Research ArticleCorrelation of Global Solar Radiation of Eight SynopticStations in Burkina Faso Based on Linear and MultipleLinear Regression Methods
Ousmane Coulibaly1 and Abdoulaye Ouedraogo2
1Laboratoire de Physique et Chimie de lrsquoEnvironnement (LPCE) Unite de Formation et de Recherche en SciencesExactes et Appliquee Universite de Ouagadougou 03 BP 7021 Ouagadougou 03 Burkina Faso2Unite de Formation et de Recherche en Sciences Exactes et Appliquee Universite de Ouagadougou 03 BP 7021Ouagadougou 03 Burkina Faso
Correspondence should be addressed to Ousmane Coulibaly coulous2005yahoofr
Received 7 August 2015 Revised 11 December 2015 Accepted 31 January 2016
Academic Editor Yoji Saito
Copyright copy 2016 O Coulibaly and A Ouedraogo This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited
We utilize the multiple linear regression method to analyse meteorological data for eight cities in Burkina Faso A correlationbetween themonthlymean daily global solar radiation on a horizontal surface and fivemeteorological and geographical parameterswhich are the mean daily extraterrestrial solar radiation intensity the average daily ratio of sunshine duration the mean dailyrelative humidity the mean daily maximum air temperature and the sine of the solar declination angle was examined A secondcorrelation is established for the entire country using this time the monthly mean global solar radiation on a horizontal surfaceand the following climatic variables the average daily ratio of sunshine duration the latitude and the longitude The results showthat the coefficients of correlation vary between 096 and 099 depending on the station while the relative errors spread betweenminus316 (Po) and 365 (Dedougou) The maximum value of the RMSD which is 31236 kJm2 is obtained at Dori which receivesthe strongest radiation For the entire cities the values of the MBD are found to be in the acceptable margin
1 Introduction
The quantification of the solar energy potential depends onmany parameters such as the availability the number andlocation of synoptic stations and the utilization of adequateformalism for its evaluation A review of solar radiationmodels [1] and measurement techniques [2] are presentedby Pandey and Katiyar They noted that the first correlationhas been suggested by Angstrom [3] it relates the globalsolar radiation to sunshine duration The modification ofthe Angstrom relation has been made by Page [4] andPrescott [5] Afterwards many other researches have beenaccomplished in specific countries throughout the world forexample in Romania [6] inMalaysia [7] in Iran [8] in China[9] and in Ghana [10] In 2006 some of these countries havebeen compiled by Skeiker [11] Many investigators [12 13]
have utilized the latitude and the solar declination Yet othershave introduced geographical andmeteorological parameters[14ndash16] Recently Dumas et al presented a new correlationbetween global solar energy radiation and daily temperaturevariations [17]
In Burkina Faso preliminary investigations have beenmade by Garane [18] and Baldy [19] who established a cor-relation between the solar radiation and the sunshine dura-tion spanning from 1971 to 1990 (Garane) and 1971 to 1975(Baldy) for five cities In the present study we look forward toextending the early investigations by determining first of allthe coefficients of the modified Angstrom correlation notedas 119886 and 119887 for eight cities Next we seek to establish suc-cessively correlation relations between the global radiationand five climatic variables for the eight cities Finally themonthly mean global solar radiation on a horizontal surface
Hindawi Publishing CorporationJournal of Solar EnergyVolume 2016 Article ID 7870907 9 pageshttpdxdoiorg10115520167870907
2 Journal of Solar Energy
Table 1 Geographical locations of the eight cities of concern [20]
Cities Ouaga Dori Bobo Gaoua Fada Boromo Po DedougouLatitude (N) 12∘211015840 14∘021015840 11∘111015840 10∘201015840 12∘021015840 11∘451015840 11∘101015840 12∘281015840
Longitude (W) 01∘311015840 00∘021015840 04∘191015840 03∘111015840 00∘221015840E 02∘561015840 01∘091015840 03∘291015840
Altitude (m) 296 277 432 333 308 270 326 308
and the following climatic variables the average daily ratio ofsunshine duration the latitude and the longitude would beinvestigated
2 Equipment and Data Collection
21 Equipment Setup and Data Acquisition The sunshinedurations are meteorological data and are measured by aheliograph of Campbell-Stokes type designed by CASELLAThe data acquisition process is made according to the worldorganization of meteorology standards from heliographbands The global radiation is measured utilizing KIPP andZONEN Pyranometer with numerical ELSB-2 integratorswhich integrates the values of the daily solar radiation Twostations Dedougou and Fada Nrsquogourma are equipped withpyranometer-integrator of CIMEL type which integrates thehourly values of the global solar radiation intensityThe appa-ratuses are installed on concrete construction approximately15 meter in height in places released in order to avoidthe shadow of the surrounding objects Table 1 indicates thelatitude the longitude and the altitude of the eight stations ofconcern Data for global solar radiation sunshine durationthe maximum temperature and relative humidity have beencollected for all cities from 1977 to 2006 [20]
22 Estimation of the Extraterrestrial Solar Radiation on aHorizontal Surface (119867
119900) and the Maximum Sunshine Dura-
tion The extraterrestrial radiation on a horizontal surface(119867119900 kJm2) is determined utilizing the following relation [21ndash
23] Indeed the measurement data of global solar radiationprovided by the national meteorological service are in kJm2Consider
119867
119900= 3795
sdot 10
4 cos (120601) cos (120575) [sin (120596119904) minus
120587120596
119904
180
cos (120596119904)]
(1)
The quantity 3795 sdot 104 given by Jannot [22] to convert theextraterrestrial radiation into kJm2 comes from the term(24120587)lowast119868
0The value of the solar constant 119868
0used by Jannot is
1380Wm2 This quantity takes into account the eccentricitycorrection factor of Earthrsquos orbit which is calculated using thefollowing relation
119862 = 1 + 0034 cos [30 (119898 minus 1) + 119889] (2)
In relations (2) and (4)119898 is the number of the month in theyear starting with January and 119889 the number of the day in themonth Let us announce that by carrying out the calculationprogramme under the Matlab software we took account ofconversions on each time the need is essential
In relations (1) and (3)120601 is the latitude120596119904is the solar angle
of the sundown obtained from the next relation
120596
119904= 119886119903 cos (minus tan (120601) tan (120575)) (3)
120575 is the declination which is inferred from the followingequation
120575 = 2345
∘ cos (30119898 + 119889 minus 202) (4)
We also define the hour angle 120596 as follows
120596(∘) = minus15
∘(12 minus 119879
119904) (5)
where 119879119904is the solar hour of the day The hour angle 120596
119888at
sunset is opposite to its sundown equivalent therefore 120596119888=
minus120596
119897The solar hour at sunrise is given by
(119879
119904)
119897= 12 minus
120596
119904
15
(6)
At sunset the equivalent solar hour becomes
(119879
119904)
119888= 12 +
120596
119904
15
(7)
We can then infer the maximum daily sunshine duration asfollows
119873 =
2120596
119904
15
(8)
3 Estimation of the Regression Coefficients
First of all we averaged over one-year interval the globalradiation (119867) and the sunshine duration data collected bythe national meteorological service from 1992 to 2006 Nextwe estimate the extraterrestrial radiation on a horizontalsurface (119867
119900) and the maximum sunshine duration (119873) for
each station for the entire year Finally a linear relation ofAngstrom type is utilized for a correlation between the indexof clearness (119867119867
119900) and the daily ratio of sunshine duration
(119899119873)Now let us recall the original Angstrom formula which is
[3]
119867 = 119867
1015840
119900(119886
1015840+ 119887
1015840 119899
119873
) (9)
where 119899 is the number of hours of daily sunshine duration119873is the maximum number of hours of daily sunshine duration119867 is the daily global radiation on a horizontal surface 1198671015840
119900is
the daily global radiation on a horizontal surface by clear skyand 1198861015840 and 1198871015840 are coefficients to be determined
Journal of Solar Energy 3
In the original Angstrom formula (9) 119867
1015840
119900is found
to be difficult to determine Thus Page [4] and Prescott[5] formulated a modified relation in a manner that theextraterrestrial radiation on a horizontal surface119867
119900appears
that is
119867 = 119867
119900(119886 + 119887
119899
119873
) (10)
Here 119886 and 119887 are constants to be determined experimentallyfor each region
We rewrite relation (10) in a more useful form as follows
119867
119867
119900
= 119886 + 119887
119899
119873
(11)
In this relation the ratio 119867119867
119900usually denoted by 119870
119879is
known as the index of clearness It is an indication of thedegree of purity of the atmosphere it indicates the presence ofaerosols or water molecules in the atmosphereThe ratio 119899119873is the fraction of sunshine duration expressed as the quotientof the actual (119899) divided by the theoretical (119873) sunshineduration The coefficients 119886 and 119887 are obtained by drawingthe fraction of sunshine duration as a function of the indexof clearness then 119886 is the ordinate and is an indication of thevalue of the fraction of the incident radiation for a coveredsky 119887 on the other hand is the slope of the regression lineThe sum (119886 + 119887) gives an indication on the transmissivity ofthe atmosphere in condition of clear sky [18]
For each city a correlation is established between theglobal solar radiation on a horizontal surface and five mete-orological parameters which are the mean daily extrater-restrial solar radiation intensity the average daily ratio ofsunshine duration the mean daily relative humidity themean daily maximum air temperature and the sine of thesolar declination angle For the entire country a correlationis realized involving the index of clearness the average dailyratio of sunshine duration and the latitude and longitude Forthe relations of correlation involving many parameters wehave utilized amultiple linear regression suggested by Skeiker[11]
119910 = 119888 + 119889119909
1+ 119890119909
2+ 119891119909
3+ 119892119909
4+ ℎ119909
5 (12)
where 119888 119889 119890 119891 119892 ℎ are the regression coefficients and 119909
1
119909
2 1199093 1199094 1199095the correlation parameters The relative error
between the measured and estimated quantities is calculatedfrom the following relation
119890 = [
(119867
119894119898minus 119867
119894119888)
119867
119894119898
] sdot 100
(13)
where 119867119894119898
is the monthly average of daily global radiationmeasured over a horizontal surface for the 119894thmonth and119867
119894119888
is its value obtained from the relation of correlationUsually aprecision in the interval of minus10 to 10 is acceptable Skeiker[11] For the same purpose we can also compute statistical testparameters such as the root mean square differences (RMSD)
035040045050055060065070
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov DecMonth
HH
o
Ouaga
DoriFada
Boromo
Bobo
GaouaDeacutedougou
Pocirc
Figure 1 Indexes of clearness for the eight synoptic stations
and the mean bias differences (MBD) given by the followingrelations
RMSD = (
1
119899
119899
sum
119894=1
(119867
119894119898minus 119867
119894119888)
2
)
12
(14)
Equation (14) provides information on the short term perfor-mances of the correlations by allowing a term by term com-parison between the calculated and the measured valuesThesmaller the deviations are the better themodelrsquos performancesare Consider
MBD =
1
119899
119899
sum
119894=1
(119867
119894119898minus 119867
119894119888) (15)
The above test relation provides information on the longterm performance A low MBD is desired A positive valuegives the average amount of underestimation in the cal-culated value and vice versa A drawback of this test isthat overestimation of an individual observation will cancelunderestimation in a separate observation
On the other hand the performance of themodel is testedby the following statistical equation
119905 = [
(119899 minus 1)MBD2
RMSD2 minusMBD2]
12
(16)
The smaller the value of 119905 the better themodelrsquos performanceThe critical quantity is calculated at 119905
1205722where 120572 is the level of
significance and (119899minus1) the degrees of freedomThe degree ofconfidence is about 95 which sets 120572 = 5 and 1205722 = 25
4 Results and Discussion
41 Index of Clearness and Daily Ratio of Sunshine DurationFigure 1 indicates the mean values of the indexes of clearnessfor the eight synoptic stations The indexes are comprisedbetween 036 and 066 which indicates that the atmospherecontains impurities all year longThe lowest value is obtainedat Gaoua a region with a tradition of relatively heavy rainfallThis lowest index is therefore due to the albedo of the cloud
4 Journal of Solar Energy
Table 2 Statistics of regression with modified Angstrom model comparison of the results obtained by the current investigation with thoseof other investigations
TownRegression coefficients 119886 119887 119877
119886 119887 119886 + 119887
(1) (2) (3) (1) (2) (3) (1) (2) (3) (1) (2) (3)Dori 013 014 024 062 058 052 075 072 076 095 084 gt90Fada NrsquoGourma 021 020 026 045 049 048 066 069 074 091 071 gt90Ouagadougou 017 022 027 047 045 048 064 067 075 095 090 gt90Bobo Dioulasso 021 026 031 046 043 048 067 069 079 090 079 gt90Gaoua 015 022 026 046 046 048 061 068 074 096 092 gt90Boromo 018 mdash mdash 053 mdash mdash 071 mdash mdash 097 mdash mdashPo 021 mdash mdash 043 mdash mdash 064 mdash mdash 093 mdash mdashDedougou 023 mdash mdash 04 mdash mdash 063 mdash mdash 091 mdash mdashBurkina Faso 018 023 026 049 044 042 067 067 068 081 078 mdash(1) Results obtained by the actual investigation(2) Results obtained by Garane J Ali Period 1971ndash1990(3) Results obtained by Baldy Period 1971ndash1975
and the presence of water molecules in the atmosphere Thehighest index 066 is obtained at Dori a city located atthe northern tip of the country with scarce rainfalls For alleight stations the highest values are observed between themonths of November and February This period correspondsto the dry season with no cloud in the sky However the066 index is an indication of the presence of impurities inthe atmosphere which is due to the important phenomenonof absorption and diffusion of solar radiation by the aerosolparticles During this period the strong winds of harmattancarrying dust sand and many other small objects feed theatmosphere with aerosol particles of all sizes Indeed Lathaand Badarinath [24] have noticed that the concentration ofaerosol particles of sizes PM
10and PM
25is strong during
the same period (harmattan) and weak on the other handduring June to October (monsoon) in urban area in tropicalregions At Gaoua Fada and Bobo Po and Boromo thepermanence and the concentration of the clouds during themonth of August explain the strong drop of the indexes ofclearness On the contrary the increase during the month ofOctober is due to the purity of the atmosphere just after theend of the raining season Figure 2Thedaily ratio of sunshineduration varies between 045 and 086 and represents the ratioof the real sunshine duration (119899) and the theoretical sunshineduration (119873) the nationalmean value being 068 Townswithlower latitudes have lower value of the daily ratio of sunshineduration once again due to the heavy rainfalls which shortenthe sunshine duration
42 The Regression Coefficients of the Modified AngstromrsquosRelation We show in Table 2 the results of this researchbased on the relation of Angstrom For all the stationsthe correlation coefficient 119877 is greater than 090 We nextcompare the actual coefficients with the preliminary resultsestablished by Garane [18] and Baldy [19] for five stations
The values of (119886 + 119887) are quite similar For the valuesobtained throughout the country the coefficient (119886) ratherdecreases from (3)
119888 to (1)
119886 and (119887) increases somehow in
040045050055060065070075080085090
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov DecMonth
nN
Ouaga
DoriFada
Boromo
Bobo
GaouaDeacutedougou
Pocirc
Figure 2 Daily ratio of sunshine duration for the eight synopticstations
the same period from (3)
119888 to (1)
119886 This is an indication ofthe presence of aerosols in the atmosphere The values of thecorrelation coefficients 119877 which are greater than 090 for allcities tend to indicate good correlations between the globalradiation and the sunshine duration On the other hand themean value of 081 for the entire country is a good indicationof the disparities between the radiation intensities of theregions due to the latitude especially when we move fromnorth to south We present next the correlation results whenwe take into account the latitude and longitude
43 Correlation of the Radiation Intensity for the Eight Syn-optic Stations Table 3 shows the regression and correlationcoefficients obtained for each synoptic station Substitutingthe correlation parameters 119909
1 1199092 1199093 1199094 and 119909
5in relation
(12) respectively by119867o 119899119873119867119903 119879max and sin 120575 we obtain
the following
119867 = 119888 + 119889119867
119900+ 119890
119899
119873
+ 119891119867
119903+ 119892119879max + ℎ sin 120575 (17)
Journal of Solar Energy 5
Table 3 Regression and correlation coefficients for the eight synoptic stations
Town Regression coefficients Correlation coefficients 119877119888 119889 119890 119891 119892 ℎ
Ouagadougou minus4202917 147 2827241 minus5234 minus28851 minus715912 09921Dori minus2970840 118 2470840 minus4267 minus21596 minus566502 09663Bobo minus2534865 125 1946764 minus7046 minus30073 minus496691 09716Fada minus1252850 084 1191321 minus5395 minus13242 minus279462 09703Boromo minus1867415 088 2633683 minus5352 minus23908 mdash 09718Gaoua minus3259717 118 2239381 minus2937 minus20406 minus608006 09958Po minus5851229 231 4106196 minus8936 minus84351 minus1058665 09661Dedougou minus5879168 176 3619121 minus1337 minus29869 minus980501 09782
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Mon
thly
mea
n da
ily g
loba
lso
lar r
adia
tion
(kJ(
m2middotd
ay))
15
16
17
18
19
20times10
3
Measured valuesMultiple regressionAngstrom equation
Figure 3 Comparison between measured and correlated values atOuagadougou
Hence for a given station the correlation between the globalradiation on a horizontal surface and the five parameters isobtained by replacing the regression coefficients 119888 119889 119890 119891 119892and ℎ with their respective numerical values
The values of the regression coefficients 119888 119889 119890 119891 119892 andℎ vary both with and within the same location The studyof Skeiker [11] showed that when the number of regressioncoefficients for the multiple linear regression models ishigher results obtained are better The correlation obtained isnevertheless good between the parameters The lowest valueof the correlation coefficient 119877 is obtained at Po (119877 = 09661)while the highest is reached at Gaoua (119877 = 09958) Forthe city of Boromo a correlation is established between themonthly mean daily global solar radiation on a horizontalsurface and four parameters because the coefficient ldquoℎrdquo showsa different behavior to the rest of the city when we take intoaccount the solar declination angle
We compare in the following Figures 3ndash6 the measuredsolar radiation intensity its estimated values obtained fromthe Angstrom relation and the results obtained from thecorrelations based on the five meteorological parametersThe figures clearly show two picks corresponding to two hotseasons respectively fromMarch to June and in October Asfor the indexes of clearness and the ratio of sunshine durationthe lowest radiation values are observed during the rainingseason
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Mon
thly
mea
n da
ily g
loba
lso
lar r
adia
tion
(kJ(
m2middotd
ay))
times103
15
17
19
21
23
Measured valuesMultiple regressionAngstrom equation
Figure 4 Comparison between measured and correlated values atDori
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Mon
thly
mea
n da
ily g
loba
lso
lar r
adia
tion
(kJ(
m2middotd
ay))
times103
15
16
17
18
19
20
Measured valuesMultiple regressionAngstrom equation
Figure 5 Comparison between measured and correlated values atBoromo
The histograms show clearly when comparing the mea-sured and the correlation values with the Angstrom relationresults that the meteorological parameters (humidity tem-perature and declination) have an influence on the globalradiation intensity received by a horizontal surface Tables4(a)ndash4(d) display the values of the measured global radiationand the correlated values based on the five meteorologi-cal parameters We present also the statistical parametersobtained in each case
6 Journal of Solar Energy
Table4(a)119890M
BDR
MSD
119905and
119905-criticforO
uagado
ugou
andDori(b)119890M
BDR
MSD
119905and
119905-criticforB
oboandFada(c)119890M
BDR
MSD
119905and
119905-criticforB
orom
oandGaoua(d)
119890M
BDR
MSD
119905and
119905-criticforP
oandDedou
gou
(a)
Mon
thOuagado
ugou
Dori
Ann
ualstatistics
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Janu
ary
1593619
1580818
080
12802
1883522
189091
6minus039
minus7394
February
179438
1181673
8minus12
5minus22357
211576
9210470
1053
11068
March
1871065
1846550
131
24515
2237844
2194349
198
43495
April
1860
079
1871814
minus063
minus11734
220313
42259076
minus248
minus5594
2May
189695
7191010
0minus069
minus1314
32228402
2241255
minus057
minus12854
June
1851597
1830751
113
20846
2164
215
2128711
167
35504
July
1709075
1712545
minus020
minus3470
2110696
208818
710
822509
August
156770
1157890
0minus071
minus1119
92025322
2083244
minus278
minus5792
3Septem
ber
1738429
1735441
017
2988
212670
7209595
514
730752
Octob
er1783503
1770843
071
12660
2075201
2067421
038
7780
Novem
ber
168916
9169873
6minus057
minus9567
1980527
1983045
minus013
minus2518
Decem
ber
1583508
1585848
minus015
minus2341
1852580
1867057
minus078
minus14477
minus273Eminus12
909E
minus13
MBD
1418
131236
RMSD
638Eminus14
966E
minus15
119905
2201
2201
119905-critic
(b)
Mon
thBo
boFada
Ann
ualstatistics
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Janu
ary
1670671
1693578
minus13
7minus2290
7177792
01761675
091
16245
February
1927308
191292
7075
14381
1947206
1919814
141
27392
March
193975
81946355
minus034
minus6597
199476
41993531
006
1233
April
1892000
1885458
035
6541
1977473
2004
124
minus13
5minus26651
May
188078
31901057
minus10
8minus20275
1990334
1990476
minus001
minus14
2June
181798
51795433
124
22551
1919464
1905735
072
1372
9July
1687848
1687692
001
156
1825211
182194
5018
3266
August
1607626
163990
3minus201
minus32277
175710
4174992
4041
7181
Septem
ber
1774492
1722878
291
51614
1757560
179695
4minus224
minus39394
Octob
er1736800
1783496
minus269
minus46
696
180374
31764
291
219
39452
Novem
ber
1734772
1703431
181
31341
1776281
177078
2031
5498
Decem
ber
160979
61607629
013
2167
1692480
1740289
minus282
minus47809
144E
minus11
142E
minus11
MBD
2678
724835
RMSD
178E
minus13
190E
minus13
119905
2201
2201
119905-critic
Journal of Solar Energy 7
(c)
Mon
thBo
romo
Gaoua
Ann
ualstatistics
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Janu
ary
1722759
17119
58
063
10801
1534755
155413
7minus12
6minus19383
February
188579
41895517
minus052
minus9723
172016
6170593
4083
14232
March
193870
41919834
097
18870
1738572
1726071
072
12501
April
1928661
1942054
minus069
minus13392
1729266
1748253
minus110
minus1898
8May
195699
3198478
1minus14
2minus2778
8174898
21759066
minus058
minus10084
June
189094
8184817
0226
4277
81666223
1652431
083
1379
2July
1770250
1752081
103
1817
01478479
1476378
014
2101
August
1660503
168813
9minus16
6minus27636
1385025
138510
1minus001
minus076
Septem
ber
1778886
1800818
minus12
3minus2193
21527047
1530628
minus023
minus3581
Octob
er1890286
1856596
178
33690
1673526
1669872
022
3654
Novem
ber
1785876
1804
286
minus10
3minus18409
1561020
155818
6018
2835
Decem
ber
1690628
1696056
minus032
minus5429
1463367
1460369
020
2997
minus849Eminus12
440
Eminus12
MBD
2314
31093
4RM
SD12
2Eminus13
133E
minus13
119905
2201
2201
119905-critic
(d)
Mon
thPo
Dedou
gou
Ann
ualstatistics
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Janu
ary
1673449
166977
9022
3669
1664
515
160379
5365
6072
0February
1854006
186291
9minus048
minus8913
1857876
1865884
minus043
minus8008
March
1899224
1855346
231
43878
19114
69
1943673
minus16
8minus32204
April
1775381
1831460
minus316
minus56078
194899
51925219
122
23776
May
1919388
1909568
051
9820
202519
0200578
1096
19409
June
185472
2183297
7117
2174
51909455
1910229
minus004
minus774
July
1650000
1676535
minus16
1minus26535
1821364
1837366
minus088
minus16002
August
1591200
1554206
232
3699
4172390
91743045
minus111
minus1913
5Septem
ber
1740
550
1777604
minus213
minus37054
1941336
192178
510
119551
Octob
er1866
828
1845435
115
21393
191479
21907477
038
7316
Novem
ber
1700718
1687818
076
1290
0170896
3173612
8minus15
9minus2716
6Decem
ber
1592868
1614687
minus13
7minus21819
1598303
162578
5minus17
2minus27483
minus256Eminus11
minus10
6Eminus11
MBD
29266
26271
RMSD
290Eminus13
134E
minus13
119905
2201
2201
119905-critic
8 Journal of Solar Energy
Table 5 Calculated and estimated quantities along with the error based on relation (18)
Quantities Ouaga Dori Bobo Gaoua Fada Boromo Po DedougouCalculated 049 059 050 045 051 052 050 052Correlated 052 058 048 044 051 051 049 051119890 () minus612 169 400 222 192 192 200 192
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Mon
thly
mea
n da
ily g
loba
lso
lar r
adia
tion
(kJ(
m2middotd
ay))
times103
15
16
17
18
19
20
21
Measured valuesMultiple regressionAngstrom equation
Figure 6 Comparison between measured and correlated values atDedougou
For the station of Ouagadougou the relative error variesbetween minus125 and 131 while the RMSD is estimatedto be 14181 kJm2 For Dori station the relative error iscomprised between ndash278 and 198 and the RMSD is equalto 31236 kJm2 All these results are in the acceptable marginWe obtained small errors because the values simulated arecompared with the average of measurement data over theperiod of the study (1977ndash2006) We would obtain highererrors if we carried out the comparisons with the measureddata for unspecified year
The relative errors vary between minus269 and 291 andbetween ndash282 and 219 respectively for the stations ofBobo and Fadawhile the RMSD are equal to 26787 kJm2 and24835 kJm2 for the same stations Once again the marginerror is acceptable
For the station of Boromo the relative error fluctuatesbetween minus166 and 226 while the RMSD is equal to23143 kJm2 The relative error varies between minus126 and083 and the RMSD is equal to 10934 kJm2 for the stationof Gaoua Once again these quantities are acceptable
For the two stations Po and Dedougou the respectiverelative errors vary between minus316 and 232 and betweenndash172 and 365 while the RMSD are equal to 29266 kJm2and 26271 kJm2 respectively The margin is acceptable TheMBD for the eight stations is comprised between 10minus11 kJm2and 10minus13 kJm2
44 Correlation between the Average Daily Ratio of SunshineDuration the Index of Clearness and the Latitude and Lon-gitude Equation (18) is obtained by substituting the valuesof the regression coefficients and the parameters in relation(12) This equation is valid nationwide and can be utilized to
compute the global solar radiation for the stations measuringthe sunshine duration Consider
119867
119867
119900
= 02689 minus 03108
119899
119873
+ 22147120601 minus 02729119871 (18)
where 119871 (in radian) stands for the longitude and the otherparameters have been defined already
The value of 094 for the correlation coefficient 119877 isan indication of good correlation between the parametersTable 5 gives the calculated and the estimated values of(18) and the corresponding relative error on the indexesof clearness These errors vary from minus612 for the stationat Ouagadougou to 400 for the station at Bobo whichis an indication of good agreement between estimated andcalculated values
5 Conclusions
Besides the indication of the presence of aerosols in theatmosphere we established a correlation relation betweenthe global radiation and five geographical andmeteorologicalparameters for eight stations disseminated throughout thecountry This correlation of the global radiation intensityshows particularly its dependency with the latitude as thehigher the latitude the greater the global radiation Howeverthis trend no longer stands around urban area like Oua-gadougou which experiences lower radiation than BoromoAnother main contribution is the establishment of a relationof correlation which is valid for the entire countryThereforefor better calibration of solar equipment care must be madein gathering solar radiation data For instance in BurkinaFaso not only are the meteorological stations scarce but alsothey lack direct radiation measurement equipment whichmakes it difficult to quantify this parameter known to be veryimportant for the calibration of solar thermal technologiesAlthough the correlation equations of direct and diffuseradiation exist in the literature they need to be rather inferredfrom the measurements of the countryrsquos stations
This work can be itself extended by incorporating theinfluence of parameters such as the atmospheric pressure andthe dew point temperature or by choosing a reference yearThe actual results will be of great importance for the quan-tification of the global solar radiation especially for thosestations which are only measuring solar sunshine durationFinally the correlation relations obtained will facilitate theestimation of the solar systems performances
Journal of Solar Energy 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to thank the Head of the NationalMeteorological Service for fruitful discussion and for givinggraciously precious weather data
References
[1] A K Katiyar and C K Pandey ldquoA review of solar radiationmodelsmdashpart Irdquo Journal of Renewable Energy vol 2013 ArticleID 168048 11 pages 2013
[2] C K Pandey and A K Katiyar ldquoSolar radiation models andmeasurement techniquesrdquo Journal of Energy vol 2013 ArticleID 305207 8 pages 2013
[3] A Angstrom ldquoSolar and terrestrial radiation Report to theinternational commission for solar research on actinometricinvestigations of solar and atmospheric radiationrdquo QuarterlyJournal of the Royal Meteorological Society vol 50 no 210 pp121ndash126 1924
[4] J K Page ldquoThe estimation ofmonthlymean values of daily totalshort wave radiation on-vertical and inclined surfaces fromsun shine records for latitudes 400Nndash400 Srdquo Proceedings of theUnited Nations Conference on New Sources of Energy vol 98 no4 pp 378ndash390 1961
[5] J A Prescott ldquoEvaporation from water surface in relationto solar radiationrdquo Transactions of the Royal Society of SouthAustralia vol 64 pp 114ndash118 1940
[6] S V Tahas D Ristoiu andC Cosma ldquoTrends of the global solarradiation and air temperature in Cluj-Napoca Romania (1984ndash2008)rdquo Romanian Journal in Physics vol 56 no 5-6 pp 784ndash789 2011
[7] T Khatib A Mohamed K Sopian and M Mahmoud ldquoSolarenergy prediction forMalaysia using artificial neural networksrdquoInternational Journal of Photoenergy vol 2012 Article ID419504 16 pages 2012
[8] A A Sabziparvar ldquoGeneral formula for estimation of monthlymean global solar radiation in different climates on the southand north coasts of Iranrdquo International Journal of Photoenergyvol 2007 Article ID 94786 7 pages 2007
[9] H Li F Cao XWang andWMa ldquoA temperature-basedmodelfor estimating monthly average daily global solar radiation inChinardquoTheScientificWorld Journal vol 2014Article ID 1287549 pages 2014
[10] E Quansah L K Amekudzi K Preko et al ldquoEmpirical modelsfor estimating global solar radiation over the Ashanti Region ofGhanardquo Journal of Solar Energy vol 2014 Article ID 897970 6pages 2014
[11] K Skeiker ldquoCorrelation of global solar radiation with commongeographical and meteorological parameters for Damascusprovince Syriardquo Energy Conversion amp Management vol 47 no4 pp 331ndash345 2006
[12] O P Singh S K Srivastava and A Gaur ldquoEmpirical rela-tionship to estimate global radiation from hours of sunshinerdquoEnergy Conversion and Management vol 37 no 4 pp 501ndash5041996
[13] I Sezai and E Tasdemiroglu ldquoEvaluation of the meteorologicaldata in Northern Cyprusrdquo Energy Conversion andManagementvol 36 no 10 pp 953ndash961 1995
[14] A A Trabea and M A M Shaltout ldquoCorrelation of globalsolar radiation with meteorological parameters over EgyptrdquoRenewable Energy vol 21 no 2 pp 297ndash308 2000
[15] J C Ododo and A Usman ldquoCorrelation of total solar radiationwith common meteorological parameters for Yola and CalabarNigeriardquo Energy Conversion amp Management vol 37 no 5 pp521ndash530 1996
[16] S Neske ldquoAbout the relation between sunshine duration andcloudiness on the basis of data fromHamburgrdquo Journal of SolarEnergy vol 2014 Article ID 306871 7 pages 2014
[17] A Dumas A Andrisani M Bonnici et al ldquoA new correlationbetween global solar energy radiation and daily temperaturevariationsrdquo Solar Energy vol 116 pp 117ndash124 2015
[18] A J Garane Climatologie du rayonnement solaire global duBurkina Faso Niamey Niger [Memoire de fin drsquoEtudes drsquoInge-nieurs] 1992
[19] C Baldy Contribution a Lrsquoetude du Rayonnement Global et dela Duree Drsquoinsolation en Haute-Volta Service MeteorologigueOuagdougou Burkina Faso 1976
[20] O Coulibaly 2011 Contribution a lrsquoelaboration drsquoune reglemen-tation thermique et energetique des batiments au Burkina FasoDonnees de base multiparametriques et modelisation thermo-aeraulique sous CoDyBa et TRNSYS [these de doctorat] Univer-site de Ouagadougou Burkina Faso 2011
[21] M Daguenet Les Sechoirs Solaires Theories et PratiquesUNESCO Paris France 1982
[22] Y JannotThermique Solaire EIER mars Ouagadougou Burk-ina Faso 1993
[23] P J Lunde Solar Thermal Engineering Space Heating and HotWater Systems John Wiley amp Sons New York NY USA 1980
[24] K M Latha and K V S Badarinath ldquoSeasonal variations ofPM10and PM
25particles loading over tropical urban environ-
mentrdquo International Journal of Environmental Health Researchvol 15 no 1 pp 63ndash68 2005
TribologyAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FuelsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
CombustionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Renewable Energy
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
StructuresJournal of
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear InstallationsScience and Technology of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solar EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Wind EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear EnergyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
2 Journal of Solar Energy
Table 1 Geographical locations of the eight cities of concern [20]
Cities Ouaga Dori Bobo Gaoua Fada Boromo Po DedougouLatitude (N) 12∘211015840 14∘021015840 11∘111015840 10∘201015840 12∘021015840 11∘451015840 11∘101015840 12∘281015840
Longitude (W) 01∘311015840 00∘021015840 04∘191015840 03∘111015840 00∘221015840E 02∘561015840 01∘091015840 03∘291015840
Altitude (m) 296 277 432 333 308 270 326 308
and the following climatic variables the average daily ratio ofsunshine duration the latitude and the longitude would beinvestigated
2 Equipment and Data Collection
21 Equipment Setup and Data Acquisition The sunshinedurations are meteorological data and are measured by aheliograph of Campbell-Stokes type designed by CASELLAThe data acquisition process is made according to the worldorganization of meteorology standards from heliographbands The global radiation is measured utilizing KIPP andZONEN Pyranometer with numerical ELSB-2 integratorswhich integrates the values of the daily solar radiation Twostations Dedougou and Fada Nrsquogourma are equipped withpyranometer-integrator of CIMEL type which integrates thehourly values of the global solar radiation intensityThe appa-ratuses are installed on concrete construction approximately15 meter in height in places released in order to avoidthe shadow of the surrounding objects Table 1 indicates thelatitude the longitude and the altitude of the eight stations ofconcern Data for global solar radiation sunshine durationthe maximum temperature and relative humidity have beencollected for all cities from 1977 to 2006 [20]
22 Estimation of the Extraterrestrial Solar Radiation on aHorizontal Surface (119867
119900) and the Maximum Sunshine Dura-
tion The extraterrestrial radiation on a horizontal surface(119867119900 kJm2) is determined utilizing the following relation [21ndash
23] Indeed the measurement data of global solar radiationprovided by the national meteorological service are in kJm2Consider
119867
119900= 3795
sdot 10
4 cos (120601) cos (120575) [sin (120596119904) minus
120587120596
119904
180
cos (120596119904)]
(1)
The quantity 3795 sdot 104 given by Jannot [22] to convert theextraterrestrial radiation into kJm2 comes from the term(24120587)lowast119868
0The value of the solar constant 119868
0used by Jannot is
1380Wm2 This quantity takes into account the eccentricitycorrection factor of Earthrsquos orbit which is calculated using thefollowing relation
119862 = 1 + 0034 cos [30 (119898 minus 1) + 119889] (2)
In relations (2) and (4)119898 is the number of the month in theyear starting with January and 119889 the number of the day in themonth Let us announce that by carrying out the calculationprogramme under the Matlab software we took account ofconversions on each time the need is essential
In relations (1) and (3)120601 is the latitude120596119904is the solar angle
of the sundown obtained from the next relation
120596
119904= 119886119903 cos (minus tan (120601) tan (120575)) (3)
120575 is the declination which is inferred from the followingequation
120575 = 2345
∘ cos (30119898 + 119889 minus 202) (4)
We also define the hour angle 120596 as follows
120596(∘) = minus15
∘(12 minus 119879
119904) (5)
where 119879119904is the solar hour of the day The hour angle 120596
119888at
sunset is opposite to its sundown equivalent therefore 120596119888=
minus120596
119897The solar hour at sunrise is given by
(119879
119904)
119897= 12 minus
120596
119904
15
(6)
At sunset the equivalent solar hour becomes
(119879
119904)
119888= 12 +
120596
119904
15
(7)
We can then infer the maximum daily sunshine duration asfollows
119873 =
2120596
119904
15
(8)
3 Estimation of the Regression Coefficients
First of all we averaged over one-year interval the globalradiation (119867) and the sunshine duration data collected bythe national meteorological service from 1992 to 2006 Nextwe estimate the extraterrestrial radiation on a horizontalsurface (119867
119900) and the maximum sunshine duration (119873) for
each station for the entire year Finally a linear relation ofAngstrom type is utilized for a correlation between the indexof clearness (119867119867
119900) and the daily ratio of sunshine duration
(119899119873)Now let us recall the original Angstrom formula which is
[3]
119867 = 119867
1015840
119900(119886
1015840+ 119887
1015840 119899
119873
) (9)
where 119899 is the number of hours of daily sunshine duration119873is the maximum number of hours of daily sunshine duration119867 is the daily global radiation on a horizontal surface 1198671015840
119900is
the daily global radiation on a horizontal surface by clear skyand 1198861015840 and 1198871015840 are coefficients to be determined
Journal of Solar Energy 3
In the original Angstrom formula (9) 119867
1015840
119900is found
to be difficult to determine Thus Page [4] and Prescott[5] formulated a modified relation in a manner that theextraterrestrial radiation on a horizontal surface119867
119900appears
that is
119867 = 119867
119900(119886 + 119887
119899
119873
) (10)
Here 119886 and 119887 are constants to be determined experimentallyfor each region
We rewrite relation (10) in a more useful form as follows
119867
119867
119900
= 119886 + 119887
119899
119873
(11)
In this relation the ratio 119867119867
119900usually denoted by 119870
119879is
known as the index of clearness It is an indication of thedegree of purity of the atmosphere it indicates the presence ofaerosols or water molecules in the atmosphereThe ratio 119899119873is the fraction of sunshine duration expressed as the quotientof the actual (119899) divided by the theoretical (119873) sunshineduration The coefficients 119886 and 119887 are obtained by drawingthe fraction of sunshine duration as a function of the indexof clearness then 119886 is the ordinate and is an indication of thevalue of the fraction of the incident radiation for a coveredsky 119887 on the other hand is the slope of the regression lineThe sum (119886 + 119887) gives an indication on the transmissivity ofthe atmosphere in condition of clear sky [18]
For each city a correlation is established between theglobal solar radiation on a horizontal surface and five mete-orological parameters which are the mean daily extrater-restrial solar radiation intensity the average daily ratio ofsunshine duration the mean daily relative humidity themean daily maximum air temperature and the sine of thesolar declination angle For the entire country a correlationis realized involving the index of clearness the average dailyratio of sunshine duration and the latitude and longitude Forthe relations of correlation involving many parameters wehave utilized amultiple linear regression suggested by Skeiker[11]
119910 = 119888 + 119889119909
1+ 119890119909
2+ 119891119909
3+ 119892119909
4+ ℎ119909
5 (12)
where 119888 119889 119890 119891 119892 ℎ are the regression coefficients and 119909
1
119909
2 1199093 1199094 1199095the correlation parameters The relative error
between the measured and estimated quantities is calculatedfrom the following relation
119890 = [
(119867
119894119898minus 119867
119894119888)
119867
119894119898
] sdot 100
(13)
where 119867119894119898
is the monthly average of daily global radiationmeasured over a horizontal surface for the 119894thmonth and119867
119894119888
is its value obtained from the relation of correlationUsually aprecision in the interval of minus10 to 10 is acceptable Skeiker[11] For the same purpose we can also compute statistical testparameters such as the root mean square differences (RMSD)
035040045050055060065070
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov DecMonth
HH
o
Ouaga
DoriFada
Boromo
Bobo
GaouaDeacutedougou
Pocirc
Figure 1 Indexes of clearness for the eight synoptic stations
and the mean bias differences (MBD) given by the followingrelations
RMSD = (
1
119899
119899
sum
119894=1
(119867
119894119898minus 119867
119894119888)
2
)
12
(14)
Equation (14) provides information on the short term perfor-mances of the correlations by allowing a term by term com-parison between the calculated and the measured valuesThesmaller the deviations are the better themodelrsquos performancesare Consider
MBD =
1
119899
119899
sum
119894=1
(119867
119894119898minus 119867
119894119888) (15)
The above test relation provides information on the longterm performance A low MBD is desired A positive valuegives the average amount of underestimation in the cal-culated value and vice versa A drawback of this test isthat overestimation of an individual observation will cancelunderestimation in a separate observation
On the other hand the performance of themodel is testedby the following statistical equation
119905 = [
(119899 minus 1)MBD2
RMSD2 minusMBD2]
12
(16)
The smaller the value of 119905 the better themodelrsquos performanceThe critical quantity is calculated at 119905
1205722where 120572 is the level of
significance and (119899minus1) the degrees of freedomThe degree ofconfidence is about 95 which sets 120572 = 5 and 1205722 = 25
4 Results and Discussion
41 Index of Clearness and Daily Ratio of Sunshine DurationFigure 1 indicates the mean values of the indexes of clearnessfor the eight synoptic stations The indexes are comprisedbetween 036 and 066 which indicates that the atmospherecontains impurities all year longThe lowest value is obtainedat Gaoua a region with a tradition of relatively heavy rainfallThis lowest index is therefore due to the albedo of the cloud
4 Journal of Solar Energy
Table 2 Statistics of regression with modified Angstrom model comparison of the results obtained by the current investigation with thoseof other investigations
TownRegression coefficients 119886 119887 119877
119886 119887 119886 + 119887
(1) (2) (3) (1) (2) (3) (1) (2) (3) (1) (2) (3)Dori 013 014 024 062 058 052 075 072 076 095 084 gt90Fada NrsquoGourma 021 020 026 045 049 048 066 069 074 091 071 gt90Ouagadougou 017 022 027 047 045 048 064 067 075 095 090 gt90Bobo Dioulasso 021 026 031 046 043 048 067 069 079 090 079 gt90Gaoua 015 022 026 046 046 048 061 068 074 096 092 gt90Boromo 018 mdash mdash 053 mdash mdash 071 mdash mdash 097 mdash mdashPo 021 mdash mdash 043 mdash mdash 064 mdash mdash 093 mdash mdashDedougou 023 mdash mdash 04 mdash mdash 063 mdash mdash 091 mdash mdashBurkina Faso 018 023 026 049 044 042 067 067 068 081 078 mdash(1) Results obtained by the actual investigation(2) Results obtained by Garane J Ali Period 1971ndash1990(3) Results obtained by Baldy Period 1971ndash1975
and the presence of water molecules in the atmosphere Thehighest index 066 is obtained at Dori a city located atthe northern tip of the country with scarce rainfalls For alleight stations the highest values are observed between themonths of November and February This period correspondsto the dry season with no cloud in the sky However the066 index is an indication of the presence of impurities inthe atmosphere which is due to the important phenomenonof absorption and diffusion of solar radiation by the aerosolparticles During this period the strong winds of harmattancarrying dust sand and many other small objects feed theatmosphere with aerosol particles of all sizes Indeed Lathaand Badarinath [24] have noticed that the concentration ofaerosol particles of sizes PM
10and PM
25is strong during
the same period (harmattan) and weak on the other handduring June to October (monsoon) in urban area in tropicalregions At Gaoua Fada and Bobo Po and Boromo thepermanence and the concentration of the clouds during themonth of August explain the strong drop of the indexes ofclearness On the contrary the increase during the month ofOctober is due to the purity of the atmosphere just after theend of the raining season Figure 2Thedaily ratio of sunshineduration varies between 045 and 086 and represents the ratioof the real sunshine duration (119899) and the theoretical sunshineduration (119873) the nationalmean value being 068 Townswithlower latitudes have lower value of the daily ratio of sunshineduration once again due to the heavy rainfalls which shortenthe sunshine duration
42 The Regression Coefficients of the Modified AngstromrsquosRelation We show in Table 2 the results of this researchbased on the relation of Angstrom For all the stationsthe correlation coefficient 119877 is greater than 090 We nextcompare the actual coefficients with the preliminary resultsestablished by Garane [18] and Baldy [19] for five stations
The values of (119886 + 119887) are quite similar For the valuesobtained throughout the country the coefficient (119886) ratherdecreases from (3)
119888 to (1)
119886 and (119887) increases somehow in
040045050055060065070075080085090
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov DecMonth
nN
Ouaga
DoriFada
Boromo
Bobo
GaouaDeacutedougou
Pocirc
Figure 2 Daily ratio of sunshine duration for the eight synopticstations
the same period from (3)
119888 to (1)
119886 This is an indication ofthe presence of aerosols in the atmosphere The values of thecorrelation coefficients 119877 which are greater than 090 for allcities tend to indicate good correlations between the globalradiation and the sunshine duration On the other hand themean value of 081 for the entire country is a good indicationof the disparities between the radiation intensities of theregions due to the latitude especially when we move fromnorth to south We present next the correlation results whenwe take into account the latitude and longitude
43 Correlation of the Radiation Intensity for the Eight Syn-optic Stations Table 3 shows the regression and correlationcoefficients obtained for each synoptic station Substitutingthe correlation parameters 119909
1 1199092 1199093 1199094 and 119909
5in relation
(12) respectively by119867o 119899119873119867119903 119879max and sin 120575 we obtain
the following
119867 = 119888 + 119889119867
119900+ 119890
119899
119873
+ 119891119867
119903+ 119892119879max + ℎ sin 120575 (17)
Journal of Solar Energy 5
Table 3 Regression and correlation coefficients for the eight synoptic stations
Town Regression coefficients Correlation coefficients 119877119888 119889 119890 119891 119892 ℎ
Ouagadougou minus4202917 147 2827241 minus5234 minus28851 minus715912 09921Dori minus2970840 118 2470840 minus4267 minus21596 minus566502 09663Bobo minus2534865 125 1946764 minus7046 minus30073 minus496691 09716Fada minus1252850 084 1191321 minus5395 minus13242 minus279462 09703Boromo minus1867415 088 2633683 minus5352 minus23908 mdash 09718Gaoua minus3259717 118 2239381 minus2937 minus20406 minus608006 09958Po minus5851229 231 4106196 minus8936 minus84351 minus1058665 09661Dedougou minus5879168 176 3619121 minus1337 minus29869 minus980501 09782
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Mon
thly
mea
n da
ily g
loba
lso
lar r
adia
tion
(kJ(
m2middotd
ay))
15
16
17
18
19
20times10
3
Measured valuesMultiple regressionAngstrom equation
Figure 3 Comparison between measured and correlated values atOuagadougou
Hence for a given station the correlation between the globalradiation on a horizontal surface and the five parameters isobtained by replacing the regression coefficients 119888 119889 119890 119891 119892and ℎ with their respective numerical values
The values of the regression coefficients 119888 119889 119890 119891 119892 andℎ vary both with and within the same location The studyof Skeiker [11] showed that when the number of regressioncoefficients for the multiple linear regression models ishigher results obtained are better The correlation obtained isnevertheless good between the parameters The lowest valueof the correlation coefficient 119877 is obtained at Po (119877 = 09661)while the highest is reached at Gaoua (119877 = 09958) Forthe city of Boromo a correlation is established between themonthly mean daily global solar radiation on a horizontalsurface and four parameters because the coefficient ldquoℎrdquo showsa different behavior to the rest of the city when we take intoaccount the solar declination angle
We compare in the following Figures 3ndash6 the measuredsolar radiation intensity its estimated values obtained fromthe Angstrom relation and the results obtained from thecorrelations based on the five meteorological parametersThe figures clearly show two picks corresponding to two hotseasons respectively fromMarch to June and in October Asfor the indexes of clearness and the ratio of sunshine durationthe lowest radiation values are observed during the rainingseason
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Mon
thly
mea
n da
ily g
loba
lso
lar r
adia
tion
(kJ(
m2middotd
ay))
times103
15
17
19
21
23
Measured valuesMultiple regressionAngstrom equation
Figure 4 Comparison between measured and correlated values atDori
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Mon
thly
mea
n da
ily g
loba
lso
lar r
adia
tion
(kJ(
m2middotd
ay))
times103
15
16
17
18
19
20
Measured valuesMultiple regressionAngstrom equation
Figure 5 Comparison between measured and correlated values atBoromo
The histograms show clearly when comparing the mea-sured and the correlation values with the Angstrom relationresults that the meteorological parameters (humidity tem-perature and declination) have an influence on the globalradiation intensity received by a horizontal surface Tables4(a)ndash4(d) display the values of the measured global radiationand the correlated values based on the five meteorologi-cal parameters We present also the statistical parametersobtained in each case
6 Journal of Solar Energy
Table4(a)119890M
BDR
MSD
119905and
119905-criticforO
uagado
ugou
andDori(b)119890M
BDR
MSD
119905and
119905-criticforB
oboandFada(c)119890M
BDR
MSD
119905and
119905-criticforB
orom
oandGaoua(d)
119890M
BDR
MSD
119905and
119905-criticforP
oandDedou
gou
(a)
Mon
thOuagado
ugou
Dori
Ann
ualstatistics
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Janu
ary
1593619
1580818
080
12802
1883522
189091
6minus039
minus7394
February
179438
1181673
8minus12
5minus22357
211576
9210470
1053
11068
March
1871065
1846550
131
24515
2237844
2194349
198
43495
April
1860
079
1871814
minus063
minus11734
220313
42259076
minus248
minus5594
2May
189695
7191010
0minus069
minus1314
32228402
2241255
minus057
minus12854
June
1851597
1830751
113
20846
2164
215
2128711
167
35504
July
1709075
1712545
minus020
minus3470
2110696
208818
710
822509
August
156770
1157890
0minus071
minus1119
92025322
2083244
minus278
minus5792
3Septem
ber
1738429
1735441
017
2988
212670
7209595
514
730752
Octob
er1783503
1770843
071
12660
2075201
2067421
038
7780
Novem
ber
168916
9169873
6minus057
minus9567
1980527
1983045
minus013
minus2518
Decem
ber
1583508
1585848
minus015
minus2341
1852580
1867057
minus078
minus14477
minus273Eminus12
909E
minus13
MBD
1418
131236
RMSD
638Eminus14
966E
minus15
119905
2201
2201
119905-critic
(b)
Mon
thBo
boFada
Ann
ualstatistics
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Janu
ary
1670671
1693578
minus13
7minus2290
7177792
01761675
091
16245
February
1927308
191292
7075
14381
1947206
1919814
141
27392
March
193975
81946355
minus034
minus6597
199476
41993531
006
1233
April
1892000
1885458
035
6541
1977473
2004
124
minus13
5minus26651
May
188078
31901057
minus10
8minus20275
1990334
1990476
minus001
minus14
2June
181798
51795433
124
22551
1919464
1905735
072
1372
9July
1687848
1687692
001
156
1825211
182194
5018
3266
August
1607626
163990
3minus201
minus32277
175710
4174992
4041
7181
Septem
ber
1774492
1722878
291
51614
1757560
179695
4minus224
minus39394
Octob
er1736800
1783496
minus269
minus46
696
180374
31764
291
219
39452
Novem
ber
1734772
1703431
181
31341
1776281
177078
2031
5498
Decem
ber
160979
61607629
013
2167
1692480
1740289
minus282
minus47809
144E
minus11
142E
minus11
MBD
2678
724835
RMSD
178E
minus13
190E
minus13
119905
2201
2201
119905-critic
Journal of Solar Energy 7
(c)
Mon
thBo
romo
Gaoua
Ann
ualstatistics
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Janu
ary
1722759
17119
58
063
10801
1534755
155413
7minus12
6minus19383
February
188579
41895517
minus052
minus9723
172016
6170593
4083
14232
March
193870
41919834
097
18870
1738572
1726071
072
12501
April
1928661
1942054
minus069
minus13392
1729266
1748253
minus110
minus1898
8May
195699
3198478
1minus14
2minus2778
8174898
21759066
minus058
minus10084
June
189094
8184817
0226
4277
81666223
1652431
083
1379
2July
1770250
1752081
103
1817
01478479
1476378
014
2101
August
1660503
168813
9minus16
6minus27636
1385025
138510
1minus001
minus076
Septem
ber
1778886
1800818
minus12
3minus2193
21527047
1530628
minus023
minus3581
Octob
er1890286
1856596
178
33690
1673526
1669872
022
3654
Novem
ber
1785876
1804
286
minus10
3minus18409
1561020
155818
6018
2835
Decem
ber
1690628
1696056
minus032
minus5429
1463367
1460369
020
2997
minus849Eminus12
440
Eminus12
MBD
2314
31093
4RM
SD12
2Eminus13
133E
minus13
119905
2201
2201
119905-critic
(d)
Mon
thPo
Dedou
gou
Ann
ualstatistics
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Janu
ary
1673449
166977
9022
3669
1664
515
160379
5365
6072
0February
1854006
186291
9minus048
minus8913
1857876
1865884
minus043
minus8008
March
1899224
1855346
231
43878
19114
69
1943673
minus16
8minus32204
April
1775381
1831460
minus316
minus56078
194899
51925219
122
23776
May
1919388
1909568
051
9820
202519
0200578
1096
19409
June
185472
2183297
7117
2174
51909455
1910229
minus004
minus774
July
1650000
1676535
minus16
1minus26535
1821364
1837366
minus088
minus16002
August
1591200
1554206
232
3699
4172390
91743045
minus111
minus1913
5Septem
ber
1740
550
1777604
minus213
minus37054
1941336
192178
510
119551
Octob
er1866
828
1845435
115
21393
191479
21907477
038
7316
Novem
ber
1700718
1687818
076
1290
0170896
3173612
8minus15
9minus2716
6Decem
ber
1592868
1614687
minus13
7minus21819
1598303
162578
5minus17
2minus27483
minus256Eminus11
minus10
6Eminus11
MBD
29266
26271
RMSD
290Eminus13
134E
minus13
119905
2201
2201
119905-critic
8 Journal of Solar Energy
Table 5 Calculated and estimated quantities along with the error based on relation (18)
Quantities Ouaga Dori Bobo Gaoua Fada Boromo Po DedougouCalculated 049 059 050 045 051 052 050 052Correlated 052 058 048 044 051 051 049 051119890 () minus612 169 400 222 192 192 200 192
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Mon
thly
mea
n da
ily g
loba
lso
lar r
adia
tion
(kJ(
m2middotd
ay))
times103
15
16
17
18
19
20
21
Measured valuesMultiple regressionAngstrom equation
Figure 6 Comparison between measured and correlated values atDedougou
For the station of Ouagadougou the relative error variesbetween minus125 and 131 while the RMSD is estimatedto be 14181 kJm2 For Dori station the relative error iscomprised between ndash278 and 198 and the RMSD is equalto 31236 kJm2 All these results are in the acceptable marginWe obtained small errors because the values simulated arecompared with the average of measurement data over theperiod of the study (1977ndash2006) We would obtain highererrors if we carried out the comparisons with the measureddata for unspecified year
The relative errors vary between minus269 and 291 andbetween ndash282 and 219 respectively for the stations ofBobo and Fadawhile the RMSD are equal to 26787 kJm2 and24835 kJm2 for the same stations Once again the marginerror is acceptable
For the station of Boromo the relative error fluctuatesbetween minus166 and 226 while the RMSD is equal to23143 kJm2 The relative error varies between minus126 and083 and the RMSD is equal to 10934 kJm2 for the stationof Gaoua Once again these quantities are acceptable
For the two stations Po and Dedougou the respectiverelative errors vary between minus316 and 232 and betweenndash172 and 365 while the RMSD are equal to 29266 kJm2and 26271 kJm2 respectively The margin is acceptable TheMBD for the eight stations is comprised between 10minus11 kJm2and 10minus13 kJm2
44 Correlation between the Average Daily Ratio of SunshineDuration the Index of Clearness and the Latitude and Lon-gitude Equation (18) is obtained by substituting the valuesof the regression coefficients and the parameters in relation(12) This equation is valid nationwide and can be utilized to
compute the global solar radiation for the stations measuringthe sunshine duration Consider
119867
119867
119900
= 02689 minus 03108
119899
119873
+ 22147120601 minus 02729119871 (18)
where 119871 (in radian) stands for the longitude and the otherparameters have been defined already
The value of 094 for the correlation coefficient 119877 isan indication of good correlation between the parametersTable 5 gives the calculated and the estimated values of(18) and the corresponding relative error on the indexesof clearness These errors vary from minus612 for the stationat Ouagadougou to 400 for the station at Bobo whichis an indication of good agreement between estimated andcalculated values
5 Conclusions
Besides the indication of the presence of aerosols in theatmosphere we established a correlation relation betweenthe global radiation and five geographical andmeteorologicalparameters for eight stations disseminated throughout thecountry This correlation of the global radiation intensityshows particularly its dependency with the latitude as thehigher the latitude the greater the global radiation Howeverthis trend no longer stands around urban area like Oua-gadougou which experiences lower radiation than BoromoAnother main contribution is the establishment of a relationof correlation which is valid for the entire countryThereforefor better calibration of solar equipment care must be madein gathering solar radiation data For instance in BurkinaFaso not only are the meteorological stations scarce but alsothey lack direct radiation measurement equipment whichmakes it difficult to quantify this parameter known to be veryimportant for the calibration of solar thermal technologiesAlthough the correlation equations of direct and diffuseradiation exist in the literature they need to be rather inferredfrom the measurements of the countryrsquos stations
This work can be itself extended by incorporating theinfluence of parameters such as the atmospheric pressure andthe dew point temperature or by choosing a reference yearThe actual results will be of great importance for the quan-tification of the global solar radiation especially for thosestations which are only measuring solar sunshine durationFinally the correlation relations obtained will facilitate theestimation of the solar systems performances
Journal of Solar Energy 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to thank the Head of the NationalMeteorological Service for fruitful discussion and for givinggraciously precious weather data
References
[1] A K Katiyar and C K Pandey ldquoA review of solar radiationmodelsmdashpart Irdquo Journal of Renewable Energy vol 2013 ArticleID 168048 11 pages 2013
[2] C K Pandey and A K Katiyar ldquoSolar radiation models andmeasurement techniquesrdquo Journal of Energy vol 2013 ArticleID 305207 8 pages 2013
[3] A Angstrom ldquoSolar and terrestrial radiation Report to theinternational commission for solar research on actinometricinvestigations of solar and atmospheric radiationrdquo QuarterlyJournal of the Royal Meteorological Society vol 50 no 210 pp121ndash126 1924
[4] J K Page ldquoThe estimation ofmonthlymean values of daily totalshort wave radiation on-vertical and inclined surfaces fromsun shine records for latitudes 400Nndash400 Srdquo Proceedings of theUnited Nations Conference on New Sources of Energy vol 98 no4 pp 378ndash390 1961
[5] J A Prescott ldquoEvaporation from water surface in relationto solar radiationrdquo Transactions of the Royal Society of SouthAustralia vol 64 pp 114ndash118 1940
[6] S V Tahas D Ristoiu andC Cosma ldquoTrends of the global solarradiation and air temperature in Cluj-Napoca Romania (1984ndash2008)rdquo Romanian Journal in Physics vol 56 no 5-6 pp 784ndash789 2011
[7] T Khatib A Mohamed K Sopian and M Mahmoud ldquoSolarenergy prediction forMalaysia using artificial neural networksrdquoInternational Journal of Photoenergy vol 2012 Article ID419504 16 pages 2012
[8] A A Sabziparvar ldquoGeneral formula for estimation of monthlymean global solar radiation in different climates on the southand north coasts of Iranrdquo International Journal of Photoenergyvol 2007 Article ID 94786 7 pages 2007
[9] H Li F Cao XWang andWMa ldquoA temperature-basedmodelfor estimating monthly average daily global solar radiation inChinardquoTheScientificWorld Journal vol 2014Article ID 1287549 pages 2014
[10] E Quansah L K Amekudzi K Preko et al ldquoEmpirical modelsfor estimating global solar radiation over the Ashanti Region ofGhanardquo Journal of Solar Energy vol 2014 Article ID 897970 6pages 2014
[11] K Skeiker ldquoCorrelation of global solar radiation with commongeographical and meteorological parameters for Damascusprovince Syriardquo Energy Conversion amp Management vol 47 no4 pp 331ndash345 2006
[12] O P Singh S K Srivastava and A Gaur ldquoEmpirical rela-tionship to estimate global radiation from hours of sunshinerdquoEnergy Conversion and Management vol 37 no 4 pp 501ndash5041996
[13] I Sezai and E Tasdemiroglu ldquoEvaluation of the meteorologicaldata in Northern Cyprusrdquo Energy Conversion andManagementvol 36 no 10 pp 953ndash961 1995
[14] A A Trabea and M A M Shaltout ldquoCorrelation of globalsolar radiation with meteorological parameters over EgyptrdquoRenewable Energy vol 21 no 2 pp 297ndash308 2000
[15] J C Ododo and A Usman ldquoCorrelation of total solar radiationwith common meteorological parameters for Yola and CalabarNigeriardquo Energy Conversion amp Management vol 37 no 5 pp521ndash530 1996
[16] S Neske ldquoAbout the relation between sunshine duration andcloudiness on the basis of data fromHamburgrdquo Journal of SolarEnergy vol 2014 Article ID 306871 7 pages 2014
[17] A Dumas A Andrisani M Bonnici et al ldquoA new correlationbetween global solar energy radiation and daily temperaturevariationsrdquo Solar Energy vol 116 pp 117ndash124 2015
[18] A J Garane Climatologie du rayonnement solaire global duBurkina Faso Niamey Niger [Memoire de fin drsquoEtudes drsquoInge-nieurs] 1992
[19] C Baldy Contribution a Lrsquoetude du Rayonnement Global et dela Duree Drsquoinsolation en Haute-Volta Service MeteorologigueOuagdougou Burkina Faso 1976
[20] O Coulibaly 2011 Contribution a lrsquoelaboration drsquoune reglemen-tation thermique et energetique des batiments au Burkina FasoDonnees de base multiparametriques et modelisation thermo-aeraulique sous CoDyBa et TRNSYS [these de doctorat] Univer-site de Ouagadougou Burkina Faso 2011
[21] M Daguenet Les Sechoirs Solaires Theories et PratiquesUNESCO Paris France 1982
[22] Y JannotThermique Solaire EIER mars Ouagadougou Burk-ina Faso 1993
[23] P J Lunde Solar Thermal Engineering Space Heating and HotWater Systems John Wiley amp Sons New York NY USA 1980
[24] K M Latha and K V S Badarinath ldquoSeasonal variations ofPM10and PM
25particles loading over tropical urban environ-
mentrdquo International Journal of Environmental Health Researchvol 15 no 1 pp 63ndash68 2005
TribologyAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FuelsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
CombustionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Renewable Energy
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
StructuresJournal of
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear InstallationsScience and Technology of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solar EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Wind EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear EnergyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of Solar Energy 3
In the original Angstrom formula (9) 119867
1015840
119900is found
to be difficult to determine Thus Page [4] and Prescott[5] formulated a modified relation in a manner that theextraterrestrial radiation on a horizontal surface119867
119900appears
that is
119867 = 119867
119900(119886 + 119887
119899
119873
) (10)
Here 119886 and 119887 are constants to be determined experimentallyfor each region
We rewrite relation (10) in a more useful form as follows
119867
119867
119900
= 119886 + 119887
119899
119873
(11)
In this relation the ratio 119867119867
119900usually denoted by 119870
119879is
known as the index of clearness It is an indication of thedegree of purity of the atmosphere it indicates the presence ofaerosols or water molecules in the atmosphereThe ratio 119899119873is the fraction of sunshine duration expressed as the quotientof the actual (119899) divided by the theoretical (119873) sunshineduration The coefficients 119886 and 119887 are obtained by drawingthe fraction of sunshine duration as a function of the indexof clearness then 119886 is the ordinate and is an indication of thevalue of the fraction of the incident radiation for a coveredsky 119887 on the other hand is the slope of the regression lineThe sum (119886 + 119887) gives an indication on the transmissivity ofthe atmosphere in condition of clear sky [18]
For each city a correlation is established between theglobal solar radiation on a horizontal surface and five mete-orological parameters which are the mean daily extrater-restrial solar radiation intensity the average daily ratio ofsunshine duration the mean daily relative humidity themean daily maximum air temperature and the sine of thesolar declination angle For the entire country a correlationis realized involving the index of clearness the average dailyratio of sunshine duration and the latitude and longitude Forthe relations of correlation involving many parameters wehave utilized amultiple linear regression suggested by Skeiker[11]
119910 = 119888 + 119889119909
1+ 119890119909
2+ 119891119909
3+ 119892119909
4+ ℎ119909
5 (12)
where 119888 119889 119890 119891 119892 ℎ are the regression coefficients and 119909
1
119909
2 1199093 1199094 1199095the correlation parameters The relative error
between the measured and estimated quantities is calculatedfrom the following relation
119890 = [
(119867
119894119898minus 119867
119894119888)
119867
119894119898
] sdot 100
(13)
where 119867119894119898
is the monthly average of daily global radiationmeasured over a horizontal surface for the 119894thmonth and119867
119894119888
is its value obtained from the relation of correlationUsually aprecision in the interval of minus10 to 10 is acceptable Skeiker[11] For the same purpose we can also compute statistical testparameters such as the root mean square differences (RMSD)
035040045050055060065070
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov DecMonth
HH
o
Ouaga
DoriFada
Boromo
Bobo
GaouaDeacutedougou
Pocirc
Figure 1 Indexes of clearness for the eight synoptic stations
and the mean bias differences (MBD) given by the followingrelations
RMSD = (
1
119899
119899
sum
119894=1
(119867
119894119898minus 119867
119894119888)
2
)
12
(14)
Equation (14) provides information on the short term perfor-mances of the correlations by allowing a term by term com-parison between the calculated and the measured valuesThesmaller the deviations are the better themodelrsquos performancesare Consider
MBD =
1
119899
119899
sum
119894=1
(119867
119894119898minus 119867
119894119888) (15)
The above test relation provides information on the longterm performance A low MBD is desired A positive valuegives the average amount of underestimation in the cal-culated value and vice versa A drawback of this test isthat overestimation of an individual observation will cancelunderestimation in a separate observation
On the other hand the performance of themodel is testedby the following statistical equation
119905 = [
(119899 minus 1)MBD2
RMSD2 minusMBD2]
12
(16)
The smaller the value of 119905 the better themodelrsquos performanceThe critical quantity is calculated at 119905
1205722where 120572 is the level of
significance and (119899minus1) the degrees of freedomThe degree ofconfidence is about 95 which sets 120572 = 5 and 1205722 = 25
4 Results and Discussion
41 Index of Clearness and Daily Ratio of Sunshine DurationFigure 1 indicates the mean values of the indexes of clearnessfor the eight synoptic stations The indexes are comprisedbetween 036 and 066 which indicates that the atmospherecontains impurities all year longThe lowest value is obtainedat Gaoua a region with a tradition of relatively heavy rainfallThis lowest index is therefore due to the albedo of the cloud
4 Journal of Solar Energy
Table 2 Statistics of regression with modified Angstrom model comparison of the results obtained by the current investigation with thoseof other investigations
TownRegression coefficients 119886 119887 119877
119886 119887 119886 + 119887
(1) (2) (3) (1) (2) (3) (1) (2) (3) (1) (2) (3)Dori 013 014 024 062 058 052 075 072 076 095 084 gt90Fada NrsquoGourma 021 020 026 045 049 048 066 069 074 091 071 gt90Ouagadougou 017 022 027 047 045 048 064 067 075 095 090 gt90Bobo Dioulasso 021 026 031 046 043 048 067 069 079 090 079 gt90Gaoua 015 022 026 046 046 048 061 068 074 096 092 gt90Boromo 018 mdash mdash 053 mdash mdash 071 mdash mdash 097 mdash mdashPo 021 mdash mdash 043 mdash mdash 064 mdash mdash 093 mdash mdashDedougou 023 mdash mdash 04 mdash mdash 063 mdash mdash 091 mdash mdashBurkina Faso 018 023 026 049 044 042 067 067 068 081 078 mdash(1) Results obtained by the actual investigation(2) Results obtained by Garane J Ali Period 1971ndash1990(3) Results obtained by Baldy Period 1971ndash1975
and the presence of water molecules in the atmosphere Thehighest index 066 is obtained at Dori a city located atthe northern tip of the country with scarce rainfalls For alleight stations the highest values are observed between themonths of November and February This period correspondsto the dry season with no cloud in the sky However the066 index is an indication of the presence of impurities inthe atmosphere which is due to the important phenomenonof absorption and diffusion of solar radiation by the aerosolparticles During this period the strong winds of harmattancarrying dust sand and many other small objects feed theatmosphere with aerosol particles of all sizes Indeed Lathaand Badarinath [24] have noticed that the concentration ofaerosol particles of sizes PM
10and PM
25is strong during
the same period (harmattan) and weak on the other handduring June to October (monsoon) in urban area in tropicalregions At Gaoua Fada and Bobo Po and Boromo thepermanence and the concentration of the clouds during themonth of August explain the strong drop of the indexes ofclearness On the contrary the increase during the month ofOctober is due to the purity of the atmosphere just after theend of the raining season Figure 2Thedaily ratio of sunshineduration varies between 045 and 086 and represents the ratioof the real sunshine duration (119899) and the theoretical sunshineduration (119873) the nationalmean value being 068 Townswithlower latitudes have lower value of the daily ratio of sunshineduration once again due to the heavy rainfalls which shortenthe sunshine duration
42 The Regression Coefficients of the Modified AngstromrsquosRelation We show in Table 2 the results of this researchbased on the relation of Angstrom For all the stationsthe correlation coefficient 119877 is greater than 090 We nextcompare the actual coefficients with the preliminary resultsestablished by Garane [18] and Baldy [19] for five stations
The values of (119886 + 119887) are quite similar For the valuesobtained throughout the country the coefficient (119886) ratherdecreases from (3)
119888 to (1)
119886 and (119887) increases somehow in
040045050055060065070075080085090
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov DecMonth
nN
Ouaga
DoriFada
Boromo
Bobo
GaouaDeacutedougou
Pocirc
Figure 2 Daily ratio of sunshine duration for the eight synopticstations
the same period from (3)
119888 to (1)
119886 This is an indication ofthe presence of aerosols in the atmosphere The values of thecorrelation coefficients 119877 which are greater than 090 for allcities tend to indicate good correlations between the globalradiation and the sunshine duration On the other hand themean value of 081 for the entire country is a good indicationof the disparities between the radiation intensities of theregions due to the latitude especially when we move fromnorth to south We present next the correlation results whenwe take into account the latitude and longitude
43 Correlation of the Radiation Intensity for the Eight Syn-optic Stations Table 3 shows the regression and correlationcoefficients obtained for each synoptic station Substitutingthe correlation parameters 119909
1 1199092 1199093 1199094 and 119909
5in relation
(12) respectively by119867o 119899119873119867119903 119879max and sin 120575 we obtain
the following
119867 = 119888 + 119889119867
119900+ 119890
119899
119873
+ 119891119867
119903+ 119892119879max + ℎ sin 120575 (17)
Journal of Solar Energy 5
Table 3 Regression and correlation coefficients for the eight synoptic stations
Town Regression coefficients Correlation coefficients 119877119888 119889 119890 119891 119892 ℎ
Ouagadougou minus4202917 147 2827241 minus5234 minus28851 minus715912 09921Dori minus2970840 118 2470840 minus4267 minus21596 minus566502 09663Bobo minus2534865 125 1946764 minus7046 minus30073 minus496691 09716Fada minus1252850 084 1191321 minus5395 minus13242 minus279462 09703Boromo minus1867415 088 2633683 minus5352 minus23908 mdash 09718Gaoua minus3259717 118 2239381 minus2937 minus20406 minus608006 09958Po minus5851229 231 4106196 minus8936 minus84351 minus1058665 09661Dedougou minus5879168 176 3619121 minus1337 minus29869 minus980501 09782
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Mon
thly
mea
n da
ily g
loba
lso
lar r
adia
tion
(kJ(
m2middotd
ay))
15
16
17
18
19
20times10
3
Measured valuesMultiple regressionAngstrom equation
Figure 3 Comparison between measured and correlated values atOuagadougou
Hence for a given station the correlation between the globalradiation on a horizontal surface and the five parameters isobtained by replacing the regression coefficients 119888 119889 119890 119891 119892and ℎ with their respective numerical values
The values of the regression coefficients 119888 119889 119890 119891 119892 andℎ vary both with and within the same location The studyof Skeiker [11] showed that when the number of regressioncoefficients for the multiple linear regression models ishigher results obtained are better The correlation obtained isnevertheless good between the parameters The lowest valueof the correlation coefficient 119877 is obtained at Po (119877 = 09661)while the highest is reached at Gaoua (119877 = 09958) Forthe city of Boromo a correlation is established between themonthly mean daily global solar radiation on a horizontalsurface and four parameters because the coefficient ldquoℎrdquo showsa different behavior to the rest of the city when we take intoaccount the solar declination angle
We compare in the following Figures 3ndash6 the measuredsolar radiation intensity its estimated values obtained fromthe Angstrom relation and the results obtained from thecorrelations based on the five meteorological parametersThe figures clearly show two picks corresponding to two hotseasons respectively fromMarch to June and in October Asfor the indexes of clearness and the ratio of sunshine durationthe lowest radiation values are observed during the rainingseason
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Mon
thly
mea
n da
ily g
loba
lso
lar r
adia
tion
(kJ(
m2middotd
ay))
times103
15
17
19
21
23
Measured valuesMultiple regressionAngstrom equation
Figure 4 Comparison between measured and correlated values atDori
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Mon
thly
mea
n da
ily g
loba
lso
lar r
adia
tion
(kJ(
m2middotd
ay))
times103
15
16
17
18
19
20
Measured valuesMultiple regressionAngstrom equation
Figure 5 Comparison between measured and correlated values atBoromo
The histograms show clearly when comparing the mea-sured and the correlation values with the Angstrom relationresults that the meteorological parameters (humidity tem-perature and declination) have an influence on the globalradiation intensity received by a horizontal surface Tables4(a)ndash4(d) display the values of the measured global radiationand the correlated values based on the five meteorologi-cal parameters We present also the statistical parametersobtained in each case
6 Journal of Solar Energy
Table4(a)119890M
BDR
MSD
119905and
119905-criticforO
uagado
ugou
andDori(b)119890M
BDR
MSD
119905and
119905-criticforB
oboandFada(c)119890M
BDR
MSD
119905and
119905-criticforB
orom
oandGaoua(d)
119890M
BDR
MSD
119905and
119905-criticforP
oandDedou
gou
(a)
Mon
thOuagado
ugou
Dori
Ann
ualstatistics
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Janu
ary
1593619
1580818
080
12802
1883522
189091
6minus039
minus7394
February
179438
1181673
8minus12
5minus22357
211576
9210470
1053
11068
March
1871065
1846550
131
24515
2237844
2194349
198
43495
April
1860
079
1871814
minus063
minus11734
220313
42259076
minus248
minus5594
2May
189695
7191010
0minus069
minus1314
32228402
2241255
minus057
minus12854
June
1851597
1830751
113
20846
2164
215
2128711
167
35504
July
1709075
1712545
minus020
minus3470
2110696
208818
710
822509
August
156770
1157890
0minus071
minus1119
92025322
2083244
minus278
minus5792
3Septem
ber
1738429
1735441
017
2988
212670
7209595
514
730752
Octob
er1783503
1770843
071
12660
2075201
2067421
038
7780
Novem
ber
168916
9169873
6minus057
minus9567
1980527
1983045
minus013
minus2518
Decem
ber
1583508
1585848
minus015
minus2341
1852580
1867057
minus078
minus14477
minus273Eminus12
909E
minus13
MBD
1418
131236
RMSD
638Eminus14
966E
minus15
119905
2201
2201
119905-critic
(b)
Mon
thBo
boFada
Ann
ualstatistics
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Janu
ary
1670671
1693578
minus13
7minus2290
7177792
01761675
091
16245
February
1927308
191292
7075
14381
1947206
1919814
141
27392
March
193975
81946355
minus034
minus6597
199476
41993531
006
1233
April
1892000
1885458
035
6541
1977473
2004
124
minus13
5minus26651
May
188078
31901057
minus10
8minus20275
1990334
1990476
minus001
minus14
2June
181798
51795433
124
22551
1919464
1905735
072
1372
9July
1687848
1687692
001
156
1825211
182194
5018
3266
August
1607626
163990
3minus201
minus32277
175710
4174992
4041
7181
Septem
ber
1774492
1722878
291
51614
1757560
179695
4minus224
minus39394
Octob
er1736800
1783496
minus269
minus46
696
180374
31764
291
219
39452
Novem
ber
1734772
1703431
181
31341
1776281
177078
2031
5498
Decem
ber
160979
61607629
013
2167
1692480
1740289
minus282
minus47809
144E
minus11
142E
minus11
MBD
2678
724835
RMSD
178E
minus13
190E
minus13
119905
2201
2201
119905-critic
Journal of Solar Energy 7
(c)
Mon
thBo
romo
Gaoua
Ann
ualstatistics
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Janu
ary
1722759
17119
58
063
10801
1534755
155413
7minus12
6minus19383
February
188579
41895517
minus052
minus9723
172016
6170593
4083
14232
March
193870
41919834
097
18870
1738572
1726071
072
12501
April
1928661
1942054
minus069
minus13392
1729266
1748253
minus110
minus1898
8May
195699
3198478
1minus14
2minus2778
8174898
21759066
minus058
minus10084
June
189094
8184817
0226
4277
81666223
1652431
083
1379
2July
1770250
1752081
103
1817
01478479
1476378
014
2101
August
1660503
168813
9minus16
6minus27636
1385025
138510
1minus001
minus076
Septem
ber
1778886
1800818
minus12
3minus2193
21527047
1530628
minus023
minus3581
Octob
er1890286
1856596
178
33690
1673526
1669872
022
3654
Novem
ber
1785876
1804
286
minus10
3minus18409
1561020
155818
6018
2835
Decem
ber
1690628
1696056
minus032
minus5429
1463367
1460369
020
2997
minus849Eminus12
440
Eminus12
MBD
2314
31093
4RM
SD12
2Eminus13
133E
minus13
119905
2201
2201
119905-critic
(d)
Mon
thPo
Dedou
gou
Ann
ualstatistics
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Janu
ary
1673449
166977
9022
3669
1664
515
160379
5365
6072
0February
1854006
186291
9minus048
minus8913
1857876
1865884
minus043
minus8008
March
1899224
1855346
231
43878
19114
69
1943673
minus16
8minus32204
April
1775381
1831460
minus316
minus56078
194899
51925219
122
23776
May
1919388
1909568
051
9820
202519
0200578
1096
19409
June
185472
2183297
7117
2174
51909455
1910229
minus004
minus774
July
1650000
1676535
minus16
1minus26535
1821364
1837366
minus088
minus16002
August
1591200
1554206
232
3699
4172390
91743045
minus111
minus1913
5Septem
ber
1740
550
1777604
minus213
minus37054
1941336
192178
510
119551
Octob
er1866
828
1845435
115
21393
191479
21907477
038
7316
Novem
ber
1700718
1687818
076
1290
0170896
3173612
8minus15
9minus2716
6Decem
ber
1592868
1614687
minus13
7minus21819
1598303
162578
5minus17
2minus27483
minus256Eminus11
minus10
6Eminus11
MBD
29266
26271
RMSD
290Eminus13
134E
minus13
119905
2201
2201
119905-critic
8 Journal of Solar Energy
Table 5 Calculated and estimated quantities along with the error based on relation (18)
Quantities Ouaga Dori Bobo Gaoua Fada Boromo Po DedougouCalculated 049 059 050 045 051 052 050 052Correlated 052 058 048 044 051 051 049 051119890 () minus612 169 400 222 192 192 200 192
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Mon
thly
mea
n da
ily g
loba
lso
lar r
adia
tion
(kJ(
m2middotd
ay))
times103
15
16
17
18
19
20
21
Measured valuesMultiple regressionAngstrom equation
Figure 6 Comparison between measured and correlated values atDedougou
For the station of Ouagadougou the relative error variesbetween minus125 and 131 while the RMSD is estimatedto be 14181 kJm2 For Dori station the relative error iscomprised between ndash278 and 198 and the RMSD is equalto 31236 kJm2 All these results are in the acceptable marginWe obtained small errors because the values simulated arecompared with the average of measurement data over theperiod of the study (1977ndash2006) We would obtain highererrors if we carried out the comparisons with the measureddata for unspecified year
The relative errors vary between minus269 and 291 andbetween ndash282 and 219 respectively for the stations ofBobo and Fadawhile the RMSD are equal to 26787 kJm2 and24835 kJm2 for the same stations Once again the marginerror is acceptable
For the station of Boromo the relative error fluctuatesbetween minus166 and 226 while the RMSD is equal to23143 kJm2 The relative error varies between minus126 and083 and the RMSD is equal to 10934 kJm2 for the stationof Gaoua Once again these quantities are acceptable
For the two stations Po and Dedougou the respectiverelative errors vary between minus316 and 232 and betweenndash172 and 365 while the RMSD are equal to 29266 kJm2and 26271 kJm2 respectively The margin is acceptable TheMBD for the eight stations is comprised between 10minus11 kJm2and 10minus13 kJm2
44 Correlation between the Average Daily Ratio of SunshineDuration the Index of Clearness and the Latitude and Lon-gitude Equation (18) is obtained by substituting the valuesof the regression coefficients and the parameters in relation(12) This equation is valid nationwide and can be utilized to
compute the global solar radiation for the stations measuringthe sunshine duration Consider
119867
119867
119900
= 02689 minus 03108
119899
119873
+ 22147120601 minus 02729119871 (18)
where 119871 (in radian) stands for the longitude and the otherparameters have been defined already
The value of 094 for the correlation coefficient 119877 isan indication of good correlation between the parametersTable 5 gives the calculated and the estimated values of(18) and the corresponding relative error on the indexesof clearness These errors vary from minus612 for the stationat Ouagadougou to 400 for the station at Bobo whichis an indication of good agreement between estimated andcalculated values
5 Conclusions
Besides the indication of the presence of aerosols in theatmosphere we established a correlation relation betweenthe global radiation and five geographical andmeteorologicalparameters for eight stations disseminated throughout thecountry This correlation of the global radiation intensityshows particularly its dependency with the latitude as thehigher the latitude the greater the global radiation Howeverthis trend no longer stands around urban area like Oua-gadougou which experiences lower radiation than BoromoAnother main contribution is the establishment of a relationof correlation which is valid for the entire countryThereforefor better calibration of solar equipment care must be madein gathering solar radiation data For instance in BurkinaFaso not only are the meteorological stations scarce but alsothey lack direct radiation measurement equipment whichmakes it difficult to quantify this parameter known to be veryimportant for the calibration of solar thermal technologiesAlthough the correlation equations of direct and diffuseradiation exist in the literature they need to be rather inferredfrom the measurements of the countryrsquos stations
This work can be itself extended by incorporating theinfluence of parameters such as the atmospheric pressure andthe dew point temperature or by choosing a reference yearThe actual results will be of great importance for the quan-tification of the global solar radiation especially for thosestations which are only measuring solar sunshine durationFinally the correlation relations obtained will facilitate theestimation of the solar systems performances
Journal of Solar Energy 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to thank the Head of the NationalMeteorological Service for fruitful discussion and for givinggraciously precious weather data
References
[1] A K Katiyar and C K Pandey ldquoA review of solar radiationmodelsmdashpart Irdquo Journal of Renewable Energy vol 2013 ArticleID 168048 11 pages 2013
[2] C K Pandey and A K Katiyar ldquoSolar radiation models andmeasurement techniquesrdquo Journal of Energy vol 2013 ArticleID 305207 8 pages 2013
[3] A Angstrom ldquoSolar and terrestrial radiation Report to theinternational commission for solar research on actinometricinvestigations of solar and atmospheric radiationrdquo QuarterlyJournal of the Royal Meteorological Society vol 50 no 210 pp121ndash126 1924
[4] J K Page ldquoThe estimation ofmonthlymean values of daily totalshort wave radiation on-vertical and inclined surfaces fromsun shine records for latitudes 400Nndash400 Srdquo Proceedings of theUnited Nations Conference on New Sources of Energy vol 98 no4 pp 378ndash390 1961
[5] J A Prescott ldquoEvaporation from water surface in relationto solar radiationrdquo Transactions of the Royal Society of SouthAustralia vol 64 pp 114ndash118 1940
[6] S V Tahas D Ristoiu andC Cosma ldquoTrends of the global solarradiation and air temperature in Cluj-Napoca Romania (1984ndash2008)rdquo Romanian Journal in Physics vol 56 no 5-6 pp 784ndash789 2011
[7] T Khatib A Mohamed K Sopian and M Mahmoud ldquoSolarenergy prediction forMalaysia using artificial neural networksrdquoInternational Journal of Photoenergy vol 2012 Article ID419504 16 pages 2012
[8] A A Sabziparvar ldquoGeneral formula for estimation of monthlymean global solar radiation in different climates on the southand north coasts of Iranrdquo International Journal of Photoenergyvol 2007 Article ID 94786 7 pages 2007
[9] H Li F Cao XWang andWMa ldquoA temperature-basedmodelfor estimating monthly average daily global solar radiation inChinardquoTheScientificWorld Journal vol 2014Article ID 1287549 pages 2014
[10] E Quansah L K Amekudzi K Preko et al ldquoEmpirical modelsfor estimating global solar radiation over the Ashanti Region ofGhanardquo Journal of Solar Energy vol 2014 Article ID 897970 6pages 2014
[11] K Skeiker ldquoCorrelation of global solar radiation with commongeographical and meteorological parameters for Damascusprovince Syriardquo Energy Conversion amp Management vol 47 no4 pp 331ndash345 2006
[12] O P Singh S K Srivastava and A Gaur ldquoEmpirical rela-tionship to estimate global radiation from hours of sunshinerdquoEnergy Conversion and Management vol 37 no 4 pp 501ndash5041996
[13] I Sezai and E Tasdemiroglu ldquoEvaluation of the meteorologicaldata in Northern Cyprusrdquo Energy Conversion andManagementvol 36 no 10 pp 953ndash961 1995
[14] A A Trabea and M A M Shaltout ldquoCorrelation of globalsolar radiation with meteorological parameters over EgyptrdquoRenewable Energy vol 21 no 2 pp 297ndash308 2000
[15] J C Ododo and A Usman ldquoCorrelation of total solar radiationwith common meteorological parameters for Yola and CalabarNigeriardquo Energy Conversion amp Management vol 37 no 5 pp521ndash530 1996
[16] S Neske ldquoAbout the relation between sunshine duration andcloudiness on the basis of data fromHamburgrdquo Journal of SolarEnergy vol 2014 Article ID 306871 7 pages 2014
[17] A Dumas A Andrisani M Bonnici et al ldquoA new correlationbetween global solar energy radiation and daily temperaturevariationsrdquo Solar Energy vol 116 pp 117ndash124 2015
[18] A J Garane Climatologie du rayonnement solaire global duBurkina Faso Niamey Niger [Memoire de fin drsquoEtudes drsquoInge-nieurs] 1992
[19] C Baldy Contribution a Lrsquoetude du Rayonnement Global et dela Duree Drsquoinsolation en Haute-Volta Service MeteorologigueOuagdougou Burkina Faso 1976
[20] O Coulibaly 2011 Contribution a lrsquoelaboration drsquoune reglemen-tation thermique et energetique des batiments au Burkina FasoDonnees de base multiparametriques et modelisation thermo-aeraulique sous CoDyBa et TRNSYS [these de doctorat] Univer-site de Ouagadougou Burkina Faso 2011
[21] M Daguenet Les Sechoirs Solaires Theories et PratiquesUNESCO Paris France 1982
[22] Y JannotThermique Solaire EIER mars Ouagadougou Burk-ina Faso 1993
[23] P J Lunde Solar Thermal Engineering Space Heating and HotWater Systems John Wiley amp Sons New York NY USA 1980
[24] K M Latha and K V S Badarinath ldquoSeasonal variations ofPM10and PM
25particles loading over tropical urban environ-
mentrdquo International Journal of Environmental Health Researchvol 15 no 1 pp 63ndash68 2005
TribologyAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
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FuelsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
CombustionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Renewable Energy
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
StructuresJournal of
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear InstallationsScience and Technology of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solar EnergyJournal of
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Wind EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear EnergyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
4 Journal of Solar Energy
Table 2 Statistics of regression with modified Angstrom model comparison of the results obtained by the current investigation with thoseof other investigations
TownRegression coefficients 119886 119887 119877
119886 119887 119886 + 119887
(1) (2) (3) (1) (2) (3) (1) (2) (3) (1) (2) (3)Dori 013 014 024 062 058 052 075 072 076 095 084 gt90Fada NrsquoGourma 021 020 026 045 049 048 066 069 074 091 071 gt90Ouagadougou 017 022 027 047 045 048 064 067 075 095 090 gt90Bobo Dioulasso 021 026 031 046 043 048 067 069 079 090 079 gt90Gaoua 015 022 026 046 046 048 061 068 074 096 092 gt90Boromo 018 mdash mdash 053 mdash mdash 071 mdash mdash 097 mdash mdashPo 021 mdash mdash 043 mdash mdash 064 mdash mdash 093 mdash mdashDedougou 023 mdash mdash 04 mdash mdash 063 mdash mdash 091 mdash mdashBurkina Faso 018 023 026 049 044 042 067 067 068 081 078 mdash(1) Results obtained by the actual investigation(2) Results obtained by Garane J Ali Period 1971ndash1990(3) Results obtained by Baldy Period 1971ndash1975
and the presence of water molecules in the atmosphere Thehighest index 066 is obtained at Dori a city located atthe northern tip of the country with scarce rainfalls For alleight stations the highest values are observed between themonths of November and February This period correspondsto the dry season with no cloud in the sky However the066 index is an indication of the presence of impurities inthe atmosphere which is due to the important phenomenonof absorption and diffusion of solar radiation by the aerosolparticles During this period the strong winds of harmattancarrying dust sand and many other small objects feed theatmosphere with aerosol particles of all sizes Indeed Lathaand Badarinath [24] have noticed that the concentration ofaerosol particles of sizes PM
10and PM
25is strong during
the same period (harmattan) and weak on the other handduring June to October (monsoon) in urban area in tropicalregions At Gaoua Fada and Bobo Po and Boromo thepermanence and the concentration of the clouds during themonth of August explain the strong drop of the indexes ofclearness On the contrary the increase during the month ofOctober is due to the purity of the atmosphere just after theend of the raining season Figure 2Thedaily ratio of sunshineduration varies between 045 and 086 and represents the ratioof the real sunshine duration (119899) and the theoretical sunshineduration (119873) the nationalmean value being 068 Townswithlower latitudes have lower value of the daily ratio of sunshineduration once again due to the heavy rainfalls which shortenthe sunshine duration
42 The Regression Coefficients of the Modified AngstromrsquosRelation We show in Table 2 the results of this researchbased on the relation of Angstrom For all the stationsthe correlation coefficient 119877 is greater than 090 We nextcompare the actual coefficients with the preliminary resultsestablished by Garane [18] and Baldy [19] for five stations
The values of (119886 + 119887) are quite similar For the valuesobtained throughout the country the coefficient (119886) ratherdecreases from (3)
119888 to (1)
119886 and (119887) increases somehow in
040045050055060065070075080085090
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov DecMonth
nN
Ouaga
DoriFada
Boromo
Bobo
GaouaDeacutedougou
Pocirc
Figure 2 Daily ratio of sunshine duration for the eight synopticstations
the same period from (3)
119888 to (1)
119886 This is an indication ofthe presence of aerosols in the atmosphere The values of thecorrelation coefficients 119877 which are greater than 090 for allcities tend to indicate good correlations between the globalradiation and the sunshine duration On the other hand themean value of 081 for the entire country is a good indicationof the disparities between the radiation intensities of theregions due to the latitude especially when we move fromnorth to south We present next the correlation results whenwe take into account the latitude and longitude
43 Correlation of the Radiation Intensity for the Eight Syn-optic Stations Table 3 shows the regression and correlationcoefficients obtained for each synoptic station Substitutingthe correlation parameters 119909
1 1199092 1199093 1199094 and 119909
5in relation
(12) respectively by119867o 119899119873119867119903 119879max and sin 120575 we obtain
the following
119867 = 119888 + 119889119867
119900+ 119890
119899
119873
+ 119891119867
119903+ 119892119879max + ℎ sin 120575 (17)
Journal of Solar Energy 5
Table 3 Regression and correlation coefficients for the eight synoptic stations
Town Regression coefficients Correlation coefficients 119877119888 119889 119890 119891 119892 ℎ
Ouagadougou minus4202917 147 2827241 minus5234 minus28851 minus715912 09921Dori minus2970840 118 2470840 minus4267 minus21596 minus566502 09663Bobo minus2534865 125 1946764 minus7046 minus30073 minus496691 09716Fada minus1252850 084 1191321 minus5395 minus13242 minus279462 09703Boromo minus1867415 088 2633683 minus5352 minus23908 mdash 09718Gaoua minus3259717 118 2239381 minus2937 minus20406 minus608006 09958Po minus5851229 231 4106196 minus8936 minus84351 minus1058665 09661Dedougou minus5879168 176 3619121 minus1337 minus29869 minus980501 09782
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Mon
thly
mea
n da
ily g
loba
lso
lar r
adia
tion
(kJ(
m2middotd
ay))
15
16
17
18
19
20times10
3
Measured valuesMultiple regressionAngstrom equation
Figure 3 Comparison between measured and correlated values atOuagadougou
Hence for a given station the correlation between the globalradiation on a horizontal surface and the five parameters isobtained by replacing the regression coefficients 119888 119889 119890 119891 119892and ℎ with their respective numerical values
The values of the regression coefficients 119888 119889 119890 119891 119892 andℎ vary both with and within the same location The studyof Skeiker [11] showed that when the number of regressioncoefficients for the multiple linear regression models ishigher results obtained are better The correlation obtained isnevertheless good between the parameters The lowest valueof the correlation coefficient 119877 is obtained at Po (119877 = 09661)while the highest is reached at Gaoua (119877 = 09958) Forthe city of Boromo a correlation is established between themonthly mean daily global solar radiation on a horizontalsurface and four parameters because the coefficient ldquoℎrdquo showsa different behavior to the rest of the city when we take intoaccount the solar declination angle
We compare in the following Figures 3ndash6 the measuredsolar radiation intensity its estimated values obtained fromthe Angstrom relation and the results obtained from thecorrelations based on the five meteorological parametersThe figures clearly show two picks corresponding to two hotseasons respectively fromMarch to June and in October Asfor the indexes of clearness and the ratio of sunshine durationthe lowest radiation values are observed during the rainingseason
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Mon
thly
mea
n da
ily g
loba
lso
lar r
adia
tion
(kJ(
m2middotd
ay))
times103
15
17
19
21
23
Measured valuesMultiple regressionAngstrom equation
Figure 4 Comparison between measured and correlated values atDori
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Mon
thly
mea
n da
ily g
loba
lso
lar r
adia
tion
(kJ(
m2middotd
ay))
times103
15
16
17
18
19
20
Measured valuesMultiple regressionAngstrom equation
Figure 5 Comparison between measured and correlated values atBoromo
The histograms show clearly when comparing the mea-sured and the correlation values with the Angstrom relationresults that the meteorological parameters (humidity tem-perature and declination) have an influence on the globalradiation intensity received by a horizontal surface Tables4(a)ndash4(d) display the values of the measured global radiationand the correlated values based on the five meteorologi-cal parameters We present also the statistical parametersobtained in each case
6 Journal of Solar Energy
Table4(a)119890M
BDR
MSD
119905and
119905-criticforO
uagado
ugou
andDori(b)119890M
BDR
MSD
119905and
119905-criticforB
oboandFada(c)119890M
BDR
MSD
119905and
119905-criticforB
orom
oandGaoua(d)
119890M
BDR
MSD
119905and
119905-criticforP
oandDedou
gou
(a)
Mon
thOuagado
ugou
Dori
Ann
ualstatistics
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Janu
ary
1593619
1580818
080
12802
1883522
189091
6minus039
minus7394
February
179438
1181673
8minus12
5minus22357
211576
9210470
1053
11068
March
1871065
1846550
131
24515
2237844
2194349
198
43495
April
1860
079
1871814
minus063
minus11734
220313
42259076
minus248
minus5594
2May
189695
7191010
0minus069
minus1314
32228402
2241255
minus057
minus12854
June
1851597
1830751
113
20846
2164
215
2128711
167
35504
July
1709075
1712545
minus020
minus3470
2110696
208818
710
822509
August
156770
1157890
0minus071
minus1119
92025322
2083244
minus278
minus5792
3Septem
ber
1738429
1735441
017
2988
212670
7209595
514
730752
Octob
er1783503
1770843
071
12660
2075201
2067421
038
7780
Novem
ber
168916
9169873
6minus057
minus9567
1980527
1983045
minus013
minus2518
Decem
ber
1583508
1585848
minus015
minus2341
1852580
1867057
minus078
minus14477
minus273Eminus12
909E
minus13
MBD
1418
131236
RMSD
638Eminus14
966E
minus15
119905
2201
2201
119905-critic
(b)
Mon
thBo
boFada
Ann
ualstatistics
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Janu
ary
1670671
1693578
minus13
7minus2290
7177792
01761675
091
16245
February
1927308
191292
7075
14381
1947206
1919814
141
27392
March
193975
81946355
minus034
minus6597
199476
41993531
006
1233
April
1892000
1885458
035
6541
1977473
2004
124
minus13
5minus26651
May
188078
31901057
minus10
8minus20275
1990334
1990476
minus001
minus14
2June
181798
51795433
124
22551
1919464
1905735
072
1372
9July
1687848
1687692
001
156
1825211
182194
5018
3266
August
1607626
163990
3minus201
minus32277
175710
4174992
4041
7181
Septem
ber
1774492
1722878
291
51614
1757560
179695
4minus224
minus39394
Octob
er1736800
1783496
minus269
minus46
696
180374
31764
291
219
39452
Novem
ber
1734772
1703431
181
31341
1776281
177078
2031
5498
Decem
ber
160979
61607629
013
2167
1692480
1740289
minus282
minus47809
144E
minus11
142E
minus11
MBD
2678
724835
RMSD
178E
minus13
190E
minus13
119905
2201
2201
119905-critic
Journal of Solar Energy 7
(c)
Mon
thBo
romo
Gaoua
Ann
ualstatistics
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Janu
ary
1722759
17119
58
063
10801
1534755
155413
7minus12
6minus19383
February
188579
41895517
minus052
minus9723
172016
6170593
4083
14232
March
193870
41919834
097
18870
1738572
1726071
072
12501
April
1928661
1942054
minus069
minus13392
1729266
1748253
minus110
minus1898
8May
195699
3198478
1minus14
2minus2778
8174898
21759066
minus058
minus10084
June
189094
8184817
0226
4277
81666223
1652431
083
1379
2July
1770250
1752081
103
1817
01478479
1476378
014
2101
August
1660503
168813
9minus16
6minus27636
1385025
138510
1minus001
minus076
Septem
ber
1778886
1800818
minus12
3minus2193
21527047
1530628
minus023
minus3581
Octob
er1890286
1856596
178
33690
1673526
1669872
022
3654
Novem
ber
1785876
1804
286
minus10
3minus18409
1561020
155818
6018
2835
Decem
ber
1690628
1696056
minus032
minus5429
1463367
1460369
020
2997
minus849Eminus12
440
Eminus12
MBD
2314
31093
4RM
SD12
2Eminus13
133E
minus13
119905
2201
2201
119905-critic
(d)
Mon
thPo
Dedou
gou
Ann
ualstatistics
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Janu
ary
1673449
166977
9022
3669
1664
515
160379
5365
6072
0February
1854006
186291
9minus048
minus8913
1857876
1865884
minus043
minus8008
March
1899224
1855346
231
43878
19114
69
1943673
minus16
8minus32204
April
1775381
1831460
minus316
minus56078
194899
51925219
122
23776
May
1919388
1909568
051
9820
202519
0200578
1096
19409
June
185472
2183297
7117
2174
51909455
1910229
minus004
minus774
July
1650000
1676535
minus16
1minus26535
1821364
1837366
minus088
minus16002
August
1591200
1554206
232
3699
4172390
91743045
minus111
minus1913
5Septem
ber
1740
550
1777604
minus213
minus37054
1941336
192178
510
119551
Octob
er1866
828
1845435
115
21393
191479
21907477
038
7316
Novem
ber
1700718
1687818
076
1290
0170896
3173612
8minus15
9minus2716
6Decem
ber
1592868
1614687
minus13
7minus21819
1598303
162578
5minus17
2minus27483
minus256Eminus11
minus10
6Eminus11
MBD
29266
26271
RMSD
290Eminus13
134E
minus13
119905
2201
2201
119905-critic
8 Journal of Solar Energy
Table 5 Calculated and estimated quantities along with the error based on relation (18)
Quantities Ouaga Dori Bobo Gaoua Fada Boromo Po DedougouCalculated 049 059 050 045 051 052 050 052Correlated 052 058 048 044 051 051 049 051119890 () minus612 169 400 222 192 192 200 192
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Mon
thly
mea
n da
ily g
loba
lso
lar r
adia
tion
(kJ(
m2middotd
ay))
times103
15
16
17
18
19
20
21
Measured valuesMultiple regressionAngstrom equation
Figure 6 Comparison between measured and correlated values atDedougou
For the station of Ouagadougou the relative error variesbetween minus125 and 131 while the RMSD is estimatedto be 14181 kJm2 For Dori station the relative error iscomprised between ndash278 and 198 and the RMSD is equalto 31236 kJm2 All these results are in the acceptable marginWe obtained small errors because the values simulated arecompared with the average of measurement data over theperiod of the study (1977ndash2006) We would obtain highererrors if we carried out the comparisons with the measureddata for unspecified year
The relative errors vary between minus269 and 291 andbetween ndash282 and 219 respectively for the stations ofBobo and Fadawhile the RMSD are equal to 26787 kJm2 and24835 kJm2 for the same stations Once again the marginerror is acceptable
For the station of Boromo the relative error fluctuatesbetween minus166 and 226 while the RMSD is equal to23143 kJm2 The relative error varies between minus126 and083 and the RMSD is equal to 10934 kJm2 for the stationof Gaoua Once again these quantities are acceptable
For the two stations Po and Dedougou the respectiverelative errors vary between minus316 and 232 and betweenndash172 and 365 while the RMSD are equal to 29266 kJm2and 26271 kJm2 respectively The margin is acceptable TheMBD for the eight stations is comprised between 10minus11 kJm2and 10minus13 kJm2
44 Correlation between the Average Daily Ratio of SunshineDuration the Index of Clearness and the Latitude and Lon-gitude Equation (18) is obtained by substituting the valuesof the regression coefficients and the parameters in relation(12) This equation is valid nationwide and can be utilized to
compute the global solar radiation for the stations measuringthe sunshine duration Consider
119867
119867
119900
= 02689 minus 03108
119899
119873
+ 22147120601 minus 02729119871 (18)
where 119871 (in radian) stands for the longitude and the otherparameters have been defined already
The value of 094 for the correlation coefficient 119877 isan indication of good correlation between the parametersTable 5 gives the calculated and the estimated values of(18) and the corresponding relative error on the indexesof clearness These errors vary from minus612 for the stationat Ouagadougou to 400 for the station at Bobo whichis an indication of good agreement between estimated andcalculated values
5 Conclusions
Besides the indication of the presence of aerosols in theatmosphere we established a correlation relation betweenthe global radiation and five geographical andmeteorologicalparameters for eight stations disseminated throughout thecountry This correlation of the global radiation intensityshows particularly its dependency with the latitude as thehigher the latitude the greater the global radiation Howeverthis trend no longer stands around urban area like Oua-gadougou which experiences lower radiation than BoromoAnother main contribution is the establishment of a relationof correlation which is valid for the entire countryThereforefor better calibration of solar equipment care must be madein gathering solar radiation data For instance in BurkinaFaso not only are the meteorological stations scarce but alsothey lack direct radiation measurement equipment whichmakes it difficult to quantify this parameter known to be veryimportant for the calibration of solar thermal technologiesAlthough the correlation equations of direct and diffuseradiation exist in the literature they need to be rather inferredfrom the measurements of the countryrsquos stations
This work can be itself extended by incorporating theinfluence of parameters such as the atmospheric pressure andthe dew point temperature or by choosing a reference yearThe actual results will be of great importance for the quan-tification of the global solar radiation especially for thosestations which are only measuring solar sunshine durationFinally the correlation relations obtained will facilitate theestimation of the solar systems performances
Journal of Solar Energy 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to thank the Head of the NationalMeteorological Service for fruitful discussion and for givinggraciously precious weather data
References
[1] A K Katiyar and C K Pandey ldquoA review of solar radiationmodelsmdashpart Irdquo Journal of Renewable Energy vol 2013 ArticleID 168048 11 pages 2013
[2] C K Pandey and A K Katiyar ldquoSolar radiation models andmeasurement techniquesrdquo Journal of Energy vol 2013 ArticleID 305207 8 pages 2013
[3] A Angstrom ldquoSolar and terrestrial radiation Report to theinternational commission for solar research on actinometricinvestigations of solar and atmospheric radiationrdquo QuarterlyJournal of the Royal Meteorological Society vol 50 no 210 pp121ndash126 1924
[4] J K Page ldquoThe estimation ofmonthlymean values of daily totalshort wave radiation on-vertical and inclined surfaces fromsun shine records for latitudes 400Nndash400 Srdquo Proceedings of theUnited Nations Conference on New Sources of Energy vol 98 no4 pp 378ndash390 1961
[5] J A Prescott ldquoEvaporation from water surface in relationto solar radiationrdquo Transactions of the Royal Society of SouthAustralia vol 64 pp 114ndash118 1940
[6] S V Tahas D Ristoiu andC Cosma ldquoTrends of the global solarradiation and air temperature in Cluj-Napoca Romania (1984ndash2008)rdquo Romanian Journal in Physics vol 56 no 5-6 pp 784ndash789 2011
[7] T Khatib A Mohamed K Sopian and M Mahmoud ldquoSolarenergy prediction forMalaysia using artificial neural networksrdquoInternational Journal of Photoenergy vol 2012 Article ID419504 16 pages 2012
[8] A A Sabziparvar ldquoGeneral formula for estimation of monthlymean global solar radiation in different climates on the southand north coasts of Iranrdquo International Journal of Photoenergyvol 2007 Article ID 94786 7 pages 2007
[9] H Li F Cao XWang andWMa ldquoA temperature-basedmodelfor estimating monthly average daily global solar radiation inChinardquoTheScientificWorld Journal vol 2014Article ID 1287549 pages 2014
[10] E Quansah L K Amekudzi K Preko et al ldquoEmpirical modelsfor estimating global solar radiation over the Ashanti Region ofGhanardquo Journal of Solar Energy vol 2014 Article ID 897970 6pages 2014
[11] K Skeiker ldquoCorrelation of global solar radiation with commongeographical and meteorological parameters for Damascusprovince Syriardquo Energy Conversion amp Management vol 47 no4 pp 331ndash345 2006
[12] O P Singh S K Srivastava and A Gaur ldquoEmpirical rela-tionship to estimate global radiation from hours of sunshinerdquoEnergy Conversion and Management vol 37 no 4 pp 501ndash5041996
[13] I Sezai and E Tasdemiroglu ldquoEvaluation of the meteorologicaldata in Northern Cyprusrdquo Energy Conversion andManagementvol 36 no 10 pp 953ndash961 1995
[14] A A Trabea and M A M Shaltout ldquoCorrelation of globalsolar radiation with meteorological parameters over EgyptrdquoRenewable Energy vol 21 no 2 pp 297ndash308 2000
[15] J C Ododo and A Usman ldquoCorrelation of total solar radiationwith common meteorological parameters for Yola and CalabarNigeriardquo Energy Conversion amp Management vol 37 no 5 pp521ndash530 1996
[16] S Neske ldquoAbout the relation between sunshine duration andcloudiness on the basis of data fromHamburgrdquo Journal of SolarEnergy vol 2014 Article ID 306871 7 pages 2014
[17] A Dumas A Andrisani M Bonnici et al ldquoA new correlationbetween global solar energy radiation and daily temperaturevariationsrdquo Solar Energy vol 116 pp 117ndash124 2015
[18] A J Garane Climatologie du rayonnement solaire global duBurkina Faso Niamey Niger [Memoire de fin drsquoEtudes drsquoInge-nieurs] 1992
[19] C Baldy Contribution a Lrsquoetude du Rayonnement Global et dela Duree Drsquoinsolation en Haute-Volta Service MeteorologigueOuagdougou Burkina Faso 1976
[20] O Coulibaly 2011 Contribution a lrsquoelaboration drsquoune reglemen-tation thermique et energetique des batiments au Burkina FasoDonnees de base multiparametriques et modelisation thermo-aeraulique sous CoDyBa et TRNSYS [these de doctorat] Univer-site de Ouagadougou Burkina Faso 2011
[21] M Daguenet Les Sechoirs Solaires Theories et PratiquesUNESCO Paris France 1982
[22] Y JannotThermique Solaire EIER mars Ouagadougou Burk-ina Faso 1993
[23] P J Lunde Solar Thermal Engineering Space Heating and HotWater Systems John Wiley amp Sons New York NY USA 1980
[24] K M Latha and K V S Badarinath ldquoSeasonal variations ofPM10and PM
25particles loading over tropical urban environ-
mentrdquo International Journal of Environmental Health Researchvol 15 no 1 pp 63ndash68 2005
TribologyAdvances in
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International Journal of
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FuelsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
CombustionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Renewable Energy
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
StructuresJournal of
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear InstallationsScience and Technology of
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Solar EnergyJournal of
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Wind EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear EnergyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of Solar Energy 5
Table 3 Regression and correlation coefficients for the eight synoptic stations
Town Regression coefficients Correlation coefficients 119877119888 119889 119890 119891 119892 ℎ
Ouagadougou minus4202917 147 2827241 minus5234 minus28851 minus715912 09921Dori minus2970840 118 2470840 minus4267 minus21596 minus566502 09663Bobo minus2534865 125 1946764 minus7046 minus30073 minus496691 09716Fada minus1252850 084 1191321 minus5395 minus13242 minus279462 09703Boromo minus1867415 088 2633683 minus5352 minus23908 mdash 09718Gaoua minus3259717 118 2239381 minus2937 minus20406 minus608006 09958Po minus5851229 231 4106196 minus8936 minus84351 minus1058665 09661Dedougou minus5879168 176 3619121 minus1337 minus29869 minus980501 09782
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Mon
thly
mea
n da
ily g
loba
lso
lar r
adia
tion
(kJ(
m2middotd
ay))
15
16
17
18
19
20times10
3
Measured valuesMultiple regressionAngstrom equation
Figure 3 Comparison between measured and correlated values atOuagadougou
Hence for a given station the correlation between the globalradiation on a horizontal surface and the five parameters isobtained by replacing the regression coefficients 119888 119889 119890 119891 119892and ℎ with their respective numerical values
The values of the regression coefficients 119888 119889 119890 119891 119892 andℎ vary both with and within the same location The studyof Skeiker [11] showed that when the number of regressioncoefficients for the multiple linear regression models ishigher results obtained are better The correlation obtained isnevertheless good between the parameters The lowest valueof the correlation coefficient 119877 is obtained at Po (119877 = 09661)while the highest is reached at Gaoua (119877 = 09958) Forthe city of Boromo a correlation is established between themonthly mean daily global solar radiation on a horizontalsurface and four parameters because the coefficient ldquoℎrdquo showsa different behavior to the rest of the city when we take intoaccount the solar declination angle
We compare in the following Figures 3ndash6 the measuredsolar radiation intensity its estimated values obtained fromthe Angstrom relation and the results obtained from thecorrelations based on the five meteorological parametersThe figures clearly show two picks corresponding to two hotseasons respectively fromMarch to June and in October Asfor the indexes of clearness and the ratio of sunshine durationthe lowest radiation values are observed during the rainingseason
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Mon
thly
mea
n da
ily g
loba
lso
lar r
adia
tion
(kJ(
m2middotd
ay))
times103
15
17
19
21
23
Measured valuesMultiple regressionAngstrom equation
Figure 4 Comparison between measured and correlated values atDori
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Mon
thly
mea
n da
ily g
loba
lso
lar r
adia
tion
(kJ(
m2middotd
ay))
times103
15
16
17
18
19
20
Measured valuesMultiple regressionAngstrom equation
Figure 5 Comparison between measured and correlated values atBoromo
The histograms show clearly when comparing the mea-sured and the correlation values with the Angstrom relationresults that the meteorological parameters (humidity tem-perature and declination) have an influence on the globalradiation intensity received by a horizontal surface Tables4(a)ndash4(d) display the values of the measured global radiationand the correlated values based on the five meteorologi-cal parameters We present also the statistical parametersobtained in each case
6 Journal of Solar Energy
Table4(a)119890M
BDR
MSD
119905and
119905-criticforO
uagado
ugou
andDori(b)119890M
BDR
MSD
119905and
119905-criticforB
oboandFada(c)119890M
BDR
MSD
119905and
119905-criticforB
orom
oandGaoua(d)
119890M
BDR
MSD
119905and
119905-criticforP
oandDedou
gou
(a)
Mon
thOuagado
ugou
Dori
Ann
ualstatistics
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Janu
ary
1593619
1580818
080
12802
1883522
189091
6minus039
minus7394
February
179438
1181673
8minus12
5minus22357
211576
9210470
1053
11068
March
1871065
1846550
131
24515
2237844
2194349
198
43495
April
1860
079
1871814
minus063
minus11734
220313
42259076
minus248
minus5594
2May
189695
7191010
0minus069
minus1314
32228402
2241255
minus057
minus12854
June
1851597
1830751
113
20846
2164
215
2128711
167
35504
July
1709075
1712545
minus020
minus3470
2110696
208818
710
822509
August
156770
1157890
0minus071
minus1119
92025322
2083244
minus278
minus5792
3Septem
ber
1738429
1735441
017
2988
212670
7209595
514
730752
Octob
er1783503
1770843
071
12660
2075201
2067421
038
7780
Novem
ber
168916
9169873
6minus057
minus9567
1980527
1983045
minus013
minus2518
Decem
ber
1583508
1585848
minus015
minus2341
1852580
1867057
minus078
minus14477
minus273Eminus12
909E
minus13
MBD
1418
131236
RMSD
638Eminus14
966E
minus15
119905
2201
2201
119905-critic
(b)
Mon
thBo
boFada
Ann
ualstatistics
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Janu
ary
1670671
1693578
minus13
7minus2290
7177792
01761675
091
16245
February
1927308
191292
7075
14381
1947206
1919814
141
27392
March
193975
81946355
minus034
minus6597
199476
41993531
006
1233
April
1892000
1885458
035
6541
1977473
2004
124
minus13
5minus26651
May
188078
31901057
minus10
8minus20275
1990334
1990476
minus001
minus14
2June
181798
51795433
124
22551
1919464
1905735
072
1372
9July
1687848
1687692
001
156
1825211
182194
5018
3266
August
1607626
163990
3minus201
minus32277
175710
4174992
4041
7181
Septem
ber
1774492
1722878
291
51614
1757560
179695
4minus224
minus39394
Octob
er1736800
1783496
minus269
minus46
696
180374
31764
291
219
39452
Novem
ber
1734772
1703431
181
31341
1776281
177078
2031
5498
Decem
ber
160979
61607629
013
2167
1692480
1740289
minus282
minus47809
144E
minus11
142E
minus11
MBD
2678
724835
RMSD
178E
minus13
190E
minus13
119905
2201
2201
119905-critic
Journal of Solar Energy 7
(c)
Mon
thBo
romo
Gaoua
Ann
ualstatistics
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Janu
ary
1722759
17119
58
063
10801
1534755
155413
7minus12
6minus19383
February
188579
41895517
minus052
minus9723
172016
6170593
4083
14232
March
193870
41919834
097
18870
1738572
1726071
072
12501
April
1928661
1942054
minus069
minus13392
1729266
1748253
minus110
minus1898
8May
195699
3198478
1minus14
2minus2778
8174898
21759066
minus058
minus10084
June
189094
8184817
0226
4277
81666223
1652431
083
1379
2July
1770250
1752081
103
1817
01478479
1476378
014
2101
August
1660503
168813
9minus16
6minus27636
1385025
138510
1minus001
minus076
Septem
ber
1778886
1800818
minus12
3minus2193
21527047
1530628
minus023
minus3581
Octob
er1890286
1856596
178
33690
1673526
1669872
022
3654
Novem
ber
1785876
1804
286
minus10
3minus18409
1561020
155818
6018
2835
Decem
ber
1690628
1696056
minus032
minus5429
1463367
1460369
020
2997
minus849Eminus12
440
Eminus12
MBD
2314
31093
4RM
SD12
2Eminus13
133E
minus13
119905
2201
2201
119905-critic
(d)
Mon
thPo
Dedou
gou
Ann
ualstatistics
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Janu
ary
1673449
166977
9022
3669
1664
515
160379
5365
6072
0February
1854006
186291
9minus048
minus8913
1857876
1865884
minus043
minus8008
March
1899224
1855346
231
43878
19114
69
1943673
minus16
8minus32204
April
1775381
1831460
minus316
minus56078
194899
51925219
122
23776
May
1919388
1909568
051
9820
202519
0200578
1096
19409
June
185472
2183297
7117
2174
51909455
1910229
minus004
minus774
July
1650000
1676535
minus16
1minus26535
1821364
1837366
minus088
minus16002
August
1591200
1554206
232
3699
4172390
91743045
minus111
minus1913
5Septem
ber
1740
550
1777604
minus213
minus37054
1941336
192178
510
119551
Octob
er1866
828
1845435
115
21393
191479
21907477
038
7316
Novem
ber
1700718
1687818
076
1290
0170896
3173612
8minus15
9minus2716
6Decem
ber
1592868
1614687
minus13
7minus21819
1598303
162578
5minus17
2minus27483
minus256Eminus11
minus10
6Eminus11
MBD
29266
26271
RMSD
290Eminus13
134E
minus13
119905
2201
2201
119905-critic
8 Journal of Solar Energy
Table 5 Calculated and estimated quantities along with the error based on relation (18)
Quantities Ouaga Dori Bobo Gaoua Fada Boromo Po DedougouCalculated 049 059 050 045 051 052 050 052Correlated 052 058 048 044 051 051 049 051119890 () minus612 169 400 222 192 192 200 192
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Mon
thly
mea
n da
ily g
loba
lso
lar r
adia
tion
(kJ(
m2middotd
ay))
times103
15
16
17
18
19
20
21
Measured valuesMultiple regressionAngstrom equation
Figure 6 Comparison between measured and correlated values atDedougou
For the station of Ouagadougou the relative error variesbetween minus125 and 131 while the RMSD is estimatedto be 14181 kJm2 For Dori station the relative error iscomprised between ndash278 and 198 and the RMSD is equalto 31236 kJm2 All these results are in the acceptable marginWe obtained small errors because the values simulated arecompared with the average of measurement data over theperiod of the study (1977ndash2006) We would obtain highererrors if we carried out the comparisons with the measureddata for unspecified year
The relative errors vary between minus269 and 291 andbetween ndash282 and 219 respectively for the stations ofBobo and Fadawhile the RMSD are equal to 26787 kJm2 and24835 kJm2 for the same stations Once again the marginerror is acceptable
For the station of Boromo the relative error fluctuatesbetween minus166 and 226 while the RMSD is equal to23143 kJm2 The relative error varies between minus126 and083 and the RMSD is equal to 10934 kJm2 for the stationof Gaoua Once again these quantities are acceptable
For the two stations Po and Dedougou the respectiverelative errors vary between minus316 and 232 and betweenndash172 and 365 while the RMSD are equal to 29266 kJm2and 26271 kJm2 respectively The margin is acceptable TheMBD for the eight stations is comprised between 10minus11 kJm2and 10minus13 kJm2
44 Correlation between the Average Daily Ratio of SunshineDuration the Index of Clearness and the Latitude and Lon-gitude Equation (18) is obtained by substituting the valuesof the regression coefficients and the parameters in relation(12) This equation is valid nationwide and can be utilized to
compute the global solar radiation for the stations measuringthe sunshine duration Consider
119867
119867
119900
= 02689 minus 03108
119899
119873
+ 22147120601 minus 02729119871 (18)
where 119871 (in radian) stands for the longitude and the otherparameters have been defined already
The value of 094 for the correlation coefficient 119877 isan indication of good correlation between the parametersTable 5 gives the calculated and the estimated values of(18) and the corresponding relative error on the indexesof clearness These errors vary from minus612 for the stationat Ouagadougou to 400 for the station at Bobo whichis an indication of good agreement between estimated andcalculated values
5 Conclusions
Besides the indication of the presence of aerosols in theatmosphere we established a correlation relation betweenthe global radiation and five geographical andmeteorologicalparameters for eight stations disseminated throughout thecountry This correlation of the global radiation intensityshows particularly its dependency with the latitude as thehigher the latitude the greater the global radiation Howeverthis trend no longer stands around urban area like Oua-gadougou which experiences lower radiation than BoromoAnother main contribution is the establishment of a relationof correlation which is valid for the entire countryThereforefor better calibration of solar equipment care must be madein gathering solar radiation data For instance in BurkinaFaso not only are the meteorological stations scarce but alsothey lack direct radiation measurement equipment whichmakes it difficult to quantify this parameter known to be veryimportant for the calibration of solar thermal technologiesAlthough the correlation equations of direct and diffuseradiation exist in the literature they need to be rather inferredfrom the measurements of the countryrsquos stations
This work can be itself extended by incorporating theinfluence of parameters such as the atmospheric pressure andthe dew point temperature or by choosing a reference yearThe actual results will be of great importance for the quan-tification of the global solar radiation especially for thosestations which are only measuring solar sunshine durationFinally the correlation relations obtained will facilitate theestimation of the solar systems performances
Journal of Solar Energy 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to thank the Head of the NationalMeteorological Service for fruitful discussion and for givinggraciously precious weather data
References
[1] A K Katiyar and C K Pandey ldquoA review of solar radiationmodelsmdashpart Irdquo Journal of Renewable Energy vol 2013 ArticleID 168048 11 pages 2013
[2] C K Pandey and A K Katiyar ldquoSolar radiation models andmeasurement techniquesrdquo Journal of Energy vol 2013 ArticleID 305207 8 pages 2013
[3] A Angstrom ldquoSolar and terrestrial radiation Report to theinternational commission for solar research on actinometricinvestigations of solar and atmospheric radiationrdquo QuarterlyJournal of the Royal Meteorological Society vol 50 no 210 pp121ndash126 1924
[4] J K Page ldquoThe estimation ofmonthlymean values of daily totalshort wave radiation on-vertical and inclined surfaces fromsun shine records for latitudes 400Nndash400 Srdquo Proceedings of theUnited Nations Conference on New Sources of Energy vol 98 no4 pp 378ndash390 1961
[5] J A Prescott ldquoEvaporation from water surface in relationto solar radiationrdquo Transactions of the Royal Society of SouthAustralia vol 64 pp 114ndash118 1940
[6] S V Tahas D Ristoiu andC Cosma ldquoTrends of the global solarradiation and air temperature in Cluj-Napoca Romania (1984ndash2008)rdquo Romanian Journal in Physics vol 56 no 5-6 pp 784ndash789 2011
[7] T Khatib A Mohamed K Sopian and M Mahmoud ldquoSolarenergy prediction forMalaysia using artificial neural networksrdquoInternational Journal of Photoenergy vol 2012 Article ID419504 16 pages 2012
[8] A A Sabziparvar ldquoGeneral formula for estimation of monthlymean global solar radiation in different climates on the southand north coasts of Iranrdquo International Journal of Photoenergyvol 2007 Article ID 94786 7 pages 2007
[9] H Li F Cao XWang andWMa ldquoA temperature-basedmodelfor estimating monthly average daily global solar radiation inChinardquoTheScientificWorld Journal vol 2014Article ID 1287549 pages 2014
[10] E Quansah L K Amekudzi K Preko et al ldquoEmpirical modelsfor estimating global solar radiation over the Ashanti Region ofGhanardquo Journal of Solar Energy vol 2014 Article ID 897970 6pages 2014
[11] K Skeiker ldquoCorrelation of global solar radiation with commongeographical and meteorological parameters for Damascusprovince Syriardquo Energy Conversion amp Management vol 47 no4 pp 331ndash345 2006
[12] O P Singh S K Srivastava and A Gaur ldquoEmpirical rela-tionship to estimate global radiation from hours of sunshinerdquoEnergy Conversion and Management vol 37 no 4 pp 501ndash5041996
[13] I Sezai and E Tasdemiroglu ldquoEvaluation of the meteorologicaldata in Northern Cyprusrdquo Energy Conversion andManagementvol 36 no 10 pp 953ndash961 1995
[14] A A Trabea and M A M Shaltout ldquoCorrelation of globalsolar radiation with meteorological parameters over EgyptrdquoRenewable Energy vol 21 no 2 pp 297ndash308 2000
[15] J C Ododo and A Usman ldquoCorrelation of total solar radiationwith common meteorological parameters for Yola and CalabarNigeriardquo Energy Conversion amp Management vol 37 no 5 pp521ndash530 1996
[16] S Neske ldquoAbout the relation between sunshine duration andcloudiness on the basis of data fromHamburgrdquo Journal of SolarEnergy vol 2014 Article ID 306871 7 pages 2014
[17] A Dumas A Andrisani M Bonnici et al ldquoA new correlationbetween global solar energy radiation and daily temperaturevariationsrdquo Solar Energy vol 116 pp 117ndash124 2015
[18] A J Garane Climatologie du rayonnement solaire global duBurkina Faso Niamey Niger [Memoire de fin drsquoEtudes drsquoInge-nieurs] 1992
[19] C Baldy Contribution a Lrsquoetude du Rayonnement Global et dela Duree Drsquoinsolation en Haute-Volta Service MeteorologigueOuagdougou Burkina Faso 1976
[20] O Coulibaly 2011 Contribution a lrsquoelaboration drsquoune reglemen-tation thermique et energetique des batiments au Burkina FasoDonnees de base multiparametriques et modelisation thermo-aeraulique sous CoDyBa et TRNSYS [these de doctorat] Univer-site de Ouagadougou Burkina Faso 2011
[21] M Daguenet Les Sechoirs Solaires Theories et PratiquesUNESCO Paris France 1982
[22] Y JannotThermique Solaire EIER mars Ouagadougou Burk-ina Faso 1993
[23] P J Lunde Solar Thermal Engineering Space Heating and HotWater Systems John Wiley amp Sons New York NY USA 1980
[24] K M Latha and K V S Badarinath ldquoSeasonal variations ofPM10and PM
25particles loading over tropical urban environ-
mentrdquo International Journal of Environmental Health Researchvol 15 no 1 pp 63ndash68 2005
TribologyAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FuelsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
CombustionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Renewable Energy
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
StructuresJournal of
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear InstallationsScience and Technology of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solar EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Wind EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear EnergyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
6 Journal of Solar Energy
Table4(a)119890M
BDR
MSD
119905and
119905-criticforO
uagado
ugou
andDori(b)119890M
BDR
MSD
119905and
119905-criticforB
oboandFada(c)119890M
BDR
MSD
119905and
119905-criticforB
orom
oandGaoua(d)
119890M
BDR
MSD
119905and
119905-criticforP
oandDedou
gou
(a)
Mon
thOuagado
ugou
Dori
Ann
ualstatistics
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Janu
ary
1593619
1580818
080
12802
1883522
189091
6minus039
minus7394
February
179438
1181673
8minus12
5minus22357
211576
9210470
1053
11068
March
1871065
1846550
131
24515
2237844
2194349
198
43495
April
1860
079
1871814
minus063
minus11734
220313
42259076
minus248
minus5594
2May
189695
7191010
0minus069
minus1314
32228402
2241255
minus057
minus12854
June
1851597
1830751
113
20846
2164
215
2128711
167
35504
July
1709075
1712545
minus020
minus3470
2110696
208818
710
822509
August
156770
1157890
0minus071
minus1119
92025322
2083244
minus278
minus5792
3Septem
ber
1738429
1735441
017
2988
212670
7209595
514
730752
Octob
er1783503
1770843
071
12660
2075201
2067421
038
7780
Novem
ber
168916
9169873
6minus057
minus9567
1980527
1983045
minus013
minus2518
Decem
ber
1583508
1585848
minus015
minus2341
1852580
1867057
minus078
minus14477
minus273Eminus12
909E
minus13
MBD
1418
131236
RMSD
638Eminus14
966E
minus15
119905
2201
2201
119905-critic
(b)
Mon
thBo
boFada
Ann
ualstatistics
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Janu
ary
1670671
1693578
minus13
7minus2290
7177792
01761675
091
16245
February
1927308
191292
7075
14381
1947206
1919814
141
27392
March
193975
81946355
minus034
minus6597
199476
41993531
006
1233
April
1892000
1885458
035
6541
1977473
2004
124
minus13
5minus26651
May
188078
31901057
minus10
8minus20275
1990334
1990476
minus001
minus14
2June
181798
51795433
124
22551
1919464
1905735
072
1372
9July
1687848
1687692
001
156
1825211
182194
5018
3266
August
1607626
163990
3minus201
minus32277
175710
4174992
4041
7181
Septem
ber
1774492
1722878
291
51614
1757560
179695
4minus224
minus39394
Octob
er1736800
1783496
minus269
minus46
696
180374
31764
291
219
39452
Novem
ber
1734772
1703431
181
31341
1776281
177078
2031
5498
Decem
ber
160979
61607629
013
2167
1692480
1740289
minus282
minus47809
144E
minus11
142E
minus11
MBD
2678
724835
RMSD
178E
minus13
190E
minus13
119905
2201
2201
119905-critic
Journal of Solar Energy 7
(c)
Mon
thBo
romo
Gaoua
Ann
ualstatistics
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Janu
ary
1722759
17119
58
063
10801
1534755
155413
7minus12
6minus19383
February
188579
41895517
minus052
minus9723
172016
6170593
4083
14232
March
193870
41919834
097
18870
1738572
1726071
072
12501
April
1928661
1942054
minus069
minus13392
1729266
1748253
minus110
minus1898
8May
195699
3198478
1minus14
2minus2778
8174898
21759066
minus058
minus10084
June
189094
8184817
0226
4277
81666223
1652431
083
1379
2July
1770250
1752081
103
1817
01478479
1476378
014
2101
August
1660503
168813
9minus16
6minus27636
1385025
138510
1minus001
minus076
Septem
ber
1778886
1800818
minus12
3minus2193
21527047
1530628
minus023
minus3581
Octob
er1890286
1856596
178
33690
1673526
1669872
022
3654
Novem
ber
1785876
1804
286
minus10
3minus18409
1561020
155818
6018
2835
Decem
ber
1690628
1696056
minus032
minus5429
1463367
1460369
020
2997
minus849Eminus12
440
Eminus12
MBD
2314
31093
4RM
SD12
2Eminus13
133E
minus13
119905
2201
2201
119905-critic
(d)
Mon
thPo
Dedou
gou
Ann
ualstatistics
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Janu
ary
1673449
166977
9022
3669
1664
515
160379
5365
6072
0February
1854006
186291
9minus048
minus8913
1857876
1865884
minus043
minus8008
March
1899224
1855346
231
43878
19114
69
1943673
minus16
8minus32204
April
1775381
1831460
minus316
minus56078
194899
51925219
122
23776
May
1919388
1909568
051
9820
202519
0200578
1096
19409
June
185472
2183297
7117
2174
51909455
1910229
minus004
minus774
July
1650000
1676535
minus16
1minus26535
1821364
1837366
minus088
minus16002
August
1591200
1554206
232
3699
4172390
91743045
minus111
minus1913
5Septem
ber
1740
550
1777604
minus213
minus37054
1941336
192178
510
119551
Octob
er1866
828
1845435
115
21393
191479
21907477
038
7316
Novem
ber
1700718
1687818
076
1290
0170896
3173612
8minus15
9minus2716
6Decem
ber
1592868
1614687
minus13
7minus21819
1598303
162578
5minus17
2minus27483
minus256Eminus11
minus10
6Eminus11
MBD
29266
26271
RMSD
290Eminus13
134E
minus13
119905
2201
2201
119905-critic
8 Journal of Solar Energy
Table 5 Calculated and estimated quantities along with the error based on relation (18)
Quantities Ouaga Dori Bobo Gaoua Fada Boromo Po DedougouCalculated 049 059 050 045 051 052 050 052Correlated 052 058 048 044 051 051 049 051119890 () minus612 169 400 222 192 192 200 192
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Mon
thly
mea
n da
ily g
loba
lso
lar r
adia
tion
(kJ(
m2middotd
ay))
times103
15
16
17
18
19
20
21
Measured valuesMultiple regressionAngstrom equation
Figure 6 Comparison between measured and correlated values atDedougou
For the station of Ouagadougou the relative error variesbetween minus125 and 131 while the RMSD is estimatedto be 14181 kJm2 For Dori station the relative error iscomprised between ndash278 and 198 and the RMSD is equalto 31236 kJm2 All these results are in the acceptable marginWe obtained small errors because the values simulated arecompared with the average of measurement data over theperiod of the study (1977ndash2006) We would obtain highererrors if we carried out the comparisons with the measureddata for unspecified year
The relative errors vary between minus269 and 291 andbetween ndash282 and 219 respectively for the stations ofBobo and Fadawhile the RMSD are equal to 26787 kJm2 and24835 kJm2 for the same stations Once again the marginerror is acceptable
For the station of Boromo the relative error fluctuatesbetween minus166 and 226 while the RMSD is equal to23143 kJm2 The relative error varies between minus126 and083 and the RMSD is equal to 10934 kJm2 for the stationof Gaoua Once again these quantities are acceptable
For the two stations Po and Dedougou the respectiverelative errors vary between minus316 and 232 and betweenndash172 and 365 while the RMSD are equal to 29266 kJm2and 26271 kJm2 respectively The margin is acceptable TheMBD for the eight stations is comprised between 10minus11 kJm2and 10minus13 kJm2
44 Correlation between the Average Daily Ratio of SunshineDuration the Index of Clearness and the Latitude and Lon-gitude Equation (18) is obtained by substituting the valuesof the regression coefficients and the parameters in relation(12) This equation is valid nationwide and can be utilized to
compute the global solar radiation for the stations measuringthe sunshine duration Consider
119867
119867
119900
= 02689 minus 03108
119899
119873
+ 22147120601 minus 02729119871 (18)
where 119871 (in radian) stands for the longitude and the otherparameters have been defined already
The value of 094 for the correlation coefficient 119877 isan indication of good correlation between the parametersTable 5 gives the calculated and the estimated values of(18) and the corresponding relative error on the indexesof clearness These errors vary from minus612 for the stationat Ouagadougou to 400 for the station at Bobo whichis an indication of good agreement between estimated andcalculated values
5 Conclusions
Besides the indication of the presence of aerosols in theatmosphere we established a correlation relation betweenthe global radiation and five geographical andmeteorologicalparameters for eight stations disseminated throughout thecountry This correlation of the global radiation intensityshows particularly its dependency with the latitude as thehigher the latitude the greater the global radiation Howeverthis trend no longer stands around urban area like Oua-gadougou which experiences lower radiation than BoromoAnother main contribution is the establishment of a relationof correlation which is valid for the entire countryThereforefor better calibration of solar equipment care must be madein gathering solar radiation data For instance in BurkinaFaso not only are the meteorological stations scarce but alsothey lack direct radiation measurement equipment whichmakes it difficult to quantify this parameter known to be veryimportant for the calibration of solar thermal technologiesAlthough the correlation equations of direct and diffuseradiation exist in the literature they need to be rather inferredfrom the measurements of the countryrsquos stations
This work can be itself extended by incorporating theinfluence of parameters such as the atmospheric pressure andthe dew point temperature or by choosing a reference yearThe actual results will be of great importance for the quan-tification of the global solar radiation especially for thosestations which are only measuring solar sunshine durationFinally the correlation relations obtained will facilitate theestimation of the solar systems performances
Journal of Solar Energy 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to thank the Head of the NationalMeteorological Service for fruitful discussion and for givinggraciously precious weather data
References
[1] A K Katiyar and C K Pandey ldquoA review of solar radiationmodelsmdashpart Irdquo Journal of Renewable Energy vol 2013 ArticleID 168048 11 pages 2013
[2] C K Pandey and A K Katiyar ldquoSolar radiation models andmeasurement techniquesrdquo Journal of Energy vol 2013 ArticleID 305207 8 pages 2013
[3] A Angstrom ldquoSolar and terrestrial radiation Report to theinternational commission for solar research on actinometricinvestigations of solar and atmospheric radiationrdquo QuarterlyJournal of the Royal Meteorological Society vol 50 no 210 pp121ndash126 1924
[4] J K Page ldquoThe estimation ofmonthlymean values of daily totalshort wave radiation on-vertical and inclined surfaces fromsun shine records for latitudes 400Nndash400 Srdquo Proceedings of theUnited Nations Conference on New Sources of Energy vol 98 no4 pp 378ndash390 1961
[5] J A Prescott ldquoEvaporation from water surface in relationto solar radiationrdquo Transactions of the Royal Society of SouthAustralia vol 64 pp 114ndash118 1940
[6] S V Tahas D Ristoiu andC Cosma ldquoTrends of the global solarradiation and air temperature in Cluj-Napoca Romania (1984ndash2008)rdquo Romanian Journal in Physics vol 56 no 5-6 pp 784ndash789 2011
[7] T Khatib A Mohamed K Sopian and M Mahmoud ldquoSolarenergy prediction forMalaysia using artificial neural networksrdquoInternational Journal of Photoenergy vol 2012 Article ID419504 16 pages 2012
[8] A A Sabziparvar ldquoGeneral formula for estimation of monthlymean global solar radiation in different climates on the southand north coasts of Iranrdquo International Journal of Photoenergyvol 2007 Article ID 94786 7 pages 2007
[9] H Li F Cao XWang andWMa ldquoA temperature-basedmodelfor estimating monthly average daily global solar radiation inChinardquoTheScientificWorld Journal vol 2014Article ID 1287549 pages 2014
[10] E Quansah L K Amekudzi K Preko et al ldquoEmpirical modelsfor estimating global solar radiation over the Ashanti Region ofGhanardquo Journal of Solar Energy vol 2014 Article ID 897970 6pages 2014
[11] K Skeiker ldquoCorrelation of global solar radiation with commongeographical and meteorological parameters for Damascusprovince Syriardquo Energy Conversion amp Management vol 47 no4 pp 331ndash345 2006
[12] O P Singh S K Srivastava and A Gaur ldquoEmpirical rela-tionship to estimate global radiation from hours of sunshinerdquoEnergy Conversion and Management vol 37 no 4 pp 501ndash5041996
[13] I Sezai and E Tasdemiroglu ldquoEvaluation of the meteorologicaldata in Northern Cyprusrdquo Energy Conversion andManagementvol 36 no 10 pp 953ndash961 1995
[14] A A Trabea and M A M Shaltout ldquoCorrelation of globalsolar radiation with meteorological parameters over EgyptrdquoRenewable Energy vol 21 no 2 pp 297ndash308 2000
[15] J C Ododo and A Usman ldquoCorrelation of total solar radiationwith common meteorological parameters for Yola and CalabarNigeriardquo Energy Conversion amp Management vol 37 no 5 pp521ndash530 1996
[16] S Neske ldquoAbout the relation between sunshine duration andcloudiness on the basis of data fromHamburgrdquo Journal of SolarEnergy vol 2014 Article ID 306871 7 pages 2014
[17] A Dumas A Andrisani M Bonnici et al ldquoA new correlationbetween global solar energy radiation and daily temperaturevariationsrdquo Solar Energy vol 116 pp 117ndash124 2015
[18] A J Garane Climatologie du rayonnement solaire global duBurkina Faso Niamey Niger [Memoire de fin drsquoEtudes drsquoInge-nieurs] 1992
[19] C Baldy Contribution a Lrsquoetude du Rayonnement Global et dela Duree Drsquoinsolation en Haute-Volta Service MeteorologigueOuagdougou Burkina Faso 1976
[20] O Coulibaly 2011 Contribution a lrsquoelaboration drsquoune reglemen-tation thermique et energetique des batiments au Burkina FasoDonnees de base multiparametriques et modelisation thermo-aeraulique sous CoDyBa et TRNSYS [these de doctorat] Univer-site de Ouagadougou Burkina Faso 2011
[21] M Daguenet Les Sechoirs Solaires Theories et PratiquesUNESCO Paris France 1982
[22] Y JannotThermique Solaire EIER mars Ouagadougou Burk-ina Faso 1993
[23] P J Lunde Solar Thermal Engineering Space Heating and HotWater Systems John Wiley amp Sons New York NY USA 1980
[24] K M Latha and K V S Badarinath ldquoSeasonal variations ofPM10and PM
25particles loading over tropical urban environ-
mentrdquo International Journal of Environmental Health Researchvol 15 no 1 pp 63ndash68 2005
TribologyAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FuelsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
CombustionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Renewable Energy
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
StructuresJournal of
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear InstallationsScience and Technology of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solar EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Wind EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear EnergyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of Solar Energy 7
(c)
Mon
thBo
romo
Gaoua
Ann
ualstatistics
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Janu
ary
1722759
17119
58
063
10801
1534755
155413
7minus12
6minus19383
February
188579
41895517
minus052
minus9723
172016
6170593
4083
14232
March
193870
41919834
097
18870
1738572
1726071
072
12501
April
1928661
1942054
minus069
minus13392
1729266
1748253
minus110
minus1898
8May
195699
3198478
1minus14
2minus2778
8174898
21759066
minus058
minus10084
June
189094
8184817
0226
4277
81666223
1652431
083
1379
2July
1770250
1752081
103
1817
01478479
1476378
014
2101
August
1660503
168813
9minus16
6minus27636
1385025
138510
1minus001
minus076
Septem
ber
1778886
1800818
minus12
3minus2193
21527047
1530628
minus023
minus3581
Octob
er1890286
1856596
178
33690
1673526
1669872
022
3654
Novem
ber
1785876
1804
286
minus10
3minus18409
1561020
155818
6018
2835
Decem
ber
1690628
1696056
minus032
minus5429
1463367
1460369
020
2997
minus849Eminus12
440
Eminus12
MBD
2314
31093
4RM
SD12
2Eminus13
133E
minus13
119905
2201
2201
119905-critic
(d)
Mon
thPo
Dedou
gou
Ann
ualstatistics
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Measured(kJm2)
Estim
ated
(kJm2)
119890(
)MBD
(kJm2)
Janu
ary
1673449
166977
9022
3669
1664
515
160379
5365
6072
0February
1854006
186291
9minus048
minus8913
1857876
1865884
minus043
minus8008
March
1899224
1855346
231
43878
19114
69
1943673
minus16
8minus32204
April
1775381
1831460
minus316
minus56078
194899
51925219
122
23776
May
1919388
1909568
051
9820
202519
0200578
1096
19409
June
185472
2183297
7117
2174
51909455
1910229
minus004
minus774
July
1650000
1676535
minus16
1minus26535
1821364
1837366
minus088
minus16002
August
1591200
1554206
232
3699
4172390
91743045
minus111
minus1913
5Septem
ber
1740
550
1777604
minus213
minus37054
1941336
192178
510
119551
Octob
er1866
828
1845435
115
21393
191479
21907477
038
7316
Novem
ber
1700718
1687818
076
1290
0170896
3173612
8minus15
9minus2716
6Decem
ber
1592868
1614687
minus13
7minus21819
1598303
162578
5minus17
2minus27483
minus256Eminus11
minus10
6Eminus11
MBD
29266
26271
RMSD
290Eminus13
134E
minus13
119905
2201
2201
119905-critic
8 Journal of Solar Energy
Table 5 Calculated and estimated quantities along with the error based on relation (18)
Quantities Ouaga Dori Bobo Gaoua Fada Boromo Po DedougouCalculated 049 059 050 045 051 052 050 052Correlated 052 058 048 044 051 051 049 051119890 () minus612 169 400 222 192 192 200 192
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Mon
thly
mea
n da
ily g
loba
lso
lar r
adia
tion
(kJ(
m2middotd
ay))
times103
15
16
17
18
19
20
21
Measured valuesMultiple regressionAngstrom equation
Figure 6 Comparison between measured and correlated values atDedougou
For the station of Ouagadougou the relative error variesbetween minus125 and 131 while the RMSD is estimatedto be 14181 kJm2 For Dori station the relative error iscomprised between ndash278 and 198 and the RMSD is equalto 31236 kJm2 All these results are in the acceptable marginWe obtained small errors because the values simulated arecompared with the average of measurement data over theperiod of the study (1977ndash2006) We would obtain highererrors if we carried out the comparisons with the measureddata for unspecified year
The relative errors vary between minus269 and 291 andbetween ndash282 and 219 respectively for the stations ofBobo and Fadawhile the RMSD are equal to 26787 kJm2 and24835 kJm2 for the same stations Once again the marginerror is acceptable
For the station of Boromo the relative error fluctuatesbetween minus166 and 226 while the RMSD is equal to23143 kJm2 The relative error varies between minus126 and083 and the RMSD is equal to 10934 kJm2 for the stationof Gaoua Once again these quantities are acceptable
For the two stations Po and Dedougou the respectiverelative errors vary between minus316 and 232 and betweenndash172 and 365 while the RMSD are equal to 29266 kJm2and 26271 kJm2 respectively The margin is acceptable TheMBD for the eight stations is comprised between 10minus11 kJm2and 10minus13 kJm2
44 Correlation between the Average Daily Ratio of SunshineDuration the Index of Clearness and the Latitude and Lon-gitude Equation (18) is obtained by substituting the valuesof the regression coefficients and the parameters in relation(12) This equation is valid nationwide and can be utilized to
compute the global solar radiation for the stations measuringthe sunshine duration Consider
119867
119867
119900
= 02689 minus 03108
119899
119873
+ 22147120601 minus 02729119871 (18)
where 119871 (in radian) stands for the longitude and the otherparameters have been defined already
The value of 094 for the correlation coefficient 119877 isan indication of good correlation between the parametersTable 5 gives the calculated and the estimated values of(18) and the corresponding relative error on the indexesof clearness These errors vary from minus612 for the stationat Ouagadougou to 400 for the station at Bobo whichis an indication of good agreement between estimated andcalculated values
5 Conclusions
Besides the indication of the presence of aerosols in theatmosphere we established a correlation relation betweenthe global radiation and five geographical andmeteorologicalparameters for eight stations disseminated throughout thecountry This correlation of the global radiation intensityshows particularly its dependency with the latitude as thehigher the latitude the greater the global radiation Howeverthis trend no longer stands around urban area like Oua-gadougou which experiences lower radiation than BoromoAnother main contribution is the establishment of a relationof correlation which is valid for the entire countryThereforefor better calibration of solar equipment care must be madein gathering solar radiation data For instance in BurkinaFaso not only are the meteorological stations scarce but alsothey lack direct radiation measurement equipment whichmakes it difficult to quantify this parameter known to be veryimportant for the calibration of solar thermal technologiesAlthough the correlation equations of direct and diffuseradiation exist in the literature they need to be rather inferredfrom the measurements of the countryrsquos stations
This work can be itself extended by incorporating theinfluence of parameters such as the atmospheric pressure andthe dew point temperature or by choosing a reference yearThe actual results will be of great importance for the quan-tification of the global solar radiation especially for thosestations which are only measuring solar sunshine durationFinally the correlation relations obtained will facilitate theestimation of the solar systems performances
Journal of Solar Energy 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to thank the Head of the NationalMeteorological Service for fruitful discussion and for givinggraciously precious weather data
References
[1] A K Katiyar and C K Pandey ldquoA review of solar radiationmodelsmdashpart Irdquo Journal of Renewable Energy vol 2013 ArticleID 168048 11 pages 2013
[2] C K Pandey and A K Katiyar ldquoSolar radiation models andmeasurement techniquesrdquo Journal of Energy vol 2013 ArticleID 305207 8 pages 2013
[3] A Angstrom ldquoSolar and terrestrial radiation Report to theinternational commission for solar research on actinometricinvestigations of solar and atmospheric radiationrdquo QuarterlyJournal of the Royal Meteorological Society vol 50 no 210 pp121ndash126 1924
[4] J K Page ldquoThe estimation ofmonthlymean values of daily totalshort wave radiation on-vertical and inclined surfaces fromsun shine records for latitudes 400Nndash400 Srdquo Proceedings of theUnited Nations Conference on New Sources of Energy vol 98 no4 pp 378ndash390 1961
[5] J A Prescott ldquoEvaporation from water surface in relationto solar radiationrdquo Transactions of the Royal Society of SouthAustralia vol 64 pp 114ndash118 1940
[6] S V Tahas D Ristoiu andC Cosma ldquoTrends of the global solarradiation and air temperature in Cluj-Napoca Romania (1984ndash2008)rdquo Romanian Journal in Physics vol 56 no 5-6 pp 784ndash789 2011
[7] T Khatib A Mohamed K Sopian and M Mahmoud ldquoSolarenergy prediction forMalaysia using artificial neural networksrdquoInternational Journal of Photoenergy vol 2012 Article ID419504 16 pages 2012
[8] A A Sabziparvar ldquoGeneral formula for estimation of monthlymean global solar radiation in different climates on the southand north coasts of Iranrdquo International Journal of Photoenergyvol 2007 Article ID 94786 7 pages 2007
[9] H Li F Cao XWang andWMa ldquoA temperature-basedmodelfor estimating monthly average daily global solar radiation inChinardquoTheScientificWorld Journal vol 2014Article ID 1287549 pages 2014
[10] E Quansah L K Amekudzi K Preko et al ldquoEmpirical modelsfor estimating global solar radiation over the Ashanti Region ofGhanardquo Journal of Solar Energy vol 2014 Article ID 897970 6pages 2014
[11] K Skeiker ldquoCorrelation of global solar radiation with commongeographical and meteorological parameters for Damascusprovince Syriardquo Energy Conversion amp Management vol 47 no4 pp 331ndash345 2006
[12] O P Singh S K Srivastava and A Gaur ldquoEmpirical rela-tionship to estimate global radiation from hours of sunshinerdquoEnergy Conversion and Management vol 37 no 4 pp 501ndash5041996
[13] I Sezai and E Tasdemiroglu ldquoEvaluation of the meteorologicaldata in Northern Cyprusrdquo Energy Conversion andManagementvol 36 no 10 pp 953ndash961 1995
[14] A A Trabea and M A M Shaltout ldquoCorrelation of globalsolar radiation with meteorological parameters over EgyptrdquoRenewable Energy vol 21 no 2 pp 297ndash308 2000
[15] J C Ododo and A Usman ldquoCorrelation of total solar radiationwith common meteorological parameters for Yola and CalabarNigeriardquo Energy Conversion amp Management vol 37 no 5 pp521ndash530 1996
[16] S Neske ldquoAbout the relation between sunshine duration andcloudiness on the basis of data fromHamburgrdquo Journal of SolarEnergy vol 2014 Article ID 306871 7 pages 2014
[17] A Dumas A Andrisani M Bonnici et al ldquoA new correlationbetween global solar energy radiation and daily temperaturevariationsrdquo Solar Energy vol 116 pp 117ndash124 2015
[18] A J Garane Climatologie du rayonnement solaire global duBurkina Faso Niamey Niger [Memoire de fin drsquoEtudes drsquoInge-nieurs] 1992
[19] C Baldy Contribution a Lrsquoetude du Rayonnement Global et dela Duree Drsquoinsolation en Haute-Volta Service MeteorologigueOuagdougou Burkina Faso 1976
[20] O Coulibaly 2011 Contribution a lrsquoelaboration drsquoune reglemen-tation thermique et energetique des batiments au Burkina FasoDonnees de base multiparametriques et modelisation thermo-aeraulique sous CoDyBa et TRNSYS [these de doctorat] Univer-site de Ouagadougou Burkina Faso 2011
[21] M Daguenet Les Sechoirs Solaires Theories et PratiquesUNESCO Paris France 1982
[22] Y JannotThermique Solaire EIER mars Ouagadougou Burk-ina Faso 1993
[23] P J Lunde Solar Thermal Engineering Space Heating and HotWater Systems John Wiley amp Sons New York NY USA 1980
[24] K M Latha and K V S Badarinath ldquoSeasonal variations ofPM10and PM
25particles loading over tropical urban environ-
mentrdquo International Journal of Environmental Health Researchvol 15 no 1 pp 63ndash68 2005
TribologyAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FuelsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
CombustionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Renewable Energy
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
StructuresJournal of
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear InstallationsScience and Technology of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solar EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Wind EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear EnergyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
8 Journal of Solar Energy
Table 5 Calculated and estimated quantities along with the error based on relation (18)
Quantities Ouaga Dori Bobo Gaoua Fada Boromo Po DedougouCalculated 049 059 050 045 051 052 050 052Correlated 052 058 048 044 051 051 049 051119890 () minus612 169 400 222 192 192 200 192
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Mon
thly
mea
n da
ily g
loba
lso
lar r
adia
tion
(kJ(
m2middotd
ay))
times103
15
16
17
18
19
20
21
Measured valuesMultiple regressionAngstrom equation
Figure 6 Comparison between measured and correlated values atDedougou
For the station of Ouagadougou the relative error variesbetween minus125 and 131 while the RMSD is estimatedto be 14181 kJm2 For Dori station the relative error iscomprised between ndash278 and 198 and the RMSD is equalto 31236 kJm2 All these results are in the acceptable marginWe obtained small errors because the values simulated arecompared with the average of measurement data over theperiod of the study (1977ndash2006) We would obtain highererrors if we carried out the comparisons with the measureddata for unspecified year
The relative errors vary between minus269 and 291 andbetween ndash282 and 219 respectively for the stations ofBobo and Fadawhile the RMSD are equal to 26787 kJm2 and24835 kJm2 for the same stations Once again the marginerror is acceptable
For the station of Boromo the relative error fluctuatesbetween minus166 and 226 while the RMSD is equal to23143 kJm2 The relative error varies between minus126 and083 and the RMSD is equal to 10934 kJm2 for the stationof Gaoua Once again these quantities are acceptable
For the two stations Po and Dedougou the respectiverelative errors vary between minus316 and 232 and betweenndash172 and 365 while the RMSD are equal to 29266 kJm2and 26271 kJm2 respectively The margin is acceptable TheMBD for the eight stations is comprised between 10minus11 kJm2and 10minus13 kJm2
44 Correlation between the Average Daily Ratio of SunshineDuration the Index of Clearness and the Latitude and Lon-gitude Equation (18) is obtained by substituting the valuesof the regression coefficients and the parameters in relation(12) This equation is valid nationwide and can be utilized to
compute the global solar radiation for the stations measuringthe sunshine duration Consider
119867
119867
119900
= 02689 minus 03108
119899
119873
+ 22147120601 minus 02729119871 (18)
where 119871 (in radian) stands for the longitude and the otherparameters have been defined already
The value of 094 for the correlation coefficient 119877 isan indication of good correlation between the parametersTable 5 gives the calculated and the estimated values of(18) and the corresponding relative error on the indexesof clearness These errors vary from minus612 for the stationat Ouagadougou to 400 for the station at Bobo whichis an indication of good agreement between estimated andcalculated values
5 Conclusions
Besides the indication of the presence of aerosols in theatmosphere we established a correlation relation betweenthe global radiation and five geographical andmeteorologicalparameters for eight stations disseminated throughout thecountry This correlation of the global radiation intensityshows particularly its dependency with the latitude as thehigher the latitude the greater the global radiation Howeverthis trend no longer stands around urban area like Oua-gadougou which experiences lower radiation than BoromoAnother main contribution is the establishment of a relationof correlation which is valid for the entire countryThereforefor better calibration of solar equipment care must be madein gathering solar radiation data For instance in BurkinaFaso not only are the meteorological stations scarce but alsothey lack direct radiation measurement equipment whichmakes it difficult to quantify this parameter known to be veryimportant for the calibration of solar thermal technologiesAlthough the correlation equations of direct and diffuseradiation exist in the literature they need to be rather inferredfrom the measurements of the countryrsquos stations
This work can be itself extended by incorporating theinfluence of parameters such as the atmospheric pressure andthe dew point temperature or by choosing a reference yearThe actual results will be of great importance for the quan-tification of the global solar radiation especially for thosestations which are only measuring solar sunshine durationFinally the correlation relations obtained will facilitate theestimation of the solar systems performances
Journal of Solar Energy 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to thank the Head of the NationalMeteorological Service for fruitful discussion and for givinggraciously precious weather data
References
[1] A K Katiyar and C K Pandey ldquoA review of solar radiationmodelsmdashpart Irdquo Journal of Renewable Energy vol 2013 ArticleID 168048 11 pages 2013
[2] C K Pandey and A K Katiyar ldquoSolar radiation models andmeasurement techniquesrdquo Journal of Energy vol 2013 ArticleID 305207 8 pages 2013
[3] A Angstrom ldquoSolar and terrestrial radiation Report to theinternational commission for solar research on actinometricinvestigations of solar and atmospheric radiationrdquo QuarterlyJournal of the Royal Meteorological Society vol 50 no 210 pp121ndash126 1924
[4] J K Page ldquoThe estimation ofmonthlymean values of daily totalshort wave radiation on-vertical and inclined surfaces fromsun shine records for latitudes 400Nndash400 Srdquo Proceedings of theUnited Nations Conference on New Sources of Energy vol 98 no4 pp 378ndash390 1961
[5] J A Prescott ldquoEvaporation from water surface in relationto solar radiationrdquo Transactions of the Royal Society of SouthAustralia vol 64 pp 114ndash118 1940
[6] S V Tahas D Ristoiu andC Cosma ldquoTrends of the global solarradiation and air temperature in Cluj-Napoca Romania (1984ndash2008)rdquo Romanian Journal in Physics vol 56 no 5-6 pp 784ndash789 2011
[7] T Khatib A Mohamed K Sopian and M Mahmoud ldquoSolarenergy prediction forMalaysia using artificial neural networksrdquoInternational Journal of Photoenergy vol 2012 Article ID419504 16 pages 2012
[8] A A Sabziparvar ldquoGeneral formula for estimation of monthlymean global solar radiation in different climates on the southand north coasts of Iranrdquo International Journal of Photoenergyvol 2007 Article ID 94786 7 pages 2007
[9] H Li F Cao XWang andWMa ldquoA temperature-basedmodelfor estimating monthly average daily global solar radiation inChinardquoTheScientificWorld Journal vol 2014Article ID 1287549 pages 2014
[10] E Quansah L K Amekudzi K Preko et al ldquoEmpirical modelsfor estimating global solar radiation over the Ashanti Region ofGhanardquo Journal of Solar Energy vol 2014 Article ID 897970 6pages 2014
[11] K Skeiker ldquoCorrelation of global solar radiation with commongeographical and meteorological parameters for Damascusprovince Syriardquo Energy Conversion amp Management vol 47 no4 pp 331ndash345 2006
[12] O P Singh S K Srivastava and A Gaur ldquoEmpirical rela-tionship to estimate global radiation from hours of sunshinerdquoEnergy Conversion and Management vol 37 no 4 pp 501ndash5041996
[13] I Sezai and E Tasdemiroglu ldquoEvaluation of the meteorologicaldata in Northern Cyprusrdquo Energy Conversion andManagementvol 36 no 10 pp 953ndash961 1995
[14] A A Trabea and M A M Shaltout ldquoCorrelation of globalsolar radiation with meteorological parameters over EgyptrdquoRenewable Energy vol 21 no 2 pp 297ndash308 2000
[15] J C Ododo and A Usman ldquoCorrelation of total solar radiationwith common meteorological parameters for Yola and CalabarNigeriardquo Energy Conversion amp Management vol 37 no 5 pp521ndash530 1996
[16] S Neske ldquoAbout the relation between sunshine duration andcloudiness on the basis of data fromHamburgrdquo Journal of SolarEnergy vol 2014 Article ID 306871 7 pages 2014
[17] A Dumas A Andrisani M Bonnici et al ldquoA new correlationbetween global solar energy radiation and daily temperaturevariationsrdquo Solar Energy vol 116 pp 117ndash124 2015
[18] A J Garane Climatologie du rayonnement solaire global duBurkina Faso Niamey Niger [Memoire de fin drsquoEtudes drsquoInge-nieurs] 1992
[19] C Baldy Contribution a Lrsquoetude du Rayonnement Global et dela Duree Drsquoinsolation en Haute-Volta Service MeteorologigueOuagdougou Burkina Faso 1976
[20] O Coulibaly 2011 Contribution a lrsquoelaboration drsquoune reglemen-tation thermique et energetique des batiments au Burkina FasoDonnees de base multiparametriques et modelisation thermo-aeraulique sous CoDyBa et TRNSYS [these de doctorat] Univer-site de Ouagadougou Burkina Faso 2011
[21] M Daguenet Les Sechoirs Solaires Theories et PratiquesUNESCO Paris France 1982
[22] Y JannotThermique Solaire EIER mars Ouagadougou Burk-ina Faso 1993
[23] P J Lunde Solar Thermal Engineering Space Heating and HotWater Systems John Wiley amp Sons New York NY USA 1980
[24] K M Latha and K V S Badarinath ldquoSeasonal variations ofPM10and PM
25particles loading over tropical urban environ-
mentrdquo International Journal of Environmental Health Researchvol 15 no 1 pp 63ndash68 2005
TribologyAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FuelsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
CombustionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Renewable Energy
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
StructuresJournal of
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear InstallationsScience and Technology of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solar EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Wind EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear EnergyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of Solar Energy 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to thank the Head of the NationalMeteorological Service for fruitful discussion and for givinggraciously precious weather data
References
[1] A K Katiyar and C K Pandey ldquoA review of solar radiationmodelsmdashpart Irdquo Journal of Renewable Energy vol 2013 ArticleID 168048 11 pages 2013
[2] C K Pandey and A K Katiyar ldquoSolar radiation models andmeasurement techniquesrdquo Journal of Energy vol 2013 ArticleID 305207 8 pages 2013
[3] A Angstrom ldquoSolar and terrestrial radiation Report to theinternational commission for solar research on actinometricinvestigations of solar and atmospheric radiationrdquo QuarterlyJournal of the Royal Meteorological Society vol 50 no 210 pp121ndash126 1924
[4] J K Page ldquoThe estimation ofmonthlymean values of daily totalshort wave radiation on-vertical and inclined surfaces fromsun shine records for latitudes 400Nndash400 Srdquo Proceedings of theUnited Nations Conference on New Sources of Energy vol 98 no4 pp 378ndash390 1961
[5] J A Prescott ldquoEvaporation from water surface in relationto solar radiationrdquo Transactions of the Royal Society of SouthAustralia vol 64 pp 114ndash118 1940
[6] S V Tahas D Ristoiu andC Cosma ldquoTrends of the global solarradiation and air temperature in Cluj-Napoca Romania (1984ndash2008)rdquo Romanian Journal in Physics vol 56 no 5-6 pp 784ndash789 2011
[7] T Khatib A Mohamed K Sopian and M Mahmoud ldquoSolarenergy prediction forMalaysia using artificial neural networksrdquoInternational Journal of Photoenergy vol 2012 Article ID419504 16 pages 2012
[8] A A Sabziparvar ldquoGeneral formula for estimation of monthlymean global solar radiation in different climates on the southand north coasts of Iranrdquo International Journal of Photoenergyvol 2007 Article ID 94786 7 pages 2007
[9] H Li F Cao XWang andWMa ldquoA temperature-basedmodelfor estimating monthly average daily global solar radiation inChinardquoTheScientificWorld Journal vol 2014Article ID 1287549 pages 2014
[10] E Quansah L K Amekudzi K Preko et al ldquoEmpirical modelsfor estimating global solar radiation over the Ashanti Region ofGhanardquo Journal of Solar Energy vol 2014 Article ID 897970 6pages 2014
[11] K Skeiker ldquoCorrelation of global solar radiation with commongeographical and meteorological parameters for Damascusprovince Syriardquo Energy Conversion amp Management vol 47 no4 pp 331ndash345 2006
[12] O P Singh S K Srivastava and A Gaur ldquoEmpirical rela-tionship to estimate global radiation from hours of sunshinerdquoEnergy Conversion and Management vol 37 no 4 pp 501ndash5041996
[13] I Sezai and E Tasdemiroglu ldquoEvaluation of the meteorologicaldata in Northern Cyprusrdquo Energy Conversion andManagementvol 36 no 10 pp 953ndash961 1995
[14] A A Trabea and M A M Shaltout ldquoCorrelation of globalsolar radiation with meteorological parameters over EgyptrdquoRenewable Energy vol 21 no 2 pp 297ndash308 2000
[15] J C Ododo and A Usman ldquoCorrelation of total solar radiationwith common meteorological parameters for Yola and CalabarNigeriardquo Energy Conversion amp Management vol 37 no 5 pp521ndash530 1996
[16] S Neske ldquoAbout the relation between sunshine duration andcloudiness on the basis of data fromHamburgrdquo Journal of SolarEnergy vol 2014 Article ID 306871 7 pages 2014
[17] A Dumas A Andrisani M Bonnici et al ldquoA new correlationbetween global solar energy radiation and daily temperaturevariationsrdquo Solar Energy vol 116 pp 117ndash124 2015
[18] A J Garane Climatologie du rayonnement solaire global duBurkina Faso Niamey Niger [Memoire de fin drsquoEtudes drsquoInge-nieurs] 1992
[19] C Baldy Contribution a Lrsquoetude du Rayonnement Global et dela Duree Drsquoinsolation en Haute-Volta Service MeteorologigueOuagdougou Burkina Faso 1976
[20] O Coulibaly 2011 Contribution a lrsquoelaboration drsquoune reglemen-tation thermique et energetique des batiments au Burkina FasoDonnees de base multiparametriques et modelisation thermo-aeraulique sous CoDyBa et TRNSYS [these de doctorat] Univer-site de Ouagadougou Burkina Faso 2011
[21] M Daguenet Les Sechoirs Solaires Theories et PratiquesUNESCO Paris France 1982
[22] Y JannotThermique Solaire EIER mars Ouagadougou Burk-ina Faso 1993
[23] P J Lunde Solar Thermal Engineering Space Heating and HotWater Systems John Wiley amp Sons New York NY USA 1980
[24] K M Latha and K V S Badarinath ldquoSeasonal variations ofPM10and PM
25particles loading over tropical urban environ-
mentrdquo International Journal of Environmental Health Researchvol 15 no 1 pp 63ndash68 2005
TribologyAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FuelsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
CombustionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Renewable Energy
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
StructuresJournal of
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear InstallationsScience and Technology of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solar EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Wind EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear EnergyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
TribologyAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FuelsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
CombustionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Renewable Energy
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
StructuresJournal of
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear InstallationsScience and Technology of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solar EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Wind EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear EnergyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014