can be used successfully fr estimatin f fr any lcatin f Egypt with a reasnable accuracy and may be extended utside Egypt fr lcatins f similar meterlgical characteristics. 2. Methdlgy: The mst widely used relatinship t estimate mnthly average daily glbal radiatin n a hrizntal surface is that given by Angström [1], Eq. (1). The fllwing secnd and third rder Angström type crrelatins have been als prpsed by different authrs [12-14, 16] / a b( n / N ) + c( n / N ) 2 = +, (2) / a b( n / N ) c( n / N ) + d( n / N ) 2 3 = + +, (3) where a, b, c and d are the regressin cnstants that depend n the lcatin. The data f glbal radiatin, which ured by the Epply Precisin Pyranmeters (with linearity ± 5% frm 0 t 2800 W/m 2, accuracy better than 0.5% and reslutin f 1 W/m 2 ) and the number f bright sunshine hurs fr five lcatins in Egypt are used in linear and multilinear regressin analysis t find the regressin cnstants f Eqs. (1)-(3). Fr all lcatins except fr Tanta, the data ured n a perid f 5 years ( ) are used fr the present analysis. Fr Tanta, the data ured during three years ( ) are emplyed [17]. Table 1 gives a list f the five lcatins and their gegraphical lcatins. Prper cmputer prgrams are prepared fr the analysis. The mnthly mean daily extraterrestrial radiatin and the maximum pssible mnthly average daily sunshine duratin N needed fr the ulatins are estimated using the standard prcedure [18]. The develped crrelatins are then emplyed t ulate the glbal radiatin fr the five lcatins. The ulated values f glbal radiatin are then cmpared with the ured data fr these lcatins. The accuracy f the estimated glbal radiatin data is tested by

4 A.A. El-Sebaii and A.A. Trabea 166 ulating the mean bias (MBE), rt mean square (RMSE) and the mean percentage (MPE) errrs. The MBE (MJ/m 2 day), RMSE (MJ/m 2 day) and MPE (%) are defined as fllws: where i, cal and i, ( MBE = [ i, cal i, )]/ n, (4) 2 1/ 2 RMSE = {[ ( i, cal i, ) / n}, (5) i, i, cal MPE = [ ( 0)]/ n, (6) i, is the ith ulated and ured values and n is the ttal number f bservatins. In general, a lw RMSE is desirable. The psitive MBE shws verestimatin while a negative MBE indicates underestimatin. Table (1): Gegraphical lcatins f the selected statins. Lcatin Latitude (N) Lngitude (E) Elevatin (m) Matruh AL-Arish Rafah Tanta Aswan Results and discussins: The lcatins selected in the present study are Matruh, Rafah and Al-Arish (nrth Egypt); Tanta (middle Egypt) and Aswan (suth Egypt). The analysis f the ured and ulated shws that fr all lcatins in cncern, the maximum values f glbal slar radiatin are bserved in June while the minimum values are appeared in December. The btained values f the regressin cnstants f Eqs. (1)-(3) alng with the crrelatins regressin cefficients (RC) and the values f the MBE, RMSE and MPE fr the five lcatins are summarized in Table 2. Frm the results f Table 2 it is bvius that fr all selected lcatins, the values f the regressin cefficients (RC) f the prpsed crrelatins are higher than 0.95 which indicate excellent fitting between the clearness index / and the relative pssible number f sunshine hurs n / N. Furthermre, there is a remarkable agreement between the ured and ulated values f glbal radiatin fr the five lcatins. The RMSE and MPE values are als very lw, indicating fairly gd

5 Egypt. J. Slids, Vl. (28), N. (1), (05) 167 agreement. The negative values f the MPE indicate that the present crrelatins slightly verestimate. The highest value f the MPE equals 1.39% that btained fr the secnd rder crrelatin prpsed fr Tanta. As als seen frm the values f the RC, MBE, RMSE and the MPE the secnd and third rder Angström type crrelatins d nt significantly imprve the accuracy f estimatin f glbal slar radiatin fr the five lcatins. The latter results are als cnfirmed fr each mnth fr all lcatins under study. Cmparisns between ured and ulated estimated using Eqs. (1)-(3) alng with the regressin cnstants given in Table 2 indicated that the percentage errr fr a single mnth rarely exceeds ± % in any f the lcatins. Again, the secnd and third rder crrelatins d nt increase the accuracy f estimatin f glbal radiatin. Fr example, the estimated annual average daily values f glbal slar radiatin at Matruh are btained as.018,.0 and.0 (MJ/m 2.day) using Eqs. (1), (2) and (3) respectively; while, the ured value equals (MJ/m 2. day). The crrespnding values fr Aswan are fund t be , and (MJ/m 2. day) cmpared t the ured value which equals (MJ/m 2. day). Frm the abve results it can be cncluded that the fllwing simple first rder Angström crrelatins can be used fr estimatin f n a hrizntal surface at the five lcatins under study: 1. Al-Arish / = ( n / N ), (7) 2. Rafah / = ( n / N ), (8) 3. Matruh / = ( n / N ), (9) 4. Tanta / = ( n / N ), () 5. Aswan / = ( n / N ), (11) It is seen frm Eqs. (7-11) that neither a nr b vary with latitude r altitude in any systematic manner. wever, the values f the sum f the regressin cnstants a + b ; which represent the maximum clearness index ( ( n / N ) = 1) averaged ver the perid f recrding the data, are fund t be almst equal fr the cnsidered lcatins. The values f the sum a + b are btained as 0.718, 0.709, 0.694, and fr Al-Arish, Rafah, Matruh, Tanta and Aswan, respectively.

6 A.A. El-Sebaii and A.A. Trabea 168 Table (2): Regressin cnstants f Eqs. (1) (3) fr the selected lcatins and the crrespnding values f the RC, MBE, RMSE and the MPE. Lcati n Rafah AL- Arish Degree f crrelatin First Secnd Third First Secnd Third RC Regressin cnstants a b c d MBE RMSE MPE (%) Matruh First Secnd Third Tanta First Secnd Third Aswan First Secnd Third Since, the secnd and third rder crrelatins between / and n / N d nt imprved the accuracy f estimatin f, the ured data available fr the five selected lcatins are cmbined and analyzed in rder t develp a first rder crrelatin fr all Egypt. The fllwing linear crrelatin has been btained fr all Egypt: / = ( n / N ) ; (12) with RC = and a maximum clearness index equal 0.7. Similar results are btained fr sme lcatins at Yemen Arab Republic (YAR) [19]; where, the values f a + b are fund in the range Equatin (12) is then emplyed fr estimating fr the five lcatins. Sme examples f cmparisns between ured and ulated (estimated using all Egypt crrelatin) are shwn in Figs. 1, 2 and 3 fr Rafah, Tanta and Aswan, respectively. A fairly gd agreement between ured and ulated glbal radiatin fr all lcatins is clear. The percentage errr fr estimating fr Tanta and Matruh fr a single mnth never exceeds ± 12%;

7 Egypt. J. Slids, Vl. (28), N. (1), (05) 169 hwever, fr the ther lcatins (Al-Arish, Rafah and Aswan) it is less than ± 9%. Furthermre, Eq. (12) is als emplyed fr estimating the mnthly average daily glbal radiatin fr ther Egyptian lcatins which are nt included in the present regressin analysis. These lcatins include Cair ( Lat ), Bahtim (Lat ), Tahrir (Lat ) and Asyut (Lat ). The ured data (mnthly average daily glbal radiatin and bright sunshine hurs) fr these lcatins are taken frm the data given by Kamel et al. []. Figures (4-7) present cmparisns between ured and ulated, using Eq. (9), fr Cair (Fig. 4), Bahtim (Fig. 5), Tahrir (Fig. 6) and Asyut (Fig. 7). Frm the results f these figures it is bvius that the agreement between ured and ulated data fr all lcatins that are nt included in the regressin analysis is excellent. It is fund that Eq. (9) can be used fr estimating at Cair, Bahtim, Tahrir and Asyut with abslute values f the MPE f abut 2.4, 3.5, 5.9 and 3.6%, respectively. The values f the MBE are fund t be 0.032, 0.042, and fr Cair, Bahtim, Tahrir and Asyut, respectively. The lw values f the RMSE, MBE and the MPE clearly prve that the prpsed crrelatin fr all Egypt, Eq. (9), can be used fr estimatin f glbal slar radiatin n a hrizntal surface at any lcatin f Egypt. 30 RAFA (MJ/m 2.day), Eq. (9) Mnth Fig. (1): Cmparisns between ured and ulated mnthly average glbal slar radiatin n a hrizntal surface at Rafah. Calculatins perfrmed using all Egypt crrelatin, Eq. (9).

8 A.A. El-Sebaii and A.A. Trabea 170 (MJ/m 2.day), Eq. (9) Mnth Fig. (2): As the same fr Fig. 1 but fr Tanta. 30 ASWAN (MJ/m 2.day), Eq. (9) Mnth Fig. (3): As the same fr Fig. 1 but fr Aswan.

9 Egypt. J. Slids, Vl. (28), N. (1), (05) CAIRO (MJ/m 2.day) [], Eq. (9) Mnth Fig. (4): Cmparisns between ured and ulated fr Cair. Calculatins perfrmed using all Egypt crrelatin, Eq. (9). Measured data are nt included in the regressin analysis. 30 BATIM (MJ/m 2.day) [], Eq. (9) Mnth Fig. (5): As the same fr Fig. 4 but fr Bahtim.

10 A.A. El-Sebaii and A.A. Trabea TARIR TARIR (MJ/m 2.day) [], Eq. (9) Mnth Fig. (6): As the same fr Fig. 4 but fr Tahrir. 30 TARIR ASYUOT (MJ/m 2.day) [], Eq. (9) Mnth Fig. (7): As the same fr Fig. 4 but fr Asyut.

11 Egypt. J. Slids, Vl. (28), N. (1), (05) 173 Since, the maximum clearness index ( a + b ) btained frm all Egypt crrelatin is fund t be almst equal t that btained fr YAR (see Table 5 in Ref. 19), Eq. (12) is als used t estimate fr sme cities in YAR. The ulated data f are cmpared with the ured nes given in Ref. 19. The btained results are summarized in Table (3) fr five cities in YAR which include Sana a, Taiz, El Macha, Al Khaber and El Bun. It is seen frm the results f Table 3 that the agreement in general is fairly gd. The relative percentage difference between ured and ulated glbal radiatin (PE) fr all cities fr a single mnth (except n August r September fr Sana a, Al khaber and Al Bun) rarely exceeds 5% and in mst cases it is much less. It is als bvius frm the lw values btained fr the RMSE and the MBE that all Egypt crrelatin estimates the mnthly and annual averages daily f glbal radiatin fr the present YAR cities with very gd accuracy; cnsequently, the lng-term perfrmance f slar energy devices can be estimated. Table (3). Cmparisns between ured [19] and ulated (Eq. (9)) mnthly average daily glbal radiatin (MJ/m 2 day) at sme cities in YAR. J F M A M Twn Mnth Sana a.51 N Taiz N El Macha 13. N Al Khaber N El Bun.73 N

12 A.A. El-Sebaii and A.A. Trabea 174 J J A S O N D Annual Average RMSE MBE

13 Egypt. J. Slids, Vl. (28), N. (1), (05) Cnclusins: On the basis f the btained results fr five lcatins in Egypt, the fllwing cnclusins may be drawn: (i) The secnd and third rder Angström type crrelatins d nt significantly imprve the accuracy f estimatin f the mnthly average daily glbal radiatin incident n a hrizntal surface. Therefre, a first rder crrelatin is prpsed fr each lcatin, Eqs. (4) - (8). (ii) The prpsed first rder crrelatins are able t predict the glbal radiatin with percentage errr fr a single mnth never exceeds ± % in any f the lcatins. (iii) The prpsed crrelatin fr all Egypt, Eq. (9), can be used fr estimating fr any lcatin f Egypt with abslute values f the MPE less than 6%. All Egypt crrelatin may be extended utside Egypt fr places which have the same values f the maximum clearness index. References: 1. A. Angström, Q. J. Ry. Met. Sc. 50, 121 (1924). 2. J.A. Presctt, Trans. Ry. Sc. Austr. 64, 114 (1940). 3. K.K. Gpinathan, Slar Energy 41 (6), 499 (1988). 4. N. aluani, C.T. Nguyen, D. V-Ngc, Slar Energy, 50 (3), 247 (1993). 5..P. Garg and S.N. Garg, Energy Cnvers. Mgmt., 23 (2), 113 (1983). 6. Lin Venxian. Slar Energy, 41 (1), 1 (1988). 7. B.S. Attili and Y.A.G. Abdalla, Energy Cnvers. Mgmt., 34 (1), 1 (1993). 8. I. Supit and R.R. Vankappel, Slar Energy, 63 (3), 147 (1998). 9. S. Ahmed and Taher Abuain. Energy Cnvers. Mgmt., 33 (2), 117 (1992).. A.A. Trabea, M.A. Msalam Shaltut, Renewable Energy, 21, 297 (00). 11. Karsten inrichsen, Slar Energy, 52 (6), 491 (1994). 12. O.P. Singh and S.K. Srivastawa, Gaur, Energy Cnvers. Mgmt., 37 (4), 501 (1996). 13. R. Layi Fagbenle, Int. J. Energy Research, 16, 583 (1992). 14. M.A. Msalam Shaltut, ASRE, 1 (4), 35 (1986).. K. Ulgen and A. epbasli, Int. J. Energy Research, 26, 413 (02). 16. K. Ulgen and A. epbasli, Int. J Energy Research, 26, 807 (02). 17. A.A. El-Sebaii, M. Sc. Thesis, Tanta University, Egypt (1989). 18. J.A. Duffie and W.A. Beckman, Slar engineering f thermal prcesses, 2 nd editin. New Yrk: Jn Wiley and Sns Inc., (1991). 19. A. Khgali, M.R.I. Ramadan, Z.E.. Ali and Y.A. Fattah, Slar Energy, 31(1), 55 (1983).. M.A. Kamel, S.A. Shalaby and S.S. Mstafa, Slar Energy, 50 (6), 463 (1993).