research article a comparative study of some regression...
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Hindawi Publishing CorporationISRN Renewable EnergyVolume 2013 Article ID 754956 11 pageshttpdxdoiorg1011552013754956
Research ArticleA Comparative Study of Some Regression Models toEstimate the Global Solar Radiation on a Horizontal Surfacefrom Sunshine Duration and Meteorological Parameters forGhardaa Site Algeria
Kacem Gairaa and Yahia Bakelli
Unite de Recherche Appliquee en Energies Renouvelables (URAER) Centre de Developpement des Energies Renouvelable (CDER)47133 Ghardaıa Algeria
Correspondence should be addressed to Kacem Gairaa gisol47gmailcom
Received 15 April 2013 Accepted 20 May 2013
Academic Editors B Chen S S Kalligeros S Li Z Oktay and M Souliotis
Copyright copy 2013 K Gairaa and Y Bakelli This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
A comparison between some regression correlations for predicting the global solar radiation received on a horizontal plane hasbeen processed Seven models for estimating the global solar radiation from sunshine duration and twometeorological parameters(air temperature and relative humidity) are presented The root mean square error (RMSE) mean bias error (MBE) correlationcoefficient (CC) and percentage error (e) have been also computed to test the accuracy of the proposed models Comparisonsbetween the measured and the calculated values have been made The results obtained show that the linear and quadratic modelsare the most suitable for estimating the global solar radiation from sunshine duration and for the models based on meteorologicalparameters Abdalla and Ojosursquos models give the best performance with a CC of 0898 and 0892 respectively
1 Introduction
Solar energy applications require a complete knowledge anddetailed analysis about the potential of the site so a databaseat ground level is an important feature of solar energysystems
Measurements of global solar radiation reaching thesurface of the earth and its two components direct and diffuseare essential in the most research fields of solar energy Thedaily values as well as themonthly ones are needed to evaluatethe performance of existing solar devices and estimate theefficiency of the future installations [1 2]
When the site under consideration is equipped with aradiometric station operates regularly for several years it willbe easier to exploit solar energy resource However in mostcases there are no local measurements and we must resort toapproximate methods to predict the characteristics of solarradiation
In order to estimate the amount of solar energy incidenton a horizontal surface many models have been developedwhich relate the global solar radiation (H) with the sunshineduration The first one is that proposed by Angstrom [3ndash5] which predicts the monthly average daily global solarradiation from sunshine duration and clear sky radiationdata Prescott puts this equation in a more convenient formreplacing the clear sky radiation by the extraterrestrial one[6] Then the Angstrom-Prescott model was developed bymany researchers who have correlated the global solar radi-ation with the sunshine duration in another regression forms[7ndash22] and with some meteorological parameters such as airtemperature relative humidity cloudiness and wind velocity[23ndash34] Each of these factors contributes in a significantmanner in the estimation of global solar radiation
In this work a comparative study between seven modelsto estimate the global solar radiation on a horizontal surfacefrom sunshine duration and somemeteorological parameters
2 ISRN Renewable Energy
Table 1 Technical specifications of EKOMS-64 Pyranometer
Technical specifications Used PyranometerDirectional response ltplusmn10Wm2
Temperature response ltplusmn1Nonlinearity ltplusmn02Tilt response ltplusmn02Operating temperature range (∘C) minus40sim+80Wavelength range (nm) 305ndash2800
has been conducted using the local data of Ghardaıa regionThe comparison between the estimated and the measuredglobal solar radiation has been illustrated
2 Database
The data used in this study are taken from the solar radi-ation laboratory located in the Applied Research Unit forRenewable Energies (URAER) Ghardaıa site is consideredan arid and dry area located in the south of Algeria about600Km south of the capital city it is framed by the followinggeographical coordinates latitude of 32∘361015840N longitude of3∘481015840 E and altitude of 450m above MSL The global solarradiation data are measured via an EKOMS-64 Pyranometerwith the short wave sensitivity of (70mVkWm2) moretechnical specifications of this Pyranometer are describedin Table 1 The air temperature and relative humidity mea-surement data were made by TECNOEL sonde Thermo-Igromertiche its calibration accuracy is plusmn15 and tem-perature sensitivity is 01 (∘CmV) A data logger and aCampbell Scientific CR10X data acquisition systemwere usedfor reading the measurements From the raw data storedfor every five minutes the mean maximum and minimumhourly values were calculated From the hourly data setdaily and monthly statistics were made for the global solarradiation and meteorological data
The average hours of sunshine duration are illustrated inFigure 1 for the site under consideration the highest valueswere in the summer season with a mean value of 1223 hourswhile the lowest values were in the winter season with ameanvalue of 743 hours The monthly average daily global solarradiation air temperature and relative humidity are shownin Figures 2 3 and 4
3 Models Used
A brief description of the mathematical expression of thevarious models proposed in the present paper is given below
31 Angstrom-Prescott Model (Linear Model) [4 24] TheAngstrom-Prescott model is widely described by the authorsin the study of solar radiation since Prescott has developed in1940 the general form of this model is given by
119867
1198670
= 119886 + 119887(
SSSS0
) (1)
783819
1032
1085
112
12231193
1087
9
827
799743
JanuaryFebruaryMarchAprilMayJune
JulyAugustSeptemberOctoberNovemberDecember
Figure 1 The monthly average daily hours of sunshine duration
0
1000
2000
3000
4000
5000
6000
7000
8000
1 2 3 4 5 6 7 8 9 10 11 12
Glo
bal s
olar
radi
atio
n (W
hm
2)
Month
Figure 2 Global solar radiation on horizontal surface
where1198670is the monthly average daily extraterrestrial radia-
tion (MJm2 sdot day) which can be expressed as
1198670=
24
120587
119866SC (1 + 0033360 sdot 119863
119899
365
)
sdot (cos120593 cos 120575 sin120596 + 2120587
360
120596 sin120593 sin 120575) (2)
where 120596 is sunset hour angle in degree defined as
120596 = cosminus1 (minus tan120593 tan 120575) (3)
119866SC is the solar constant taken equal to 1367 (Wm2) 120593 isthe latitude of the location under consideration119863
119899is the day
ISRN Renewable Energy 3
0
5
10
15
20
25
30
35
40
45
1 2 3 4 5 6 7 8 9 10 11 12
MinimumMaximumAverage
Month
Tem
pera
ture
(∘C)
Figure 3 The minimum maximum and average air temperature
0
10
20
30
40
50
60
70
80
1 2 3 4 5 6 7 8 9 10 11 12
MinimumMaximumAverage
Relat
ive h
umid
ity (
)
Month
Figure 4The minimum maximum and average relative humidity
number of the year starting from the first of January and 120575 isthe declination angle as given below
120575 = 2345 sin[360(284 + 119863
119899)
365
] (4)
SS is the monthly daily sunshine duration SS0is the maxi-
mum possible monthly average daily sunshine hours or theday length
32 Ogelman et alrsquos Model (Quadratic Model) [24] Ogelmanet alrsquos have correlated (119867119867
0) with (SSSS
0) in the form
of second-order polynomial equation
119867
1198670
= 119886 + 119887(
SSSS0
) + 119888(
SSSS0
)
2
(5)
33 Ampratwum et alrsquos Model (Logarithmic Model) [14 24]In order to have more precision in the estimation of theglobal solar radiation Ampratwum et al have developed alogarithmic form of linear model as described below
119867
1198670
= 119886 + 119887 log( SSSS0
) (6)
34 Almorox et alrsquos Model (Exponential Model) [8 24] Theexponential correlation between (119867119867
0) and (SSSS
0) is
given by Almorox et al as119867
1198670
= 119886 + 119887119890(SSSS0)
(7)
35 Abdallarsquos Model [25 26] Abdallarsquos model correlates(119867119867
0) with the sunshine duration maximum air temper-
ature and average relative humidity in order to increase theaccuracy of the estimating coefficients This model is basedon the Gopinathan model [26] which studied the variationof (119867119867
0) as a function of the latitude and the elevation
of the site the fraction of insolation air temperature andthe maximum average relative humidity This model has thefollowing expression
119867
1198670
= 119886 + 119887(
SSSS0
) + 119888 (119879max) + 119889 (RH) (8)
where 119879max is the daily mean maximum air temperature andRH is the daily mean relative humidity as a percentage
36 Ojosu and Komolafersquos Model [31] Ojosu and Komolafeproposed the equation below
119867
1198670
= 119886 + 119887(
SSSS0
) + 119888(
119879min119879max
) + 119889(
RHminRHmax
) (9)
where 119879min 119879max RHmin and RHmax are the mean minimumair temperature mean maximum air temperature meanminimum relative humidity and mean maximum relativehumidity respectively
37 Hargreaves et alrsquos Model [29 30 32] Hargreaves et alwere the first to propose a procedure to estimate the globalsolar radiation by using the difference between daily maxi-mumanddailyminimumair temperature and extraterrestrialradiation The proposed equation has the following form
119867
1198670
= 119886 + 119887(119879max minus 119879min)05
(10)
where 119879min and 119879max are the meanminimum air temperatureand mean maximum air temperature
A program written in MATLAB allowing to determinethe empirical constants 119886 119887 119888 and 119889 for each describedmodel and comparedmodels was thus foundwith the groundmeasurements
4 ISRN Renewable Energy
Table 2 Linear model validation
119886 119887 CC RMSE MBEJanuary 0361 0457 0890 00361 minus000044February 0303 0515 0715 00664 000060March 0477 032 0916 00269 minus000028April 0425 0389 0929 00213 000035May 0466 033 0897 00344 minus001990June 0443 0332 0946 00196 000040July 0453 0307 0853 00246 minus000018August 0481 0273 0731 00284 minus000081September 0376 0402 0789 00534 0000077October 0398 0357 0934 00226 minus000032November 0451 0315 0620 00649 000045December 0373 0406 0856 00452 minus000047
Table 3 Quadratic model validation
119886 119887 119862 CC RMSE MBEJanuary 0337 0618 minus0159 0896 0035 minus000028February 0335 0408 008 0715 0066 minus000047March 0469 0361 minus0037 0917 0026 minus0000056April 0372 0574 minus0143 0935 002 minus000058May 0443 0444 minus0104 0903 0027 minus000067June 0411 0497 minus015 0956 0018 000043July 046 0282 002 0853 0025 minus000016August 0278 0937 minus0497 0833 0022 000014September 0367 0452 minus0046 079 0053 000023October 0375 0479 minus0114 094 0022 minus000033November 0466 0198 0118 0623 0063 000049December 0277 0956 minus0504 0894 0039 000057
4 Statistical Test
The accuracy of the estimated models will be judged bythe statistical indicators such as the correlation coefficient(CC) mean bias error (MBE) root mean square error(RMSE) and the percentage error (119890) These indicators areusually applied in the comparison of solar radiation modelsThe mean square error provides information about theperformance of correlations which allows comparison ofthe real differences between the estimated values and themeasured ones a low RMSE is desirable The MBE providesthe long-term performance of the model in general thepositive MBE shows overestimation while the negative MBEindicates underestimationThe correlation coefficient reflectsthe quality of the model the more CC close to 1 the more thebetter quality The expression of each statistical indicator isgiven
CC = 1 minussum119899
119894=1
(119867119894119898minus 119867119894119890)2
sum119899
119894=1
(119867119894119898minus 119867119898)
2
MBE = 1119899
(
119899
sum
119894=1
119867119894119890minus 119867119894119898
119867119894119898
)
RMSE = [1119899
119899
sum
119894=1
(
119867119894119890minus 119867119894119898
119867119894119898
)
2
]
12
119890 = [(
119867119894119898minus 119867119894119890
119867119894119898
)] 100
(11)
where 119867119894119890
and 119867119894119898
are the 119894th estimated and measuredvalues 119867
119898is the mean of observed data and 119899 is the total
number of observations
5 Results and Discussion
The results of the validation of the models that estimate theglobal solar radiation from sunshine duration on themonthlybasis are presented in Tables 2 3 4 and 5 The analysis ofthe measured and calculated values shows that the maximumof the global solar radiation is observed in June while theminimum values are appearing in December
For the linear model the correlation coefficient is signifi-cant for all months of the year except in November where it isrelatively lowThe quality of the estimate is a slightly worse for
ISRN Renewable Energy 5
Table 4 Logarithmic model validation
119886 119887 CC RMSE MBEJanuary 0741 0079 0792 0077 00235February 0795 0314 0693 0102 00536March 0734 0079 0651 0151 00566April 0792 0218 0917 0061 00369May 0757 0121 0825 0067 00338June 0734 0112 0862 0061 00294July 0735 0164 0816 0058 00393August 0743 0176 0805 0048 00321September 0714 0097 0613 0091 00281October 0708 0121 0864 0065 00330November 0724 009 0487 0088 00259December 0749 0176 0886 0088 00465
Table 5 Exponential model validation
119886 119887 CC RMSE MBEJanuary 014 0261 0861 004 minus000071February 0128 026 0713 0063 minus000047March 0342 0173 0878 0032 000003April 0295 0195 0901 0025 minus000026May 0321 0181 0868 0032 minus000077June 0295 0183 0916 0024 minus000040July 0335 0163 0846 0025 000078August 0403 0132 067 0032 minus000022September 0192 0224 0774 0055 minus000044October 0236 0199 0901 0028 minus00015November 0283 0187 0621 0045 0104December 0188 0225 0822 0073 minus00096
the months of the February and November when the RMSEis between 0064 and 0069
For the quadratic correlation the result shows a slightimprovement in the accuracy of the model for the monthof August where the coefficient of determination is equal to083 (compared to the linear model CC = 073) the qualityof estimation is also improved in the months of June andDecember with an RMSE of 0018 and 0039 respectivelyTheregression based on the logarithmic and exponential modelsdid not improve significantly the accuracy of estimation of theglobal solar radiation than the two previous models as seenfrom the values of the CC MBE and RMSE (Correlationcoefficient reached his minimum values in November (CC =048) for the logarithmic model)
Another manner of the comparison between the mea-sured and the predicted values was illustrated by the scatterdiagram plotted in Figures 5 6 7 and 8 A strong scatteringof the points in the superior or in the inferior half of theregression line indicates respectively an overestimate or anunderestimate
For the linear model the dispersion of estimated valuesaround the regression line is fairly low in the months ofJanuary March-August October and December where thecorrelation coefficient ranges between 085 and 094 while
this dispersion is small in the quadratic model this indicatesan excellent fitting between the global radiation and thesunshine duration
For the logarithmic model the dispersion of the esti-mated values is strong especially in the months of JanuaryMarch and August and it is low in the months of FebruarySeptember and November while this dispersion remainslow for the exponential model in the months of FebruarySeptember and November and it is strong too for the othermonths of the year
The confrontation between estimated and measuredmonthly average global solar radiation by the different mod-els is shown in Table 6 which indicated that the percentageerror never exceeds plusmn10 for all models It was 1903 asmaximumvalue for the linearmodel 1974 for the quadraticmodel minus8489 for the logarithmic model and 3217 forthe exponential model Among the four proposedmodels wefound in the first rank the linear and quadratic correlationswhich give results that agree well with the measured valuescompared with the other two models which underestimateor overestimate measurements
The validation of the various models on the annualbasis is shown in Table 7 For the correlation based on thesunshine duration we can note that the linear and quadratic
6 ISRN Renewable Energy
0
02
04
06
08
1
0 02 04 06 08 1
January
SSSS0
HH
0
(a)
03 04 05 06 07 08 09 1
February
0
02
04
06
08
1
SSSS0
HH
0
(b)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
March
HH
0
(c)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
April
HH
0
(d)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
May
HH
0
(e)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
June
HH
0
(f)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
July
HH
0
(g)
August
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(h)
September
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(i)
Experimental dataLinear fit
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
October
HH
0
(j)
Experimental dataLinear fit
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
November
HH
0
(k)
December
Experimental dataLinear fit
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(l)
Figure 5 Scatter diagram of linear model
ISRN Renewable Energy 7
0
02
04
06
08
1
0 02 04 06 08 1
January
SSSS0
HH
0
(a)
February
0
02
04
06
08
1
SSSS0
0 02 04 06 08 1
HH
0
(b)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
March
HH
0
(c)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
April
HH
0
(d)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
May
HH
0
(e)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
June
HH
0
(f)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
July
HH
0
(g)
August
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(h)
September
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(i)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
Experimental dataQuadratic fit
October
HH
0
(j)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
Experimental dataQuadratic fit
November
HH
0
(k)
Experimental dataQuadratic fit
December
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(l)
Figure 6 Scatter diagram of quadratic model
8 ISRN Renewable Energy
0
02
04
06
08
1
0 02 04 06 08 1
January
SSSS0
HH
0
(a)
February
0
02
04
06
08
1
SSSS0
0 02 04 06 08 1
HH
0
(b)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
March
HH
0
(c)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
April
HH
0
(d)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
May
HH
0
(e)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
June
HH
0
(f)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
July
HH
0
(g)
August
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(h)
September
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(i)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
Experimental dataLogarithmic fit
October
HH
0
(j)
Experimental dataLogarithmic fit
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
November
HH
0
(k)
Experimental dataLogarithmic fit
December
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(l)
Figure 7 Scatter diagram of logarithmic model
ISRN Renewable Energy 9
0
02
04
06
08
1
0 02 04 06 08 1
January
SSSS0
HH
0
(a)
February
0
02
04
06
08
1
SSSS0
0 02 04 06 08 1
HH
0
(b)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
March
HH
0
(c)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
April
HH
0
(d)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
May
HH
0
(e)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
June
HH
0
(f)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
July
HH
0
(g)
August
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(h)
September
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(i)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
October
Experimental dataExponential fit
HH
0
(j)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
November
Experimental dataExponential fit
HH
0
(k)
Experimental dataExponential fit
December
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(l)
Figure 8 Scatter diagram of exponential model
10 ISRN Renewable Energy
Table 6 Comparison between measured and estimated monthly global solar radiation (Whm2)
Measured Linear 119890 () Quadratic 119890 () Logarithmic 119890 () Exponential 119890 ()January 3871 387975 minus0226 392454 minus1383 405448 minus474 381238 1514February 4842 476892 1509 474643 1974 522917 minus7996 469399 3057March 5926 583664 1508 586369 1051 617679 minus4232 573538 3217April 7339 734601 minus0096 739331 minus074 77792 minus5998 726109 1062May 7745 774506 minus0001 780996 minus0839 820351 minus592 761716 1651June 7812 782641 minus0184 793014 minus1512 823929 minus547 769928 1443July 7503 749263 0138 748443 0248 79856 minus6432 743793 0867August 7090 722491 minus1903 737784 minus406 757691 minus6868 719104 minus1425September 6036 602421 0195 605437 minus0304 63717 minus5562 589847 2278October 4824 482102 0062 486969 minus0947 512876 minus6318 473796 1784November 4030 402613 0096 39782 1285 422429 minus4821 396304 1662December 3437 342706 0289 362654 minus5515 372876 minus8489 334942 2548
Table 7 Annual validation of different models
119886 119887 119888 119889 CC RMSE MBELinear 0420 0363 0785 00453 minus00012Quadratic 0403 0446 minus00737 0787 00451 minus00007Logarithmic 0701 0106 0627 00792 00281Exponential 0264 0198 0763 00511 minus00182Abdalla 0519 0357 minus00018 minus000126 0898 00429 minus000059Ojosu et al 0449 0358 minus000445 minus000619 0892 00443 minus000068Hargreaves et al 0261 0115 0431 00883 minus000073
Table 8 Comparison between measured and estimated annualglobal solar radiation (Whm2)
Measured value Model Estimated values 119890 ()Linear 585245 0316
Quadratic 585743 0231Logarithmic 610862 minus4047
5871 Exponential 584795 0393Abdalla 584603 0425
Ojosu et al 583350 0639Hargreaves et al 588797 minus0289
models usually give the best performance if we take intoaccount the statistical test while for the model based on themeteorological parameters Abdalla and Ojosu et alrsquos modelsgive the best accuracy with a CC of 0898 and 0892 andRMSE of 00429 and 00443 while Hargreaves et alrsquos modelunderestimates the global solar radiation
The comparison between the estimated and measuredannual average values of the global solar radiation arepresented in Table 8 the annual percentage error is rangedbetween minus4047 and 0639 So it is clear that the linearquadratic models Abdalla and Ojosu are also the suitablemodels to estimate the annual global solar radiation on ahorizontal surface in Ghardaıa region
6 Conclusion
Several empirical models have been tested to estimate theglobal solar radiation on a horizontal surface using the
sunshine duration and the meteorological parameters Thegoal of this paper is the validation of seven models to predictthe monthly and the annual global solar radiation withina dataset of Ghardaia area and thus select the suitablemodel The models were compared on the basis of statisticaltests
Depending on the obtained results we can conclude thatthe linear and the quadratic models are the most accuratefor estimating the monthly global solar radiation on ahorizontal surface according to the statistical tests (CC 0956RMSE 0018 and MBE 4310minus5) the percentage error neverexceeds plusmn5 which indicate an excellent fitting between theglobal solar radiation and sunshine duration On the basisof annual estimation of global solar radiation and for themodels based on the sunshine duration always the linearand the quadratic models provide the best accuracy (CC0787 RMSE 00451 andMBE minus00007) whereas formodelsusing the meteorological parameters in addition to sunshineduration we found that Abdalla and Ojosursquos models are themost suitable with a CC of 0898 and 0892 respectively andthe relative error ranges between minus0289 and 0639
References
[1] K Gairaa and S Benkaciali ldquoAnalysis of solar radiation mea-surements in Ghardaia area south Algeriardquo Energy Procediavol 6 pp 122ndash129 2011
[2] J L Desouza R M Nicaciob and M A L Mouraa ldquoGlobalsolar radiation measurements in Maceio Brazilrdquo RenewableEnergy vol 30 pp 1203ndash1220 2009
ISRN Renewable Energy 11
[3] J P Duffie and W A Beckman Solar Engineering of ThermalProcess John Wiley amp Sons New York NY USA 1991
[4] M Iqbal An Introduction to Solar Radiation Academic PressToronto Canada 1983
[5] International Energy Agency (IEA) ldquoValidation of models forestimating solar radiation on horizontal surfacesrdquo Atmosphereamp Environment service Canada 1988
[6] J A Prescott ldquoEvaporation from a water surface in relation tosolar radiationrdquo Philosophical Transactions of the Royal Societyvol 64 pp 114ndash120 1990
[7] C C Y Ma and M Iqbal ldquoStatistical comparison of solar radi-ation correlations Monthly average global and diffuse radiationon horizontal surfacesrdquo Solar Energy vol 33 no 2 pp 143ndash1481984
[8] J Almorox and C Hontoria ldquoGlobal solar radiation estimationusing sunshine duration in Spainrdquo Energy Conversion andManagement vol 45 no 9-10 pp 1529ndash1535 2004
[9] I T Togrul H Togrul and D Evin ldquoEstimation of monthlyglobal solar radiation from sunshine duration measurement inElazigrdquo Renewable Energy vol 19 no 4 pp 587ndash595 2000
[10] I T Togrul and E Onat ldquoA comparison of estimated andmeasured values of solar radiation in Elazig TurkeyrdquoRenewableEnergy vol 20 no 2 pp 243ndash252 2000
[11] A K Katiyar A Kumar K P Chanchal and B Das ldquoAcomparative study of monthly mean daily clear sky radiationover Indiardquo International Journal of Energy and Environmentvol 1 pp 177ndash182 2010
[12] G Oturanc A Hepbasli and A Genc ldquoStatistical analysis forsolar radiation datardquo Energy Sources vol 25 no 11 pp 1089ndash1097 2003
[13] M Benghanem and A A Joraid ldquoA multiple correlationbetween different solar parameters in Medina Saudi ArabiardquoRenewable Energy vol 32 no 14 pp 2424ndash2435 2007
[14] D B Ampratwum and A S S Dorvlo ldquoEstimation of solarradiation from the number of sunshine hoursrdquo Applied Energyvol 63 no 3 pp 161ndash167 1999
[15] Z Sen ldquoAngstrom equation parameter estimation by unre-stricted methodrdquo Solar Energy vol 71 no 2 pp 95ndash107 2001
[16] B T Nguyen and T L Pryor ldquoThe relationship between globalsolar radiation and sunshine duration in Vietnamrdquo RenewableEnergy vol 11 no 1 pp 47ndash60 1997
[17] N A Elagib S H Alvi and M G Mansell ldquoCorrelationshipsbetween clearness index and relative sunshine duration forSudanrdquo Renewable Energy vol 17 no 4 pp 473ndash498 1999
[18] M Hussain L Rahman and M M Rahman ldquoTechnical notetechniques to obtain improved predictions of global radiationfrom sunshine durationrdquo Renewable Energy vol 18 no 2 pp263ndash275 1999
[19] M T Y Tadros ldquoUses of sunshine duration to estimate theglobal solar radiation over eight meteorological stations inEgyptrdquo Renewable Energy vol 21 no 2 pp 231ndash246 2000
[20] I T Togrul and E Onat ldquoStudy for estimating solar radiationin Elazig using geographical and meteorological datardquo EnergyConversion and Management vol 40 no 14 pp 1577ndash15841999
[21] R Chen K Ersi J Yang S Lu and W Zhao ldquoValidation offive global radiationmodels withmeasured daily data in ChinardquoEnergy Conversion andManagement vol 45 no 11-12 pp 1759ndash1769 2004
[22] C Ertekin and O Yaldiz ldquoComparison of some existing modelsfor estimating global solar radiation for Antalya (Turkey)rdquo
Energy Conversion and Management vol 41 no 4 pp 311ndash3302000
[23] J C Ododo J A Agbakwuru and F A Ogbu ldquoCorrelation ofsolar radiationwith cloud cover and relative sunshine durationrdquoEnergy Conversion and Management vol 37 no 10 pp 1555ndash1559 1996
[24] M Yorukoglu and A N Celik ldquoA critical review on the esti-mation of daily global solar radiation from sunshine durationrdquoEnergy Conversion andManagement vol 47 no 15-16 pp 2441ndash2450 2006
[25] Y Abdalla ldquoNew correlation of global solar radiation withmeteorological parameters for Bahrainrdquo International Journalof Solar Energy vol 16 pp 111ndash120 1994
[26] K K Gopinathan ldquoA new model for estimating total solarradiation in Dohardquo Energy Conversion andManagemen vol 28pp 6ndash72 1988
[27] 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
[28] R G Allen ldquoSelf-calibrating method for estimating solar radi-ation from air temperaturerdquo Journal of Hydrologic Engineeringvol 2 no 2 pp 56ndash67 1997
[29] G H Hargreaves and R G Allen ldquoHistory and evaluation ofhargreaves evapotranspiration equationrdquo Journal of Irrigationand Drainage Engineering vol 129 no 1 pp 53ndash63 2003
[30] Z Samani G H Hargreaves V Tran and S Bawazir ldquoEstimat-ing solar radiation from temperature with spatial and temporalcalibrationrdquo Journal of Irrigation and Drainage Engineering vol137 no 11 pp 692ndash696 2011
[31] J O Ojosu and L K Komolafe ldquoModels for estimating solarradiation availability in South Western Nigeriardquo Solar Energyvol 16 pp 69ndash77 1987
[32] G H Hargreaves and Z A Samani ldquoReference crop evapotran-spiration from temperaturerdquoTransactions of theASAE vol 1 pp96ndash99 1985
[33] J I Prieto J C Martınez-Garcıa and D Garcıa ldquoCorrela-tion between global solar irradiation and air temperature inAsturias Spainrdquo Solar Energy vol 83 no 7 pp 1076ndash1085 2009
[34] M Paulescu L Fara and E Tulcan-Paulescu ldquoModels forobtaining daily global solar irradiation from air temperaturedatardquo Atmospheric Research vol 79 no 3-4 pp 227ndash240 2006
TribologyAdvances in
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Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Renewable Energy
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Journal ofEngineeringVolume 2014
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High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
2 ISRN Renewable Energy
Table 1 Technical specifications of EKOMS-64 Pyranometer
Technical specifications Used PyranometerDirectional response ltplusmn10Wm2
Temperature response ltplusmn1Nonlinearity ltplusmn02Tilt response ltplusmn02Operating temperature range (∘C) minus40sim+80Wavelength range (nm) 305ndash2800
has been conducted using the local data of Ghardaıa regionThe comparison between the estimated and the measuredglobal solar radiation has been illustrated
2 Database
The data used in this study are taken from the solar radi-ation laboratory located in the Applied Research Unit forRenewable Energies (URAER) Ghardaıa site is consideredan arid and dry area located in the south of Algeria about600Km south of the capital city it is framed by the followinggeographical coordinates latitude of 32∘361015840N longitude of3∘481015840 E and altitude of 450m above MSL The global solarradiation data are measured via an EKOMS-64 Pyranometerwith the short wave sensitivity of (70mVkWm2) moretechnical specifications of this Pyranometer are describedin Table 1 The air temperature and relative humidity mea-surement data were made by TECNOEL sonde Thermo-Igromertiche its calibration accuracy is plusmn15 and tem-perature sensitivity is 01 (∘CmV) A data logger and aCampbell Scientific CR10X data acquisition systemwere usedfor reading the measurements From the raw data storedfor every five minutes the mean maximum and minimumhourly values were calculated From the hourly data setdaily and monthly statistics were made for the global solarradiation and meteorological data
The average hours of sunshine duration are illustrated inFigure 1 for the site under consideration the highest valueswere in the summer season with a mean value of 1223 hourswhile the lowest values were in the winter season with ameanvalue of 743 hours The monthly average daily global solarradiation air temperature and relative humidity are shownin Figures 2 3 and 4
3 Models Used
A brief description of the mathematical expression of thevarious models proposed in the present paper is given below
31 Angstrom-Prescott Model (Linear Model) [4 24] TheAngstrom-Prescott model is widely described by the authorsin the study of solar radiation since Prescott has developed in1940 the general form of this model is given by
119867
1198670
= 119886 + 119887(
SSSS0
) (1)
783819
1032
1085
112
12231193
1087
9
827
799743
JanuaryFebruaryMarchAprilMayJune
JulyAugustSeptemberOctoberNovemberDecember
Figure 1 The monthly average daily hours of sunshine duration
0
1000
2000
3000
4000
5000
6000
7000
8000
1 2 3 4 5 6 7 8 9 10 11 12
Glo
bal s
olar
radi
atio
n (W
hm
2)
Month
Figure 2 Global solar radiation on horizontal surface
where1198670is the monthly average daily extraterrestrial radia-
tion (MJm2 sdot day) which can be expressed as
1198670=
24
120587
119866SC (1 + 0033360 sdot 119863
119899
365
)
sdot (cos120593 cos 120575 sin120596 + 2120587
360
120596 sin120593 sin 120575) (2)
where 120596 is sunset hour angle in degree defined as
120596 = cosminus1 (minus tan120593 tan 120575) (3)
119866SC is the solar constant taken equal to 1367 (Wm2) 120593 isthe latitude of the location under consideration119863
119899is the day
ISRN Renewable Energy 3
0
5
10
15
20
25
30
35
40
45
1 2 3 4 5 6 7 8 9 10 11 12
MinimumMaximumAverage
Month
Tem
pera
ture
(∘C)
Figure 3 The minimum maximum and average air temperature
0
10
20
30
40
50
60
70
80
1 2 3 4 5 6 7 8 9 10 11 12
MinimumMaximumAverage
Relat
ive h
umid
ity (
)
Month
Figure 4The minimum maximum and average relative humidity
number of the year starting from the first of January and 120575 isthe declination angle as given below
120575 = 2345 sin[360(284 + 119863
119899)
365
] (4)
SS is the monthly daily sunshine duration SS0is the maxi-
mum possible monthly average daily sunshine hours or theday length
32 Ogelman et alrsquos Model (Quadratic Model) [24] Ogelmanet alrsquos have correlated (119867119867
0) with (SSSS
0) in the form
of second-order polynomial equation
119867
1198670
= 119886 + 119887(
SSSS0
) + 119888(
SSSS0
)
2
(5)
33 Ampratwum et alrsquos Model (Logarithmic Model) [14 24]In order to have more precision in the estimation of theglobal solar radiation Ampratwum et al have developed alogarithmic form of linear model as described below
119867
1198670
= 119886 + 119887 log( SSSS0
) (6)
34 Almorox et alrsquos Model (Exponential Model) [8 24] Theexponential correlation between (119867119867
0) and (SSSS
0) is
given by Almorox et al as119867
1198670
= 119886 + 119887119890(SSSS0)
(7)
35 Abdallarsquos Model [25 26] Abdallarsquos model correlates(119867119867
0) with the sunshine duration maximum air temper-
ature and average relative humidity in order to increase theaccuracy of the estimating coefficients This model is basedon the Gopinathan model [26] which studied the variationof (119867119867
0) as a function of the latitude and the elevation
of the site the fraction of insolation air temperature andthe maximum average relative humidity This model has thefollowing expression
119867
1198670
= 119886 + 119887(
SSSS0
) + 119888 (119879max) + 119889 (RH) (8)
where 119879max is the daily mean maximum air temperature andRH is the daily mean relative humidity as a percentage
36 Ojosu and Komolafersquos Model [31] Ojosu and Komolafeproposed the equation below
119867
1198670
= 119886 + 119887(
SSSS0
) + 119888(
119879min119879max
) + 119889(
RHminRHmax
) (9)
where 119879min 119879max RHmin and RHmax are the mean minimumair temperature mean maximum air temperature meanminimum relative humidity and mean maximum relativehumidity respectively
37 Hargreaves et alrsquos Model [29 30 32] Hargreaves et alwere the first to propose a procedure to estimate the globalsolar radiation by using the difference between daily maxi-mumanddailyminimumair temperature and extraterrestrialradiation The proposed equation has the following form
119867
1198670
= 119886 + 119887(119879max minus 119879min)05
(10)
where 119879min and 119879max are the meanminimum air temperatureand mean maximum air temperature
A program written in MATLAB allowing to determinethe empirical constants 119886 119887 119888 and 119889 for each describedmodel and comparedmodels was thus foundwith the groundmeasurements
4 ISRN Renewable Energy
Table 2 Linear model validation
119886 119887 CC RMSE MBEJanuary 0361 0457 0890 00361 minus000044February 0303 0515 0715 00664 000060March 0477 032 0916 00269 minus000028April 0425 0389 0929 00213 000035May 0466 033 0897 00344 minus001990June 0443 0332 0946 00196 000040July 0453 0307 0853 00246 minus000018August 0481 0273 0731 00284 minus000081September 0376 0402 0789 00534 0000077October 0398 0357 0934 00226 minus000032November 0451 0315 0620 00649 000045December 0373 0406 0856 00452 minus000047
Table 3 Quadratic model validation
119886 119887 119862 CC RMSE MBEJanuary 0337 0618 minus0159 0896 0035 minus000028February 0335 0408 008 0715 0066 minus000047March 0469 0361 minus0037 0917 0026 minus0000056April 0372 0574 minus0143 0935 002 minus000058May 0443 0444 minus0104 0903 0027 minus000067June 0411 0497 minus015 0956 0018 000043July 046 0282 002 0853 0025 minus000016August 0278 0937 minus0497 0833 0022 000014September 0367 0452 minus0046 079 0053 000023October 0375 0479 minus0114 094 0022 minus000033November 0466 0198 0118 0623 0063 000049December 0277 0956 minus0504 0894 0039 000057
4 Statistical Test
The accuracy of the estimated models will be judged bythe statistical indicators such as the correlation coefficient(CC) mean bias error (MBE) root mean square error(RMSE) and the percentage error (119890) These indicators areusually applied in the comparison of solar radiation modelsThe mean square error provides information about theperformance of correlations which allows comparison ofthe real differences between the estimated values and themeasured ones a low RMSE is desirable The MBE providesthe long-term performance of the model in general thepositive MBE shows overestimation while the negative MBEindicates underestimationThe correlation coefficient reflectsthe quality of the model the more CC close to 1 the more thebetter quality The expression of each statistical indicator isgiven
CC = 1 minussum119899
119894=1
(119867119894119898minus 119867119894119890)2
sum119899
119894=1
(119867119894119898minus 119867119898)
2
MBE = 1119899
(
119899
sum
119894=1
119867119894119890minus 119867119894119898
119867119894119898
)
RMSE = [1119899
119899
sum
119894=1
(
119867119894119890minus 119867119894119898
119867119894119898
)
2
]
12
119890 = [(
119867119894119898minus 119867119894119890
119867119894119898
)] 100
(11)
where 119867119894119890
and 119867119894119898
are the 119894th estimated and measuredvalues 119867
119898is the mean of observed data and 119899 is the total
number of observations
5 Results and Discussion
The results of the validation of the models that estimate theglobal solar radiation from sunshine duration on themonthlybasis are presented in Tables 2 3 4 and 5 The analysis ofthe measured and calculated values shows that the maximumof the global solar radiation is observed in June while theminimum values are appearing in December
For the linear model the correlation coefficient is signifi-cant for all months of the year except in November where it isrelatively lowThe quality of the estimate is a slightly worse for
ISRN Renewable Energy 5
Table 4 Logarithmic model validation
119886 119887 CC RMSE MBEJanuary 0741 0079 0792 0077 00235February 0795 0314 0693 0102 00536March 0734 0079 0651 0151 00566April 0792 0218 0917 0061 00369May 0757 0121 0825 0067 00338June 0734 0112 0862 0061 00294July 0735 0164 0816 0058 00393August 0743 0176 0805 0048 00321September 0714 0097 0613 0091 00281October 0708 0121 0864 0065 00330November 0724 009 0487 0088 00259December 0749 0176 0886 0088 00465
Table 5 Exponential model validation
119886 119887 CC RMSE MBEJanuary 014 0261 0861 004 minus000071February 0128 026 0713 0063 minus000047March 0342 0173 0878 0032 000003April 0295 0195 0901 0025 minus000026May 0321 0181 0868 0032 minus000077June 0295 0183 0916 0024 minus000040July 0335 0163 0846 0025 000078August 0403 0132 067 0032 minus000022September 0192 0224 0774 0055 minus000044October 0236 0199 0901 0028 minus00015November 0283 0187 0621 0045 0104December 0188 0225 0822 0073 minus00096
the months of the February and November when the RMSEis between 0064 and 0069
For the quadratic correlation the result shows a slightimprovement in the accuracy of the model for the monthof August where the coefficient of determination is equal to083 (compared to the linear model CC = 073) the qualityof estimation is also improved in the months of June andDecember with an RMSE of 0018 and 0039 respectivelyTheregression based on the logarithmic and exponential modelsdid not improve significantly the accuracy of estimation of theglobal solar radiation than the two previous models as seenfrom the values of the CC MBE and RMSE (Correlationcoefficient reached his minimum values in November (CC =048) for the logarithmic model)
Another manner of the comparison between the mea-sured and the predicted values was illustrated by the scatterdiagram plotted in Figures 5 6 7 and 8 A strong scatteringof the points in the superior or in the inferior half of theregression line indicates respectively an overestimate or anunderestimate
For the linear model the dispersion of estimated valuesaround the regression line is fairly low in the months ofJanuary March-August October and December where thecorrelation coefficient ranges between 085 and 094 while
this dispersion is small in the quadratic model this indicatesan excellent fitting between the global radiation and thesunshine duration
For the logarithmic model the dispersion of the esti-mated values is strong especially in the months of JanuaryMarch and August and it is low in the months of FebruarySeptember and November while this dispersion remainslow for the exponential model in the months of FebruarySeptember and November and it is strong too for the othermonths of the year
The confrontation between estimated and measuredmonthly average global solar radiation by the different mod-els is shown in Table 6 which indicated that the percentageerror never exceeds plusmn10 for all models It was 1903 asmaximumvalue for the linearmodel 1974 for the quadraticmodel minus8489 for the logarithmic model and 3217 forthe exponential model Among the four proposedmodels wefound in the first rank the linear and quadratic correlationswhich give results that agree well with the measured valuescompared with the other two models which underestimateor overestimate measurements
The validation of the various models on the annualbasis is shown in Table 7 For the correlation based on thesunshine duration we can note that the linear and quadratic
6 ISRN Renewable Energy
0
02
04
06
08
1
0 02 04 06 08 1
January
SSSS0
HH
0
(a)
03 04 05 06 07 08 09 1
February
0
02
04
06
08
1
SSSS0
HH
0
(b)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
March
HH
0
(c)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
April
HH
0
(d)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
May
HH
0
(e)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
June
HH
0
(f)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
July
HH
0
(g)
August
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(h)
September
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(i)
Experimental dataLinear fit
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
October
HH
0
(j)
Experimental dataLinear fit
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
November
HH
0
(k)
December
Experimental dataLinear fit
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(l)
Figure 5 Scatter diagram of linear model
ISRN Renewable Energy 7
0
02
04
06
08
1
0 02 04 06 08 1
January
SSSS0
HH
0
(a)
February
0
02
04
06
08
1
SSSS0
0 02 04 06 08 1
HH
0
(b)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
March
HH
0
(c)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
April
HH
0
(d)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
May
HH
0
(e)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
June
HH
0
(f)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
July
HH
0
(g)
August
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(h)
September
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(i)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
Experimental dataQuadratic fit
October
HH
0
(j)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
Experimental dataQuadratic fit
November
HH
0
(k)
Experimental dataQuadratic fit
December
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(l)
Figure 6 Scatter diagram of quadratic model
8 ISRN Renewable Energy
0
02
04
06
08
1
0 02 04 06 08 1
January
SSSS0
HH
0
(a)
February
0
02
04
06
08
1
SSSS0
0 02 04 06 08 1
HH
0
(b)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
March
HH
0
(c)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
April
HH
0
(d)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
May
HH
0
(e)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
June
HH
0
(f)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
July
HH
0
(g)
August
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(h)
September
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(i)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
Experimental dataLogarithmic fit
October
HH
0
(j)
Experimental dataLogarithmic fit
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
November
HH
0
(k)
Experimental dataLogarithmic fit
December
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(l)
Figure 7 Scatter diagram of logarithmic model
ISRN Renewable Energy 9
0
02
04
06
08
1
0 02 04 06 08 1
January
SSSS0
HH
0
(a)
February
0
02
04
06
08
1
SSSS0
0 02 04 06 08 1
HH
0
(b)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
March
HH
0
(c)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
April
HH
0
(d)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
May
HH
0
(e)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
June
HH
0
(f)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
July
HH
0
(g)
August
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(h)
September
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(i)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
October
Experimental dataExponential fit
HH
0
(j)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
November
Experimental dataExponential fit
HH
0
(k)
Experimental dataExponential fit
December
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(l)
Figure 8 Scatter diagram of exponential model
10 ISRN Renewable Energy
Table 6 Comparison between measured and estimated monthly global solar radiation (Whm2)
Measured Linear 119890 () Quadratic 119890 () Logarithmic 119890 () Exponential 119890 ()January 3871 387975 minus0226 392454 minus1383 405448 minus474 381238 1514February 4842 476892 1509 474643 1974 522917 minus7996 469399 3057March 5926 583664 1508 586369 1051 617679 minus4232 573538 3217April 7339 734601 minus0096 739331 minus074 77792 minus5998 726109 1062May 7745 774506 minus0001 780996 minus0839 820351 minus592 761716 1651June 7812 782641 minus0184 793014 minus1512 823929 minus547 769928 1443July 7503 749263 0138 748443 0248 79856 minus6432 743793 0867August 7090 722491 minus1903 737784 minus406 757691 minus6868 719104 minus1425September 6036 602421 0195 605437 minus0304 63717 minus5562 589847 2278October 4824 482102 0062 486969 minus0947 512876 minus6318 473796 1784November 4030 402613 0096 39782 1285 422429 minus4821 396304 1662December 3437 342706 0289 362654 minus5515 372876 minus8489 334942 2548
Table 7 Annual validation of different models
119886 119887 119888 119889 CC RMSE MBELinear 0420 0363 0785 00453 minus00012Quadratic 0403 0446 minus00737 0787 00451 minus00007Logarithmic 0701 0106 0627 00792 00281Exponential 0264 0198 0763 00511 minus00182Abdalla 0519 0357 minus00018 minus000126 0898 00429 minus000059Ojosu et al 0449 0358 minus000445 minus000619 0892 00443 minus000068Hargreaves et al 0261 0115 0431 00883 minus000073
Table 8 Comparison between measured and estimated annualglobal solar radiation (Whm2)
Measured value Model Estimated values 119890 ()Linear 585245 0316
Quadratic 585743 0231Logarithmic 610862 minus4047
5871 Exponential 584795 0393Abdalla 584603 0425
Ojosu et al 583350 0639Hargreaves et al 588797 minus0289
models usually give the best performance if we take intoaccount the statistical test while for the model based on themeteorological parameters Abdalla and Ojosu et alrsquos modelsgive the best accuracy with a CC of 0898 and 0892 andRMSE of 00429 and 00443 while Hargreaves et alrsquos modelunderestimates the global solar radiation
The comparison between the estimated and measuredannual average values of the global solar radiation arepresented in Table 8 the annual percentage error is rangedbetween minus4047 and 0639 So it is clear that the linearquadratic models Abdalla and Ojosu are also the suitablemodels to estimate the annual global solar radiation on ahorizontal surface in Ghardaıa region
6 Conclusion
Several empirical models have been tested to estimate theglobal solar radiation on a horizontal surface using the
sunshine duration and the meteorological parameters Thegoal of this paper is the validation of seven models to predictthe monthly and the annual global solar radiation withina dataset of Ghardaia area and thus select the suitablemodel The models were compared on the basis of statisticaltests
Depending on the obtained results we can conclude thatthe linear and the quadratic models are the most accuratefor estimating the monthly global solar radiation on ahorizontal surface according to the statistical tests (CC 0956RMSE 0018 and MBE 4310minus5) the percentage error neverexceeds plusmn5 which indicate an excellent fitting between theglobal solar radiation and sunshine duration On the basisof annual estimation of global solar radiation and for themodels based on the sunshine duration always the linearand the quadratic models provide the best accuracy (CC0787 RMSE 00451 andMBE minus00007) whereas formodelsusing the meteorological parameters in addition to sunshineduration we found that Abdalla and Ojosursquos models are themost suitable with a CC of 0898 and 0892 respectively andthe relative error ranges between minus0289 and 0639
References
[1] K Gairaa and S Benkaciali ldquoAnalysis of solar radiation mea-surements in Ghardaia area south Algeriardquo Energy Procediavol 6 pp 122ndash129 2011
[2] J L Desouza R M Nicaciob and M A L Mouraa ldquoGlobalsolar radiation measurements in Maceio Brazilrdquo RenewableEnergy vol 30 pp 1203ndash1220 2009
ISRN Renewable Energy 11
[3] J P Duffie and W A Beckman Solar Engineering of ThermalProcess John Wiley amp Sons New York NY USA 1991
[4] M Iqbal An Introduction to Solar Radiation Academic PressToronto Canada 1983
[5] International Energy Agency (IEA) ldquoValidation of models forestimating solar radiation on horizontal surfacesrdquo Atmosphereamp Environment service Canada 1988
[6] J A Prescott ldquoEvaporation from a water surface in relation tosolar radiationrdquo Philosophical Transactions of the Royal Societyvol 64 pp 114ndash120 1990
[7] C C Y Ma and M Iqbal ldquoStatistical comparison of solar radi-ation correlations Monthly average global and diffuse radiationon horizontal surfacesrdquo Solar Energy vol 33 no 2 pp 143ndash1481984
[8] J Almorox and C Hontoria ldquoGlobal solar radiation estimationusing sunshine duration in Spainrdquo Energy Conversion andManagement vol 45 no 9-10 pp 1529ndash1535 2004
[9] I T Togrul H Togrul and D Evin ldquoEstimation of monthlyglobal solar radiation from sunshine duration measurement inElazigrdquo Renewable Energy vol 19 no 4 pp 587ndash595 2000
[10] I T Togrul and E Onat ldquoA comparison of estimated andmeasured values of solar radiation in Elazig TurkeyrdquoRenewableEnergy vol 20 no 2 pp 243ndash252 2000
[11] A K Katiyar A Kumar K P Chanchal and B Das ldquoAcomparative study of monthly mean daily clear sky radiationover Indiardquo International Journal of Energy and Environmentvol 1 pp 177ndash182 2010
[12] G Oturanc A Hepbasli and A Genc ldquoStatistical analysis forsolar radiation datardquo Energy Sources vol 25 no 11 pp 1089ndash1097 2003
[13] M Benghanem and A A Joraid ldquoA multiple correlationbetween different solar parameters in Medina Saudi ArabiardquoRenewable Energy vol 32 no 14 pp 2424ndash2435 2007
[14] D B Ampratwum and A S S Dorvlo ldquoEstimation of solarradiation from the number of sunshine hoursrdquo Applied Energyvol 63 no 3 pp 161ndash167 1999
[15] Z Sen ldquoAngstrom equation parameter estimation by unre-stricted methodrdquo Solar Energy vol 71 no 2 pp 95ndash107 2001
[16] B T Nguyen and T L Pryor ldquoThe relationship between globalsolar radiation and sunshine duration in Vietnamrdquo RenewableEnergy vol 11 no 1 pp 47ndash60 1997
[17] N A Elagib S H Alvi and M G Mansell ldquoCorrelationshipsbetween clearness index and relative sunshine duration forSudanrdquo Renewable Energy vol 17 no 4 pp 473ndash498 1999
[18] M Hussain L Rahman and M M Rahman ldquoTechnical notetechniques to obtain improved predictions of global radiationfrom sunshine durationrdquo Renewable Energy vol 18 no 2 pp263ndash275 1999
[19] M T Y Tadros ldquoUses of sunshine duration to estimate theglobal solar radiation over eight meteorological stations inEgyptrdquo Renewable Energy vol 21 no 2 pp 231ndash246 2000
[20] I T Togrul and E Onat ldquoStudy for estimating solar radiationin Elazig using geographical and meteorological datardquo EnergyConversion and Management vol 40 no 14 pp 1577ndash15841999
[21] R Chen K Ersi J Yang S Lu and W Zhao ldquoValidation offive global radiationmodels withmeasured daily data in ChinardquoEnergy Conversion andManagement vol 45 no 11-12 pp 1759ndash1769 2004
[22] C Ertekin and O Yaldiz ldquoComparison of some existing modelsfor estimating global solar radiation for Antalya (Turkey)rdquo
Energy Conversion and Management vol 41 no 4 pp 311ndash3302000
[23] J C Ododo J A Agbakwuru and F A Ogbu ldquoCorrelation ofsolar radiationwith cloud cover and relative sunshine durationrdquoEnergy Conversion and Management vol 37 no 10 pp 1555ndash1559 1996
[24] M Yorukoglu and A N Celik ldquoA critical review on the esti-mation of daily global solar radiation from sunshine durationrdquoEnergy Conversion andManagement vol 47 no 15-16 pp 2441ndash2450 2006
[25] Y Abdalla ldquoNew correlation of global solar radiation withmeteorological parameters for Bahrainrdquo International Journalof Solar Energy vol 16 pp 111ndash120 1994
[26] K K Gopinathan ldquoA new model for estimating total solarradiation in Dohardquo Energy Conversion andManagemen vol 28pp 6ndash72 1988
[27] 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
[28] R G Allen ldquoSelf-calibrating method for estimating solar radi-ation from air temperaturerdquo Journal of Hydrologic Engineeringvol 2 no 2 pp 56ndash67 1997
[29] G H Hargreaves and R G Allen ldquoHistory and evaluation ofhargreaves evapotranspiration equationrdquo Journal of Irrigationand Drainage Engineering vol 129 no 1 pp 53ndash63 2003
[30] Z Samani G H Hargreaves V Tran and S Bawazir ldquoEstimat-ing solar radiation from temperature with spatial and temporalcalibrationrdquo Journal of Irrigation and Drainage Engineering vol137 no 11 pp 692ndash696 2011
[31] J O Ojosu and L K Komolafe ldquoModels for estimating solarradiation availability in South Western Nigeriardquo Solar Energyvol 16 pp 69ndash77 1987
[32] G H Hargreaves and Z A Samani ldquoReference crop evapotran-spiration from temperaturerdquoTransactions of theASAE vol 1 pp96ndash99 1985
[33] J I Prieto J C Martınez-Garcıa and D Garcıa ldquoCorrela-tion between global solar irradiation and air temperature inAsturias Spainrdquo Solar Energy vol 83 no 7 pp 1076ndash1085 2009
[34] M Paulescu L Fara and E Tulcan-Paulescu ldquoModels forobtaining daily global solar irradiation from air temperaturedatardquo Atmospheric Research vol 79 no 3-4 pp 227ndash240 2006
TribologyAdvances in
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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
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High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
ISRN Renewable Energy 3
0
5
10
15
20
25
30
35
40
45
1 2 3 4 5 6 7 8 9 10 11 12
MinimumMaximumAverage
Month
Tem
pera
ture
(∘C)
Figure 3 The minimum maximum and average air temperature
0
10
20
30
40
50
60
70
80
1 2 3 4 5 6 7 8 9 10 11 12
MinimumMaximumAverage
Relat
ive h
umid
ity (
)
Month
Figure 4The minimum maximum and average relative humidity
number of the year starting from the first of January and 120575 isthe declination angle as given below
120575 = 2345 sin[360(284 + 119863
119899)
365
] (4)
SS is the monthly daily sunshine duration SS0is the maxi-
mum possible monthly average daily sunshine hours or theday length
32 Ogelman et alrsquos Model (Quadratic Model) [24] Ogelmanet alrsquos have correlated (119867119867
0) with (SSSS
0) in the form
of second-order polynomial equation
119867
1198670
= 119886 + 119887(
SSSS0
) + 119888(
SSSS0
)
2
(5)
33 Ampratwum et alrsquos Model (Logarithmic Model) [14 24]In order to have more precision in the estimation of theglobal solar radiation Ampratwum et al have developed alogarithmic form of linear model as described below
119867
1198670
= 119886 + 119887 log( SSSS0
) (6)
34 Almorox et alrsquos Model (Exponential Model) [8 24] Theexponential correlation between (119867119867
0) and (SSSS
0) is
given by Almorox et al as119867
1198670
= 119886 + 119887119890(SSSS0)
(7)
35 Abdallarsquos Model [25 26] Abdallarsquos model correlates(119867119867
0) with the sunshine duration maximum air temper-
ature and average relative humidity in order to increase theaccuracy of the estimating coefficients This model is basedon the Gopinathan model [26] which studied the variationof (119867119867
0) as a function of the latitude and the elevation
of the site the fraction of insolation air temperature andthe maximum average relative humidity This model has thefollowing expression
119867
1198670
= 119886 + 119887(
SSSS0
) + 119888 (119879max) + 119889 (RH) (8)
where 119879max is the daily mean maximum air temperature andRH is the daily mean relative humidity as a percentage
36 Ojosu and Komolafersquos Model [31] Ojosu and Komolafeproposed the equation below
119867
1198670
= 119886 + 119887(
SSSS0
) + 119888(
119879min119879max
) + 119889(
RHminRHmax
) (9)
where 119879min 119879max RHmin and RHmax are the mean minimumair temperature mean maximum air temperature meanminimum relative humidity and mean maximum relativehumidity respectively
37 Hargreaves et alrsquos Model [29 30 32] Hargreaves et alwere the first to propose a procedure to estimate the globalsolar radiation by using the difference between daily maxi-mumanddailyminimumair temperature and extraterrestrialradiation The proposed equation has the following form
119867
1198670
= 119886 + 119887(119879max minus 119879min)05
(10)
where 119879min and 119879max are the meanminimum air temperatureand mean maximum air temperature
A program written in MATLAB allowing to determinethe empirical constants 119886 119887 119888 and 119889 for each describedmodel and comparedmodels was thus foundwith the groundmeasurements
4 ISRN Renewable Energy
Table 2 Linear model validation
119886 119887 CC RMSE MBEJanuary 0361 0457 0890 00361 minus000044February 0303 0515 0715 00664 000060March 0477 032 0916 00269 minus000028April 0425 0389 0929 00213 000035May 0466 033 0897 00344 minus001990June 0443 0332 0946 00196 000040July 0453 0307 0853 00246 minus000018August 0481 0273 0731 00284 minus000081September 0376 0402 0789 00534 0000077October 0398 0357 0934 00226 minus000032November 0451 0315 0620 00649 000045December 0373 0406 0856 00452 minus000047
Table 3 Quadratic model validation
119886 119887 119862 CC RMSE MBEJanuary 0337 0618 minus0159 0896 0035 minus000028February 0335 0408 008 0715 0066 minus000047March 0469 0361 minus0037 0917 0026 minus0000056April 0372 0574 minus0143 0935 002 minus000058May 0443 0444 minus0104 0903 0027 minus000067June 0411 0497 minus015 0956 0018 000043July 046 0282 002 0853 0025 minus000016August 0278 0937 minus0497 0833 0022 000014September 0367 0452 minus0046 079 0053 000023October 0375 0479 minus0114 094 0022 minus000033November 0466 0198 0118 0623 0063 000049December 0277 0956 minus0504 0894 0039 000057
4 Statistical Test
The accuracy of the estimated models will be judged bythe statistical indicators such as the correlation coefficient(CC) mean bias error (MBE) root mean square error(RMSE) and the percentage error (119890) These indicators areusually applied in the comparison of solar radiation modelsThe mean square error provides information about theperformance of correlations which allows comparison ofthe real differences between the estimated values and themeasured ones a low RMSE is desirable The MBE providesthe long-term performance of the model in general thepositive MBE shows overestimation while the negative MBEindicates underestimationThe correlation coefficient reflectsthe quality of the model the more CC close to 1 the more thebetter quality The expression of each statistical indicator isgiven
CC = 1 minussum119899
119894=1
(119867119894119898minus 119867119894119890)2
sum119899
119894=1
(119867119894119898minus 119867119898)
2
MBE = 1119899
(
119899
sum
119894=1
119867119894119890minus 119867119894119898
119867119894119898
)
RMSE = [1119899
119899
sum
119894=1
(
119867119894119890minus 119867119894119898
119867119894119898
)
2
]
12
119890 = [(
119867119894119898minus 119867119894119890
119867119894119898
)] 100
(11)
where 119867119894119890
and 119867119894119898
are the 119894th estimated and measuredvalues 119867
119898is the mean of observed data and 119899 is the total
number of observations
5 Results and Discussion
The results of the validation of the models that estimate theglobal solar radiation from sunshine duration on themonthlybasis are presented in Tables 2 3 4 and 5 The analysis ofthe measured and calculated values shows that the maximumof the global solar radiation is observed in June while theminimum values are appearing in December
For the linear model the correlation coefficient is signifi-cant for all months of the year except in November where it isrelatively lowThe quality of the estimate is a slightly worse for
ISRN Renewable Energy 5
Table 4 Logarithmic model validation
119886 119887 CC RMSE MBEJanuary 0741 0079 0792 0077 00235February 0795 0314 0693 0102 00536March 0734 0079 0651 0151 00566April 0792 0218 0917 0061 00369May 0757 0121 0825 0067 00338June 0734 0112 0862 0061 00294July 0735 0164 0816 0058 00393August 0743 0176 0805 0048 00321September 0714 0097 0613 0091 00281October 0708 0121 0864 0065 00330November 0724 009 0487 0088 00259December 0749 0176 0886 0088 00465
Table 5 Exponential model validation
119886 119887 CC RMSE MBEJanuary 014 0261 0861 004 minus000071February 0128 026 0713 0063 minus000047March 0342 0173 0878 0032 000003April 0295 0195 0901 0025 minus000026May 0321 0181 0868 0032 minus000077June 0295 0183 0916 0024 minus000040July 0335 0163 0846 0025 000078August 0403 0132 067 0032 minus000022September 0192 0224 0774 0055 minus000044October 0236 0199 0901 0028 minus00015November 0283 0187 0621 0045 0104December 0188 0225 0822 0073 minus00096
the months of the February and November when the RMSEis between 0064 and 0069
For the quadratic correlation the result shows a slightimprovement in the accuracy of the model for the monthof August where the coefficient of determination is equal to083 (compared to the linear model CC = 073) the qualityof estimation is also improved in the months of June andDecember with an RMSE of 0018 and 0039 respectivelyTheregression based on the logarithmic and exponential modelsdid not improve significantly the accuracy of estimation of theglobal solar radiation than the two previous models as seenfrom the values of the CC MBE and RMSE (Correlationcoefficient reached his minimum values in November (CC =048) for the logarithmic model)
Another manner of the comparison between the mea-sured and the predicted values was illustrated by the scatterdiagram plotted in Figures 5 6 7 and 8 A strong scatteringof the points in the superior or in the inferior half of theregression line indicates respectively an overestimate or anunderestimate
For the linear model the dispersion of estimated valuesaround the regression line is fairly low in the months ofJanuary March-August October and December where thecorrelation coefficient ranges between 085 and 094 while
this dispersion is small in the quadratic model this indicatesan excellent fitting between the global radiation and thesunshine duration
For the logarithmic model the dispersion of the esti-mated values is strong especially in the months of JanuaryMarch and August and it is low in the months of FebruarySeptember and November while this dispersion remainslow for the exponential model in the months of FebruarySeptember and November and it is strong too for the othermonths of the year
The confrontation between estimated and measuredmonthly average global solar radiation by the different mod-els is shown in Table 6 which indicated that the percentageerror never exceeds plusmn10 for all models It was 1903 asmaximumvalue for the linearmodel 1974 for the quadraticmodel minus8489 for the logarithmic model and 3217 forthe exponential model Among the four proposedmodels wefound in the first rank the linear and quadratic correlationswhich give results that agree well with the measured valuescompared with the other two models which underestimateor overestimate measurements
The validation of the various models on the annualbasis is shown in Table 7 For the correlation based on thesunshine duration we can note that the linear and quadratic
6 ISRN Renewable Energy
0
02
04
06
08
1
0 02 04 06 08 1
January
SSSS0
HH
0
(a)
03 04 05 06 07 08 09 1
February
0
02
04
06
08
1
SSSS0
HH
0
(b)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
March
HH
0
(c)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
April
HH
0
(d)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
May
HH
0
(e)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
June
HH
0
(f)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
July
HH
0
(g)
August
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(h)
September
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(i)
Experimental dataLinear fit
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
October
HH
0
(j)
Experimental dataLinear fit
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
November
HH
0
(k)
December
Experimental dataLinear fit
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(l)
Figure 5 Scatter diagram of linear model
ISRN Renewable Energy 7
0
02
04
06
08
1
0 02 04 06 08 1
January
SSSS0
HH
0
(a)
February
0
02
04
06
08
1
SSSS0
0 02 04 06 08 1
HH
0
(b)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
March
HH
0
(c)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
April
HH
0
(d)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
May
HH
0
(e)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
June
HH
0
(f)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
July
HH
0
(g)
August
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(h)
September
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(i)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
Experimental dataQuadratic fit
October
HH
0
(j)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
Experimental dataQuadratic fit
November
HH
0
(k)
Experimental dataQuadratic fit
December
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(l)
Figure 6 Scatter diagram of quadratic model
8 ISRN Renewable Energy
0
02
04
06
08
1
0 02 04 06 08 1
January
SSSS0
HH
0
(a)
February
0
02
04
06
08
1
SSSS0
0 02 04 06 08 1
HH
0
(b)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
March
HH
0
(c)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
April
HH
0
(d)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
May
HH
0
(e)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
June
HH
0
(f)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
July
HH
0
(g)
August
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(h)
September
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(i)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
Experimental dataLogarithmic fit
October
HH
0
(j)
Experimental dataLogarithmic fit
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
November
HH
0
(k)
Experimental dataLogarithmic fit
December
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(l)
Figure 7 Scatter diagram of logarithmic model
ISRN Renewable Energy 9
0
02
04
06
08
1
0 02 04 06 08 1
January
SSSS0
HH
0
(a)
February
0
02
04
06
08
1
SSSS0
0 02 04 06 08 1
HH
0
(b)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
March
HH
0
(c)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
April
HH
0
(d)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
May
HH
0
(e)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
June
HH
0
(f)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
July
HH
0
(g)
August
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(h)
September
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(i)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
October
Experimental dataExponential fit
HH
0
(j)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
November
Experimental dataExponential fit
HH
0
(k)
Experimental dataExponential fit
December
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(l)
Figure 8 Scatter diagram of exponential model
10 ISRN Renewable Energy
Table 6 Comparison between measured and estimated monthly global solar radiation (Whm2)
Measured Linear 119890 () Quadratic 119890 () Logarithmic 119890 () Exponential 119890 ()January 3871 387975 minus0226 392454 minus1383 405448 minus474 381238 1514February 4842 476892 1509 474643 1974 522917 minus7996 469399 3057March 5926 583664 1508 586369 1051 617679 minus4232 573538 3217April 7339 734601 minus0096 739331 minus074 77792 minus5998 726109 1062May 7745 774506 minus0001 780996 minus0839 820351 minus592 761716 1651June 7812 782641 minus0184 793014 minus1512 823929 minus547 769928 1443July 7503 749263 0138 748443 0248 79856 minus6432 743793 0867August 7090 722491 minus1903 737784 minus406 757691 minus6868 719104 minus1425September 6036 602421 0195 605437 minus0304 63717 minus5562 589847 2278October 4824 482102 0062 486969 minus0947 512876 minus6318 473796 1784November 4030 402613 0096 39782 1285 422429 minus4821 396304 1662December 3437 342706 0289 362654 minus5515 372876 minus8489 334942 2548
Table 7 Annual validation of different models
119886 119887 119888 119889 CC RMSE MBELinear 0420 0363 0785 00453 minus00012Quadratic 0403 0446 minus00737 0787 00451 minus00007Logarithmic 0701 0106 0627 00792 00281Exponential 0264 0198 0763 00511 minus00182Abdalla 0519 0357 minus00018 minus000126 0898 00429 minus000059Ojosu et al 0449 0358 minus000445 minus000619 0892 00443 minus000068Hargreaves et al 0261 0115 0431 00883 minus000073
Table 8 Comparison between measured and estimated annualglobal solar radiation (Whm2)
Measured value Model Estimated values 119890 ()Linear 585245 0316
Quadratic 585743 0231Logarithmic 610862 minus4047
5871 Exponential 584795 0393Abdalla 584603 0425
Ojosu et al 583350 0639Hargreaves et al 588797 minus0289
models usually give the best performance if we take intoaccount the statistical test while for the model based on themeteorological parameters Abdalla and Ojosu et alrsquos modelsgive the best accuracy with a CC of 0898 and 0892 andRMSE of 00429 and 00443 while Hargreaves et alrsquos modelunderestimates the global solar radiation
The comparison between the estimated and measuredannual average values of the global solar radiation arepresented in Table 8 the annual percentage error is rangedbetween minus4047 and 0639 So it is clear that the linearquadratic models Abdalla and Ojosu are also the suitablemodels to estimate the annual global solar radiation on ahorizontal surface in Ghardaıa region
6 Conclusion
Several empirical models have been tested to estimate theglobal solar radiation on a horizontal surface using the
sunshine duration and the meteorological parameters Thegoal of this paper is the validation of seven models to predictthe monthly and the annual global solar radiation withina dataset of Ghardaia area and thus select the suitablemodel The models were compared on the basis of statisticaltests
Depending on the obtained results we can conclude thatthe linear and the quadratic models are the most accuratefor estimating the monthly global solar radiation on ahorizontal surface according to the statistical tests (CC 0956RMSE 0018 and MBE 4310minus5) the percentage error neverexceeds plusmn5 which indicate an excellent fitting between theglobal solar radiation and sunshine duration On the basisof annual estimation of global solar radiation and for themodels based on the sunshine duration always the linearand the quadratic models provide the best accuracy (CC0787 RMSE 00451 andMBE minus00007) whereas formodelsusing the meteorological parameters in addition to sunshineduration we found that Abdalla and Ojosursquos models are themost suitable with a CC of 0898 and 0892 respectively andthe relative error ranges between minus0289 and 0639
References
[1] K Gairaa and S Benkaciali ldquoAnalysis of solar radiation mea-surements in Ghardaia area south Algeriardquo Energy Procediavol 6 pp 122ndash129 2011
[2] J L Desouza R M Nicaciob and M A L Mouraa ldquoGlobalsolar radiation measurements in Maceio Brazilrdquo RenewableEnergy vol 30 pp 1203ndash1220 2009
ISRN Renewable Energy 11
[3] J P Duffie and W A Beckman Solar Engineering of ThermalProcess John Wiley amp Sons New York NY USA 1991
[4] M Iqbal An Introduction to Solar Radiation Academic PressToronto Canada 1983
[5] International Energy Agency (IEA) ldquoValidation of models forestimating solar radiation on horizontal surfacesrdquo Atmosphereamp Environment service Canada 1988
[6] J A Prescott ldquoEvaporation from a water surface in relation tosolar radiationrdquo Philosophical Transactions of the Royal Societyvol 64 pp 114ndash120 1990
[7] C C Y Ma and M Iqbal ldquoStatistical comparison of solar radi-ation correlations Monthly average global and diffuse radiationon horizontal surfacesrdquo Solar Energy vol 33 no 2 pp 143ndash1481984
[8] J Almorox and C Hontoria ldquoGlobal solar radiation estimationusing sunshine duration in Spainrdquo Energy Conversion andManagement vol 45 no 9-10 pp 1529ndash1535 2004
[9] I T Togrul H Togrul and D Evin ldquoEstimation of monthlyglobal solar radiation from sunshine duration measurement inElazigrdquo Renewable Energy vol 19 no 4 pp 587ndash595 2000
[10] I T Togrul and E Onat ldquoA comparison of estimated andmeasured values of solar radiation in Elazig TurkeyrdquoRenewableEnergy vol 20 no 2 pp 243ndash252 2000
[11] A K Katiyar A Kumar K P Chanchal and B Das ldquoAcomparative study of monthly mean daily clear sky radiationover Indiardquo International Journal of Energy and Environmentvol 1 pp 177ndash182 2010
[12] G Oturanc A Hepbasli and A Genc ldquoStatistical analysis forsolar radiation datardquo Energy Sources vol 25 no 11 pp 1089ndash1097 2003
[13] M Benghanem and A A Joraid ldquoA multiple correlationbetween different solar parameters in Medina Saudi ArabiardquoRenewable Energy vol 32 no 14 pp 2424ndash2435 2007
[14] D B Ampratwum and A S S Dorvlo ldquoEstimation of solarradiation from the number of sunshine hoursrdquo Applied Energyvol 63 no 3 pp 161ndash167 1999
[15] Z Sen ldquoAngstrom equation parameter estimation by unre-stricted methodrdquo Solar Energy vol 71 no 2 pp 95ndash107 2001
[16] B T Nguyen and T L Pryor ldquoThe relationship between globalsolar radiation and sunshine duration in Vietnamrdquo RenewableEnergy vol 11 no 1 pp 47ndash60 1997
[17] N A Elagib S H Alvi and M G Mansell ldquoCorrelationshipsbetween clearness index and relative sunshine duration forSudanrdquo Renewable Energy vol 17 no 4 pp 473ndash498 1999
[18] M Hussain L Rahman and M M Rahman ldquoTechnical notetechniques to obtain improved predictions of global radiationfrom sunshine durationrdquo Renewable Energy vol 18 no 2 pp263ndash275 1999
[19] M T Y Tadros ldquoUses of sunshine duration to estimate theglobal solar radiation over eight meteorological stations inEgyptrdquo Renewable Energy vol 21 no 2 pp 231ndash246 2000
[20] I T Togrul and E Onat ldquoStudy for estimating solar radiationin Elazig using geographical and meteorological datardquo EnergyConversion and Management vol 40 no 14 pp 1577ndash15841999
[21] R Chen K Ersi J Yang S Lu and W Zhao ldquoValidation offive global radiationmodels withmeasured daily data in ChinardquoEnergy Conversion andManagement vol 45 no 11-12 pp 1759ndash1769 2004
[22] C Ertekin and O Yaldiz ldquoComparison of some existing modelsfor estimating global solar radiation for Antalya (Turkey)rdquo
Energy Conversion and Management vol 41 no 4 pp 311ndash3302000
[23] J C Ododo J A Agbakwuru and F A Ogbu ldquoCorrelation ofsolar radiationwith cloud cover and relative sunshine durationrdquoEnergy Conversion and Management vol 37 no 10 pp 1555ndash1559 1996
[24] M Yorukoglu and A N Celik ldquoA critical review on the esti-mation of daily global solar radiation from sunshine durationrdquoEnergy Conversion andManagement vol 47 no 15-16 pp 2441ndash2450 2006
[25] Y Abdalla ldquoNew correlation of global solar radiation withmeteorological parameters for Bahrainrdquo International Journalof Solar Energy vol 16 pp 111ndash120 1994
[26] K K Gopinathan ldquoA new model for estimating total solarradiation in Dohardquo Energy Conversion andManagemen vol 28pp 6ndash72 1988
[27] 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
[28] R G Allen ldquoSelf-calibrating method for estimating solar radi-ation from air temperaturerdquo Journal of Hydrologic Engineeringvol 2 no 2 pp 56ndash67 1997
[29] G H Hargreaves and R G Allen ldquoHistory and evaluation ofhargreaves evapotranspiration equationrdquo Journal of Irrigationand Drainage Engineering vol 129 no 1 pp 53ndash63 2003
[30] Z Samani G H Hargreaves V Tran and S Bawazir ldquoEstimat-ing solar radiation from temperature with spatial and temporalcalibrationrdquo Journal of Irrigation and Drainage Engineering vol137 no 11 pp 692ndash696 2011
[31] J O Ojosu and L K Komolafe ldquoModels for estimating solarradiation availability in South Western Nigeriardquo Solar Energyvol 16 pp 69ndash77 1987
[32] G H Hargreaves and Z A Samani ldquoReference crop evapotran-spiration from temperaturerdquoTransactions of theASAE vol 1 pp96ndash99 1985
[33] J I Prieto J C Martınez-Garcıa and D Garcıa ldquoCorrela-tion between global solar irradiation and air temperature inAsturias Spainrdquo Solar Energy vol 83 no 7 pp 1076ndash1085 2009
[34] M Paulescu L Fara and E Tulcan-Paulescu ldquoModels forobtaining daily global solar irradiation from air temperaturedatardquo Atmospheric Research vol 79 no 3-4 pp 227ndash240 2006
TribologyAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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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
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
4 ISRN Renewable Energy
Table 2 Linear model validation
119886 119887 CC RMSE MBEJanuary 0361 0457 0890 00361 minus000044February 0303 0515 0715 00664 000060March 0477 032 0916 00269 minus000028April 0425 0389 0929 00213 000035May 0466 033 0897 00344 minus001990June 0443 0332 0946 00196 000040July 0453 0307 0853 00246 minus000018August 0481 0273 0731 00284 minus000081September 0376 0402 0789 00534 0000077October 0398 0357 0934 00226 minus000032November 0451 0315 0620 00649 000045December 0373 0406 0856 00452 minus000047
Table 3 Quadratic model validation
119886 119887 119862 CC RMSE MBEJanuary 0337 0618 minus0159 0896 0035 minus000028February 0335 0408 008 0715 0066 minus000047March 0469 0361 minus0037 0917 0026 minus0000056April 0372 0574 minus0143 0935 002 minus000058May 0443 0444 minus0104 0903 0027 minus000067June 0411 0497 minus015 0956 0018 000043July 046 0282 002 0853 0025 minus000016August 0278 0937 minus0497 0833 0022 000014September 0367 0452 minus0046 079 0053 000023October 0375 0479 minus0114 094 0022 minus000033November 0466 0198 0118 0623 0063 000049December 0277 0956 minus0504 0894 0039 000057
4 Statistical Test
The accuracy of the estimated models will be judged bythe statistical indicators such as the correlation coefficient(CC) mean bias error (MBE) root mean square error(RMSE) and the percentage error (119890) These indicators areusually applied in the comparison of solar radiation modelsThe mean square error provides information about theperformance of correlations which allows comparison ofthe real differences between the estimated values and themeasured ones a low RMSE is desirable The MBE providesthe long-term performance of the model in general thepositive MBE shows overestimation while the negative MBEindicates underestimationThe correlation coefficient reflectsthe quality of the model the more CC close to 1 the more thebetter quality The expression of each statistical indicator isgiven
CC = 1 minussum119899
119894=1
(119867119894119898minus 119867119894119890)2
sum119899
119894=1
(119867119894119898minus 119867119898)
2
MBE = 1119899
(
119899
sum
119894=1
119867119894119890minus 119867119894119898
119867119894119898
)
RMSE = [1119899
119899
sum
119894=1
(
119867119894119890minus 119867119894119898
119867119894119898
)
2
]
12
119890 = [(
119867119894119898minus 119867119894119890
119867119894119898
)] 100
(11)
where 119867119894119890
and 119867119894119898
are the 119894th estimated and measuredvalues 119867
119898is the mean of observed data and 119899 is the total
number of observations
5 Results and Discussion
The results of the validation of the models that estimate theglobal solar radiation from sunshine duration on themonthlybasis are presented in Tables 2 3 4 and 5 The analysis ofthe measured and calculated values shows that the maximumof the global solar radiation is observed in June while theminimum values are appearing in December
For the linear model the correlation coefficient is signifi-cant for all months of the year except in November where it isrelatively lowThe quality of the estimate is a slightly worse for
ISRN Renewable Energy 5
Table 4 Logarithmic model validation
119886 119887 CC RMSE MBEJanuary 0741 0079 0792 0077 00235February 0795 0314 0693 0102 00536March 0734 0079 0651 0151 00566April 0792 0218 0917 0061 00369May 0757 0121 0825 0067 00338June 0734 0112 0862 0061 00294July 0735 0164 0816 0058 00393August 0743 0176 0805 0048 00321September 0714 0097 0613 0091 00281October 0708 0121 0864 0065 00330November 0724 009 0487 0088 00259December 0749 0176 0886 0088 00465
Table 5 Exponential model validation
119886 119887 CC RMSE MBEJanuary 014 0261 0861 004 minus000071February 0128 026 0713 0063 minus000047March 0342 0173 0878 0032 000003April 0295 0195 0901 0025 minus000026May 0321 0181 0868 0032 minus000077June 0295 0183 0916 0024 minus000040July 0335 0163 0846 0025 000078August 0403 0132 067 0032 minus000022September 0192 0224 0774 0055 minus000044October 0236 0199 0901 0028 minus00015November 0283 0187 0621 0045 0104December 0188 0225 0822 0073 minus00096
the months of the February and November when the RMSEis between 0064 and 0069
For the quadratic correlation the result shows a slightimprovement in the accuracy of the model for the monthof August where the coefficient of determination is equal to083 (compared to the linear model CC = 073) the qualityof estimation is also improved in the months of June andDecember with an RMSE of 0018 and 0039 respectivelyTheregression based on the logarithmic and exponential modelsdid not improve significantly the accuracy of estimation of theglobal solar radiation than the two previous models as seenfrom the values of the CC MBE and RMSE (Correlationcoefficient reached his minimum values in November (CC =048) for the logarithmic model)
Another manner of the comparison between the mea-sured and the predicted values was illustrated by the scatterdiagram plotted in Figures 5 6 7 and 8 A strong scatteringof the points in the superior or in the inferior half of theregression line indicates respectively an overestimate or anunderestimate
For the linear model the dispersion of estimated valuesaround the regression line is fairly low in the months ofJanuary March-August October and December where thecorrelation coefficient ranges between 085 and 094 while
this dispersion is small in the quadratic model this indicatesan excellent fitting between the global radiation and thesunshine duration
For the logarithmic model the dispersion of the esti-mated values is strong especially in the months of JanuaryMarch and August and it is low in the months of FebruarySeptember and November while this dispersion remainslow for the exponential model in the months of FebruarySeptember and November and it is strong too for the othermonths of the year
The confrontation between estimated and measuredmonthly average global solar radiation by the different mod-els is shown in Table 6 which indicated that the percentageerror never exceeds plusmn10 for all models It was 1903 asmaximumvalue for the linearmodel 1974 for the quadraticmodel minus8489 for the logarithmic model and 3217 forthe exponential model Among the four proposedmodels wefound in the first rank the linear and quadratic correlationswhich give results that agree well with the measured valuescompared with the other two models which underestimateor overestimate measurements
The validation of the various models on the annualbasis is shown in Table 7 For the correlation based on thesunshine duration we can note that the linear and quadratic
6 ISRN Renewable Energy
0
02
04
06
08
1
0 02 04 06 08 1
January
SSSS0
HH
0
(a)
03 04 05 06 07 08 09 1
February
0
02
04
06
08
1
SSSS0
HH
0
(b)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
March
HH
0
(c)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
April
HH
0
(d)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
May
HH
0
(e)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
June
HH
0
(f)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
July
HH
0
(g)
August
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(h)
September
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(i)
Experimental dataLinear fit
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
October
HH
0
(j)
Experimental dataLinear fit
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
November
HH
0
(k)
December
Experimental dataLinear fit
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(l)
Figure 5 Scatter diagram of linear model
ISRN Renewable Energy 7
0
02
04
06
08
1
0 02 04 06 08 1
January
SSSS0
HH
0
(a)
February
0
02
04
06
08
1
SSSS0
0 02 04 06 08 1
HH
0
(b)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
March
HH
0
(c)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
April
HH
0
(d)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
May
HH
0
(e)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
June
HH
0
(f)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
July
HH
0
(g)
August
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(h)
September
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(i)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
Experimental dataQuadratic fit
October
HH
0
(j)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
Experimental dataQuadratic fit
November
HH
0
(k)
Experimental dataQuadratic fit
December
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(l)
Figure 6 Scatter diagram of quadratic model
8 ISRN Renewable Energy
0
02
04
06
08
1
0 02 04 06 08 1
January
SSSS0
HH
0
(a)
February
0
02
04
06
08
1
SSSS0
0 02 04 06 08 1
HH
0
(b)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
March
HH
0
(c)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
April
HH
0
(d)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
May
HH
0
(e)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
June
HH
0
(f)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
July
HH
0
(g)
August
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(h)
September
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(i)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
Experimental dataLogarithmic fit
October
HH
0
(j)
Experimental dataLogarithmic fit
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
November
HH
0
(k)
Experimental dataLogarithmic fit
December
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(l)
Figure 7 Scatter diagram of logarithmic model
ISRN Renewable Energy 9
0
02
04
06
08
1
0 02 04 06 08 1
January
SSSS0
HH
0
(a)
February
0
02
04
06
08
1
SSSS0
0 02 04 06 08 1
HH
0
(b)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
March
HH
0
(c)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
April
HH
0
(d)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
May
HH
0
(e)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
June
HH
0
(f)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
July
HH
0
(g)
August
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(h)
September
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(i)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
October
Experimental dataExponential fit
HH
0
(j)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
November
Experimental dataExponential fit
HH
0
(k)
Experimental dataExponential fit
December
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(l)
Figure 8 Scatter diagram of exponential model
10 ISRN Renewable Energy
Table 6 Comparison between measured and estimated monthly global solar radiation (Whm2)
Measured Linear 119890 () Quadratic 119890 () Logarithmic 119890 () Exponential 119890 ()January 3871 387975 minus0226 392454 minus1383 405448 minus474 381238 1514February 4842 476892 1509 474643 1974 522917 minus7996 469399 3057March 5926 583664 1508 586369 1051 617679 minus4232 573538 3217April 7339 734601 minus0096 739331 minus074 77792 minus5998 726109 1062May 7745 774506 minus0001 780996 minus0839 820351 minus592 761716 1651June 7812 782641 minus0184 793014 minus1512 823929 minus547 769928 1443July 7503 749263 0138 748443 0248 79856 minus6432 743793 0867August 7090 722491 minus1903 737784 minus406 757691 minus6868 719104 minus1425September 6036 602421 0195 605437 minus0304 63717 minus5562 589847 2278October 4824 482102 0062 486969 minus0947 512876 minus6318 473796 1784November 4030 402613 0096 39782 1285 422429 minus4821 396304 1662December 3437 342706 0289 362654 minus5515 372876 minus8489 334942 2548
Table 7 Annual validation of different models
119886 119887 119888 119889 CC RMSE MBELinear 0420 0363 0785 00453 minus00012Quadratic 0403 0446 minus00737 0787 00451 minus00007Logarithmic 0701 0106 0627 00792 00281Exponential 0264 0198 0763 00511 minus00182Abdalla 0519 0357 minus00018 minus000126 0898 00429 minus000059Ojosu et al 0449 0358 minus000445 minus000619 0892 00443 minus000068Hargreaves et al 0261 0115 0431 00883 minus000073
Table 8 Comparison between measured and estimated annualglobal solar radiation (Whm2)
Measured value Model Estimated values 119890 ()Linear 585245 0316
Quadratic 585743 0231Logarithmic 610862 minus4047
5871 Exponential 584795 0393Abdalla 584603 0425
Ojosu et al 583350 0639Hargreaves et al 588797 minus0289
models usually give the best performance if we take intoaccount the statistical test while for the model based on themeteorological parameters Abdalla and Ojosu et alrsquos modelsgive the best accuracy with a CC of 0898 and 0892 andRMSE of 00429 and 00443 while Hargreaves et alrsquos modelunderestimates the global solar radiation
The comparison between the estimated and measuredannual average values of the global solar radiation arepresented in Table 8 the annual percentage error is rangedbetween minus4047 and 0639 So it is clear that the linearquadratic models Abdalla and Ojosu are also the suitablemodels to estimate the annual global solar radiation on ahorizontal surface in Ghardaıa region
6 Conclusion
Several empirical models have been tested to estimate theglobal solar radiation on a horizontal surface using the
sunshine duration and the meteorological parameters Thegoal of this paper is the validation of seven models to predictthe monthly and the annual global solar radiation withina dataset of Ghardaia area and thus select the suitablemodel The models were compared on the basis of statisticaltests
Depending on the obtained results we can conclude thatthe linear and the quadratic models are the most accuratefor estimating the monthly global solar radiation on ahorizontal surface according to the statistical tests (CC 0956RMSE 0018 and MBE 4310minus5) the percentage error neverexceeds plusmn5 which indicate an excellent fitting between theglobal solar radiation and sunshine duration On the basisof annual estimation of global solar radiation and for themodels based on the sunshine duration always the linearand the quadratic models provide the best accuracy (CC0787 RMSE 00451 andMBE minus00007) whereas formodelsusing the meteorological parameters in addition to sunshineduration we found that Abdalla and Ojosursquos models are themost suitable with a CC of 0898 and 0892 respectively andthe relative error ranges between minus0289 and 0639
References
[1] K Gairaa and S Benkaciali ldquoAnalysis of solar radiation mea-surements in Ghardaia area south Algeriardquo Energy Procediavol 6 pp 122ndash129 2011
[2] J L Desouza R M Nicaciob and M A L Mouraa ldquoGlobalsolar radiation measurements in Maceio Brazilrdquo RenewableEnergy vol 30 pp 1203ndash1220 2009
ISRN Renewable Energy 11
[3] J P Duffie and W A Beckman Solar Engineering of ThermalProcess John Wiley amp Sons New York NY USA 1991
[4] M Iqbal An Introduction to Solar Radiation Academic PressToronto Canada 1983
[5] International Energy Agency (IEA) ldquoValidation of models forestimating solar radiation on horizontal surfacesrdquo Atmosphereamp Environment service Canada 1988
[6] J A Prescott ldquoEvaporation from a water surface in relation tosolar radiationrdquo Philosophical Transactions of the Royal Societyvol 64 pp 114ndash120 1990
[7] C C Y Ma and M Iqbal ldquoStatistical comparison of solar radi-ation correlations Monthly average global and diffuse radiationon horizontal surfacesrdquo Solar Energy vol 33 no 2 pp 143ndash1481984
[8] J Almorox and C Hontoria ldquoGlobal solar radiation estimationusing sunshine duration in Spainrdquo Energy Conversion andManagement vol 45 no 9-10 pp 1529ndash1535 2004
[9] I T Togrul H Togrul and D Evin ldquoEstimation of monthlyglobal solar radiation from sunshine duration measurement inElazigrdquo Renewable Energy vol 19 no 4 pp 587ndash595 2000
[10] I T Togrul and E Onat ldquoA comparison of estimated andmeasured values of solar radiation in Elazig TurkeyrdquoRenewableEnergy vol 20 no 2 pp 243ndash252 2000
[11] A K Katiyar A Kumar K P Chanchal and B Das ldquoAcomparative study of monthly mean daily clear sky radiationover Indiardquo International Journal of Energy and Environmentvol 1 pp 177ndash182 2010
[12] G Oturanc A Hepbasli and A Genc ldquoStatistical analysis forsolar radiation datardquo Energy Sources vol 25 no 11 pp 1089ndash1097 2003
[13] M Benghanem and A A Joraid ldquoA multiple correlationbetween different solar parameters in Medina Saudi ArabiardquoRenewable Energy vol 32 no 14 pp 2424ndash2435 2007
[14] D B Ampratwum and A S S Dorvlo ldquoEstimation of solarradiation from the number of sunshine hoursrdquo Applied Energyvol 63 no 3 pp 161ndash167 1999
[15] Z Sen ldquoAngstrom equation parameter estimation by unre-stricted methodrdquo Solar Energy vol 71 no 2 pp 95ndash107 2001
[16] B T Nguyen and T L Pryor ldquoThe relationship between globalsolar radiation and sunshine duration in Vietnamrdquo RenewableEnergy vol 11 no 1 pp 47ndash60 1997
[17] N A Elagib S H Alvi and M G Mansell ldquoCorrelationshipsbetween clearness index and relative sunshine duration forSudanrdquo Renewable Energy vol 17 no 4 pp 473ndash498 1999
[18] M Hussain L Rahman and M M Rahman ldquoTechnical notetechniques to obtain improved predictions of global radiationfrom sunshine durationrdquo Renewable Energy vol 18 no 2 pp263ndash275 1999
[19] M T Y Tadros ldquoUses of sunshine duration to estimate theglobal solar radiation over eight meteorological stations inEgyptrdquo Renewable Energy vol 21 no 2 pp 231ndash246 2000
[20] I T Togrul and E Onat ldquoStudy for estimating solar radiationin Elazig using geographical and meteorological datardquo EnergyConversion and Management vol 40 no 14 pp 1577ndash15841999
[21] R Chen K Ersi J Yang S Lu and W Zhao ldquoValidation offive global radiationmodels withmeasured daily data in ChinardquoEnergy Conversion andManagement vol 45 no 11-12 pp 1759ndash1769 2004
[22] C Ertekin and O Yaldiz ldquoComparison of some existing modelsfor estimating global solar radiation for Antalya (Turkey)rdquo
Energy Conversion and Management vol 41 no 4 pp 311ndash3302000
[23] J C Ododo J A Agbakwuru and F A Ogbu ldquoCorrelation ofsolar radiationwith cloud cover and relative sunshine durationrdquoEnergy Conversion and Management vol 37 no 10 pp 1555ndash1559 1996
[24] M Yorukoglu and A N Celik ldquoA critical review on the esti-mation of daily global solar radiation from sunshine durationrdquoEnergy Conversion andManagement vol 47 no 15-16 pp 2441ndash2450 2006
[25] Y Abdalla ldquoNew correlation of global solar radiation withmeteorological parameters for Bahrainrdquo International Journalof Solar Energy vol 16 pp 111ndash120 1994
[26] K K Gopinathan ldquoA new model for estimating total solarradiation in Dohardquo Energy Conversion andManagemen vol 28pp 6ndash72 1988
[27] 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
[28] R G Allen ldquoSelf-calibrating method for estimating solar radi-ation from air temperaturerdquo Journal of Hydrologic Engineeringvol 2 no 2 pp 56ndash67 1997
[29] G H Hargreaves and R G Allen ldquoHistory and evaluation ofhargreaves evapotranspiration equationrdquo Journal of Irrigationand Drainage Engineering vol 129 no 1 pp 53ndash63 2003
[30] Z Samani G H Hargreaves V Tran and S Bawazir ldquoEstimat-ing solar radiation from temperature with spatial and temporalcalibrationrdquo Journal of Irrigation and Drainage Engineering vol137 no 11 pp 692ndash696 2011
[31] J O Ojosu and L K Komolafe ldquoModels for estimating solarradiation availability in South Western Nigeriardquo Solar Energyvol 16 pp 69ndash77 1987
[32] G H Hargreaves and Z A Samani ldquoReference crop evapotran-spiration from temperaturerdquoTransactions of theASAE vol 1 pp96ndash99 1985
[33] J I Prieto J C Martınez-Garcıa and D Garcıa ldquoCorrela-tion between global solar irradiation and air temperature inAsturias Spainrdquo Solar Energy vol 83 no 7 pp 1076ndash1085 2009
[34] M Paulescu L Fara and E Tulcan-Paulescu ldquoModels forobtaining daily global solar irradiation from air temperaturedatardquo Atmospheric Research vol 79 no 3-4 pp 227ndash240 2006
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
ISRN Renewable Energy 5
Table 4 Logarithmic model validation
119886 119887 CC RMSE MBEJanuary 0741 0079 0792 0077 00235February 0795 0314 0693 0102 00536March 0734 0079 0651 0151 00566April 0792 0218 0917 0061 00369May 0757 0121 0825 0067 00338June 0734 0112 0862 0061 00294July 0735 0164 0816 0058 00393August 0743 0176 0805 0048 00321September 0714 0097 0613 0091 00281October 0708 0121 0864 0065 00330November 0724 009 0487 0088 00259December 0749 0176 0886 0088 00465
Table 5 Exponential model validation
119886 119887 CC RMSE MBEJanuary 014 0261 0861 004 minus000071February 0128 026 0713 0063 minus000047March 0342 0173 0878 0032 000003April 0295 0195 0901 0025 minus000026May 0321 0181 0868 0032 minus000077June 0295 0183 0916 0024 minus000040July 0335 0163 0846 0025 000078August 0403 0132 067 0032 minus000022September 0192 0224 0774 0055 minus000044October 0236 0199 0901 0028 minus00015November 0283 0187 0621 0045 0104December 0188 0225 0822 0073 minus00096
the months of the February and November when the RMSEis between 0064 and 0069
For the quadratic correlation the result shows a slightimprovement in the accuracy of the model for the monthof August where the coefficient of determination is equal to083 (compared to the linear model CC = 073) the qualityof estimation is also improved in the months of June andDecember with an RMSE of 0018 and 0039 respectivelyTheregression based on the logarithmic and exponential modelsdid not improve significantly the accuracy of estimation of theglobal solar radiation than the two previous models as seenfrom the values of the CC MBE and RMSE (Correlationcoefficient reached his minimum values in November (CC =048) for the logarithmic model)
Another manner of the comparison between the mea-sured and the predicted values was illustrated by the scatterdiagram plotted in Figures 5 6 7 and 8 A strong scatteringof the points in the superior or in the inferior half of theregression line indicates respectively an overestimate or anunderestimate
For the linear model the dispersion of estimated valuesaround the regression line is fairly low in the months ofJanuary March-August October and December where thecorrelation coefficient ranges between 085 and 094 while
this dispersion is small in the quadratic model this indicatesan excellent fitting between the global radiation and thesunshine duration
For the logarithmic model the dispersion of the esti-mated values is strong especially in the months of JanuaryMarch and August and it is low in the months of FebruarySeptember and November while this dispersion remainslow for the exponential model in the months of FebruarySeptember and November and it is strong too for the othermonths of the year
The confrontation between estimated and measuredmonthly average global solar radiation by the different mod-els is shown in Table 6 which indicated that the percentageerror never exceeds plusmn10 for all models It was 1903 asmaximumvalue for the linearmodel 1974 for the quadraticmodel minus8489 for the logarithmic model and 3217 forthe exponential model Among the four proposedmodels wefound in the first rank the linear and quadratic correlationswhich give results that agree well with the measured valuescompared with the other two models which underestimateor overestimate measurements
The validation of the various models on the annualbasis is shown in Table 7 For the correlation based on thesunshine duration we can note that the linear and quadratic
6 ISRN Renewable Energy
0
02
04
06
08
1
0 02 04 06 08 1
January
SSSS0
HH
0
(a)
03 04 05 06 07 08 09 1
February
0
02
04
06
08
1
SSSS0
HH
0
(b)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
March
HH
0
(c)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
April
HH
0
(d)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
May
HH
0
(e)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
June
HH
0
(f)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
July
HH
0
(g)
August
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(h)
September
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(i)
Experimental dataLinear fit
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
October
HH
0
(j)
Experimental dataLinear fit
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
November
HH
0
(k)
December
Experimental dataLinear fit
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(l)
Figure 5 Scatter diagram of linear model
ISRN Renewable Energy 7
0
02
04
06
08
1
0 02 04 06 08 1
January
SSSS0
HH
0
(a)
February
0
02
04
06
08
1
SSSS0
0 02 04 06 08 1
HH
0
(b)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
March
HH
0
(c)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
April
HH
0
(d)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
May
HH
0
(e)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
June
HH
0
(f)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
July
HH
0
(g)
August
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(h)
September
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(i)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
Experimental dataQuadratic fit
October
HH
0
(j)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
Experimental dataQuadratic fit
November
HH
0
(k)
Experimental dataQuadratic fit
December
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(l)
Figure 6 Scatter diagram of quadratic model
8 ISRN Renewable Energy
0
02
04
06
08
1
0 02 04 06 08 1
January
SSSS0
HH
0
(a)
February
0
02
04
06
08
1
SSSS0
0 02 04 06 08 1
HH
0
(b)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
March
HH
0
(c)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
April
HH
0
(d)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
May
HH
0
(e)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
June
HH
0
(f)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
July
HH
0
(g)
August
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(h)
September
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(i)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
Experimental dataLogarithmic fit
October
HH
0
(j)
Experimental dataLogarithmic fit
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
November
HH
0
(k)
Experimental dataLogarithmic fit
December
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(l)
Figure 7 Scatter diagram of logarithmic model
ISRN Renewable Energy 9
0
02
04
06
08
1
0 02 04 06 08 1
January
SSSS0
HH
0
(a)
February
0
02
04
06
08
1
SSSS0
0 02 04 06 08 1
HH
0
(b)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
March
HH
0
(c)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
April
HH
0
(d)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
May
HH
0
(e)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
June
HH
0
(f)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
July
HH
0
(g)
August
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(h)
September
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(i)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
October
Experimental dataExponential fit
HH
0
(j)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
November
Experimental dataExponential fit
HH
0
(k)
Experimental dataExponential fit
December
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(l)
Figure 8 Scatter diagram of exponential model
10 ISRN Renewable Energy
Table 6 Comparison between measured and estimated monthly global solar radiation (Whm2)
Measured Linear 119890 () Quadratic 119890 () Logarithmic 119890 () Exponential 119890 ()January 3871 387975 minus0226 392454 minus1383 405448 minus474 381238 1514February 4842 476892 1509 474643 1974 522917 minus7996 469399 3057March 5926 583664 1508 586369 1051 617679 minus4232 573538 3217April 7339 734601 minus0096 739331 minus074 77792 minus5998 726109 1062May 7745 774506 minus0001 780996 minus0839 820351 minus592 761716 1651June 7812 782641 minus0184 793014 minus1512 823929 minus547 769928 1443July 7503 749263 0138 748443 0248 79856 minus6432 743793 0867August 7090 722491 minus1903 737784 minus406 757691 minus6868 719104 minus1425September 6036 602421 0195 605437 minus0304 63717 minus5562 589847 2278October 4824 482102 0062 486969 minus0947 512876 minus6318 473796 1784November 4030 402613 0096 39782 1285 422429 minus4821 396304 1662December 3437 342706 0289 362654 minus5515 372876 minus8489 334942 2548
Table 7 Annual validation of different models
119886 119887 119888 119889 CC RMSE MBELinear 0420 0363 0785 00453 minus00012Quadratic 0403 0446 minus00737 0787 00451 minus00007Logarithmic 0701 0106 0627 00792 00281Exponential 0264 0198 0763 00511 minus00182Abdalla 0519 0357 minus00018 minus000126 0898 00429 minus000059Ojosu et al 0449 0358 minus000445 minus000619 0892 00443 minus000068Hargreaves et al 0261 0115 0431 00883 minus000073
Table 8 Comparison between measured and estimated annualglobal solar radiation (Whm2)
Measured value Model Estimated values 119890 ()Linear 585245 0316
Quadratic 585743 0231Logarithmic 610862 minus4047
5871 Exponential 584795 0393Abdalla 584603 0425
Ojosu et al 583350 0639Hargreaves et al 588797 minus0289
models usually give the best performance if we take intoaccount the statistical test while for the model based on themeteorological parameters Abdalla and Ojosu et alrsquos modelsgive the best accuracy with a CC of 0898 and 0892 andRMSE of 00429 and 00443 while Hargreaves et alrsquos modelunderestimates the global solar radiation
The comparison between the estimated and measuredannual average values of the global solar radiation arepresented in Table 8 the annual percentage error is rangedbetween minus4047 and 0639 So it is clear that the linearquadratic models Abdalla and Ojosu are also the suitablemodels to estimate the annual global solar radiation on ahorizontal surface in Ghardaıa region
6 Conclusion
Several empirical models have been tested to estimate theglobal solar radiation on a horizontal surface using the
sunshine duration and the meteorological parameters Thegoal of this paper is the validation of seven models to predictthe monthly and the annual global solar radiation withina dataset of Ghardaia area and thus select the suitablemodel The models were compared on the basis of statisticaltests
Depending on the obtained results we can conclude thatthe linear and the quadratic models are the most accuratefor estimating the monthly global solar radiation on ahorizontal surface according to the statistical tests (CC 0956RMSE 0018 and MBE 4310minus5) the percentage error neverexceeds plusmn5 which indicate an excellent fitting between theglobal solar radiation and sunshine duration On the basisof annual estimation of global solar radiation and for themodels based on the sunshine duration always the linearand the quadratic models provide the best accuracy (CC0787 RMSE 00451 andMBE minus00007) whereas formodelsusing the meteorological parameters in addition to sunshineduration we found that Abdalla and Ojosursquos models are themost suitable with a CC of 0898 and 0892 respectively andthe relative error ranges between minus0289 and 0639
References
[1] K Gairaa and S Benkaciali ldquoAnalysis of solar radiation mea-surements in Ghardaia area south Algeriardquo Energy Procediavol 6 pp 122ndash129 2011
[2] J L Desouza R M Nicaciob and M A L Mouraa ldquoGlobalsolar radiation measurements in Maceio Brazilrdquo RenewableEnergy vol 30 pp 1203ndash1220 2009
ISRN Renewable Energy 11
[3] J P Duffie and W A Beckman Solar Engineering of ThermalProcess John Wiley amp Sons New York NY USA 1991
[4] M Iqbal An Introduction to Solar Radiation Academic PressToronto Canada 1983
[5] International Energy Agency (IEA) ldquoValidation of models forestimating solar radiation on horizontal surfacesrdquo Atmosphereamp Environment service Canada 1988
[6] J A Prescott ldquoEvaporation from a water surface in relation tosolar radiationrdquo Philosophical Transactions of the Royal Societyvol 64 pp 114ndash120 1990
[7] C C Y Ma and M Iqbal ldquoStatistical comparison of solar radi-ation correlations Monthly average global and diffuse radiationon horizontal surfacesrdquo Solar Energy vol 33 no 2 pp 143ndash1481984
[8] J Almorox and C Hontoria ldquoGlobal solar radiation estimationusing sunshine duration in Spainrdquo Energy Conversion andManagement vol 45 no 9-10 pp 1529ndash1535 2004
[9] I T Togrul H Togrul and D Evin ldquoEstimation of monthlyglobal solar radiation from sunshine duration measurement inElazigrdquo Renewable Energy vol 19 no 4 pp 587ndash595 2000
[10] I T Togrul and E Onat ldquoA comparison of estimated andmeasured values of solar radiation in Elazig TurkeyrdquoRenewableEnergy vol 20 no 2 pp 243ndash252 2000
[11] A K Katiyar A Kumar K P Chanchal and B Das ldquoAcomparative study of monthly mean daily clear sky radiationover Indiardquo International Journal of Energy and Environmentvol 1 pp 177ndash182 2010
[12] G Oturanc A Hepbasli and A Genc ldquoStatistical analysis forsolar radiation datardquo Energy Sources vol 25 no 11 pp 1089ndash1097 2003
[13] M Benghanem and A A Joraid ldquoA multiple correlationbetween different solar parameters in Medina Saudi ArabiardquoRenewable Energy vol 32 no 14 pp 2424ndash2435 2007
[14] D B Ampratwum and A S S Dorvlo ldquoEstimation of solarradiation from the number of sunshine hoursrdquo Applied Energyvol 63 no 3 pp 161ndash167 1999
[15] Z Sen ldquoAngstrom equation parameter estimation by unre-stricted methodrdquo Solar Energy vol 71 no 2 pp 95ndash107 2001
[16] B T Nguyen and T L Pryor ldquoThe relationship between globalsolar radiation and sunshine duration in Vietnamrdquo RenewableEnergy vol 11 no 1 pp 47ndash60 1997
[17] N A Elagib S H Alvi and M G Mansell ldquoCorrelationshipsbetween clearness index and relative sunshine duration forSudanrdquo Renewable Energy vol 17 no 4 pp 473ndash498 1999
[18] M Hussain L Rahman and M M Rahman ldquoTechnical notetechniques to obtain improved predictions of global radiationfrom sunshine durationrdquo Renewable Energy vol 18 no 2 pp263ndash275 1999
[19] M T Y Tadros ldquoUses of sunshine duration to estimate theglobal solar radiation over eight meteorological stations inEgyptrdquo Renewable Energy vol 21 no 2 pp 231ndash246 2000
[20] I T Togrul and E Onat ldquoStudy for estimating solar radiationin Elazig using geographical and meteorological datardquo EnergyConversion and Management vol 40 no 14 pp 1577ndash15841999
[21] R Chen K Ersi J Yang S Lu and W Zhao ldquoValidation offive global radiationmodels withmeasured daily data in ChinardquoEnergy Conversion andManagement vol 45 no 11-12 pp 1759ndash1769 2004
[22] C Ertekin and O Yaldiz ldquoComparison of some existing modelsfor estimating global solar radiation for Antalya (Turkey)rdquo
Energy Conversion and Management vol 41 no 4 pp 311ndash3302000
[23] J C Ododo J A Agbakwuru and F A Ogbu ldquoCorrelation ofsolar radiationwith cloud cover and relative sunshine durationrdquoEnergy Conversion and Management vol 37 no 10 pp 1555ndash1559 1996
[24] M Yorukoglu and A N Celik ldquoA critical review on the esti-mation of daily global solar radiation from sunshine durationrdquoEnergy Conversion andManagement vol 47 no 15-16 pp 2441ndash2450 2006
[25] Y Abdalla ldquoNew correlation of global solar radiation withmeteorological parameters for Bahrainrdquo International Journalof Solar Energy vol 16 pp 111ndash120 1994
[26] K K Gopinathan ldquoA new model for estimating total solarradiation in Dohardquo Energy Conversion andManagemen vol 28pp 6ndash72 1988
[27] 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
[28] R G Allen ldquoSelf-calibrating method for estimating solar radi-ation from air temperaturerdquo Journal of Hydrologic Engineeringvol 2 no 2 pp 56ndash67 1997
[29] G H Hargreaves and R G Allen ldquoHistory and evaluation ofhargreaves evapotranspiration equationrdquo Journal of Irrigationand Drainage Engineering vol 129 no 1 pp 53ndash63 2003
[30] Z Samani G H Hargreaves V Tran and S Bawazir ldquoEstimat-ing solar radiation from temperature with spatial and temporalcalibrationrdquo Journal of Irrigation and Drainage Engineering vol137 no 11 pp 692ndash696 2011
[31] J O Ojosu and L K Komolafe ldquoModels for estimating solarradiation availability in South Western Nigeriardquo Solar Energyvol 16 pp 69ndash77 1987
[32] G H Hargreaves and Z A Samani ldquoReference crop evapotran-spiration from temperaturerdquoTransactions of theASAE vol 1 pp96ndash99 1985
[33] J I Prieto J C Martınez-Garcıa and D Garcıa ldquoCorrela-tion between global solar irradiation and air temperature inAsturias Spainrdquo Solar Energy vol 83 no 7 pp 1076ndash1085 2009
[34] M Paulescu L Fara and E Tulcan-Paulescu ldquoModels forobtaining daily global solar irradiation from air temperaturedatardquo Atmospheric Research vol 79 no 3-4 pp 227ndash240 2006
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 ISRN Renewable Energy
0
02
04
06
08
1
0 02 04 06 08 1
January
SSSS0
HH
0
(a)
03 04 05 06 07 08 09 1
February
0
02
04
06
08
1
SSSS0
HH
0
(b)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
March
HH
0
(c)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
April
HH
0
(d)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
May
HH
0
(e)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
June
HH
0
(f)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
July
HH
0
(g)
August
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(h)
September
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(i)
Experimental dataLinear fit
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
October
HH
0
(j)
Experimental dataLinear fit
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
November
HH
0
(k)
December
Experimental dataLinear fit
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(l)
Figure 5 Scatter diagram of linear model
ISRN Renewable Energy 7
0
02
04
06
08
1
0 02 04 06 08 1
January
SSSS0
HH
0
(a)
February
0
02
04
06
08
1
SSSS0
0 02 04 06 08 1
HH
0
(b)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
March
HH
0
(c)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
April
HH
0
(d)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
May
HH
0
(e)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
June
HH
0
(f)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
July
HH
0
(g)
August
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(h)
September
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(i)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
Experimental dataQuadratic fit
October
HH
0
(j)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
Experimental dataQuadratic fit
November
HH
0
(k)
Experimental dataQuadratic fit
December
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(l)
Figure 6 Scatter diagram of quadratic model
8 ISRN Renewable Energy
0
02
04
06
08
1
0 02 04 06 08 1
January
SSSS0
HH
0
(a)
February
0
02
04
06
08
1
SSSS0
0 02 04 06 08 1
HH
0
(b)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
March
HH
0
(c)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
April
HH
0
(d)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
May
HH
0
(e)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
June
HH
0
(f)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
July
HH
0
(g)
August
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(h)
September
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(i)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
Experimental dataLogarithmic fit
October
HH
0
(j)
Experimental dataLogarithmic fit
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
November
HH
0
(k)
Experimental dataLogarithmic fit
December
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(l)
Figure 7 Scatter diagram of logarithmic model
ISRN Renewable Energy 9
0
02
04
06
08
1
0 02 04 06 08 1
January
SSSS0
HH
0
(a)
February
0
02
04
06
08
1
SSSS0
0 02 04 06 08 1
HH
0
(b)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
March
HH
0
(c)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
April
HH
0
(d)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
May
HH
0
(e)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
June
HH
0
(f)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
July
HH
0
(g)
August
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(h)
September
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(i)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
October
Experimental dataExponential fit
HH
0
(j)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
November
Experimental dataExponential fit
HH
0
(k)
Experimental dataExponential fit
December
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(l)
Figure 8 Scatter diagram of exponential model
10 ISRN Renewable Energy
Table 6 Comparison between measured and estimated monthly global solar radiation (Whm2)
Measured Linear 119890 () Quadratic 119890 () Logarithmic 119890 () Exponential 119890 ()January 3871 387975 minus0226 392454 minus1383 405448 minus474 381238 1514February 4842 476892 1509 474643 1974 522917 minus7996 469399 3057March 5926 583664 1508 586369 1051 617679 minus4232 573538 3217April 7339 734601 minus0096 739331 minus074 77792 minus5998 726109 1062May 7745 774506 minus0001 780996 minus0839 820351 minus592 761716 1651June 7812 782641 minus0184 793014 minus1512 823929 minus547 769928 1443July 7503 749263 0138 748443 0248 79856 minus6432 743793 0867August 7090 722491 minus1903 737784 minus406 757691 minus6868 719104 minus1425September 6036 602421 0195 605437 minus0304 63717 minus5562 589847 2278October 4824 482102 0062 486969 minus0947 512876 minus6318 473796 1784November 4030 402613 0096 39782 1285 422429 minus4821 396304 1662December 3437 342706 0289 362654 minus5515 372876 minus8489 334942 2548
Table 7 Annual validation of different models
119886 119887 119888 119889 CC RMSE MBELinear 0420 0363 0785 00453 minus00012Quadratic 0403 0446 minus00737 0787 00451 minus00007Logarithmic 0701 0106 0627 00792 00281Exponential 0264 0198 0763 00511 minus00182Abdalla 0519 0357 minus00018 minus000126 0898 00429 minus000059Ojosu et al 0449 0358 minus000445 minus000619 0892 00443 minus000068Hargreaves et al 0261 0115 0431 00883 minus000073
Table 8 Comparison between measured and estimated annualglobal solar radiation (Whm2)
Measured value Model Estimated values 119890 ()Linear 585245 0316
Quadratic 585743 0231Logarithmic 610862 minus4047
5871 Exponential 584795 0393Abdalla 584603 0425
Ojosu et al 583350 0639Hargreaves et al 588797 minus0289
models usually give the best performance if we take intoaccount the statistical test while for the model based on themeteorological parameters Abdalla and Ojosu et alrsquos modelsgive the best accuracy with a CC of 0898 and 0892 andRMSE of 00429 and 00443 while Hargreaves et alrsquos modelunderestimates the global solar radiation
The comparison between the estimated and measuredannual average values of the global solar radiation arepresented in Table 8 the annual percentage error is rangedbetween minus4047 and 0639 So it is clear that the linearquadratic models Abdalla and Ojosu are also the suitablemodels to estimate the annual global solar radiation on ahorizontal surface in Ghardaıa region
6 Conclusion
Several empirical models have been tested to estimate theglobal solar radiation on a horizontal surface using the
sunshine duration and the meteorological parameters Thegoal of this paper is the validation of seven models to predictthe monthly and the annual global solar radiation withina dataset of Ghardaia area and thus select the suitablemodel The models were compared on the basis of statisticaltests
Depending on the obtained results we can conclude thatthe linear and the quadratic models are the most accuratefor estimating the monthly global solar radiation on ahorizontal surface according to the statistical tests (CC 0956RMSE 0018 and MBE 4310minus5) the percentage error neverexceeds plusmn5 which indicate an excellent fitting between theglobal solar radiation and sunshine duration On the basisof annual estimation of global solar radiation and for themodels based on the sunshine duration always the linearand the quadratic models provide the best accuracy (CC0787 RMSE 00451 andMBE minus00007) whereas formodelsusing the meteorological parameters in addition to sunshineduration we found that Abdalla and Ojosursquos models are themost suitable with a CC of 0898 and 0892 respectively andthe relative error ranges between minus0289 and 0639
References
[1] K Gairaa and S Benkaciali ldquoAnalysis of solar radiation mea-surements in Ghardaia area south Algeriardquo Energy Procediavol 6 pp 122ndash129 2011
[2] J L Desouza R M Nicaciob and M A L Mouraa ldquoGlobalsolar radiation measurements in Maceio Brazilrdquo RenewableEnergy vol 30 pp 1203ndash1220 2009
ISRN Renewable Energy 11
[3] J P Duffie and W A Beckman Solar Engineering of ThermalProcess John Wiley amp Sons New York NY USA 1991
[4] M Iqbal An Introduction to Solar Radiation Academic PressToronto Canada 1983
[5] International Energy Agency (IEA) ldquoValidation of models forestimating solar radiation on horizontal surfacesrdquo Atmosphereamp Environment service Canada 1988
[6] J A Prescott ldquoEvaporation from a water surface in relation tosolar radiationrdquo Philosophical Transactions of the Royal Societyvol 64 pp 114ndash120 1990
[7] C C Y Ma and M Iqbal ldquoStatistical comparison of solar radi-ation correlations Monthly average global and diffuse radiationon horizontal surfacesrdquo Solar Energy vol 33 no 2 pp 143ndash1481984
[8] J Almorox and C Hontoria ldquoGlobal solar radiation estimationusing sunshine duration in Spainrdquo Energy Conversion andManagement vol 45 no 9-10 pp 1529ndash1535 2004
[9] I T Togrul H Togrul and D Evin ldquoEstimation of monthlyglobal solar radiation from sunshine duration measurement inElazigrdquo Renewable Energy vol 19 no 4 pp 587ndash595 2000
[10] I T Togrul and E Onat ldquoA comparison of estimated andmeasured values of solar radiation in Elazig TurkeyrdquoRenewableEnergy vol 20 no 2 pp 243ndash252 2000
[11] A K Katiyar A Kumar K P Chanchal and B Das ldquoAcomparative study of monthly mean daily clear sky radiationover Indiardquo International Journal of Energy and Environmentvol 1 pp 177ndash182 2010
[12] G Oturanc A Hepbasli and A Genc ldquoStatistical analysis forsolar radiation datardquo Energy Sources vol 25 no 11 pp 1089ndash1097 2003
[13] M Benghanem and A A Joraid ldquoA multiple correlationbetween different solar parameters in Medina Saudi ArabiardquoRenewable Energy vol 32 no 14 pp 2424ndash2435 2007
[14] D B Ampratwum and A S S Dorvlo ldquoEstimation of solarradiation from the number of sunshine hoursrdquo Applied Energyvol 63 no 3 pp 161ndash167 1999
[15] Z Sen ldquoAngstrom equation parameter estimation by unre-stricted methodrdquo Solar Energy vol 71 no 2 pp 95ndash107 2001
[16] B T Nguyen and T L Pryor ldquoThe relationship between globalsolar radiation and sunshine duration in Vietnamrdquo RenewableEnergy vol 11 no 1 pp 47ndash60 1997
[17] N A Elagib S H Alvi and M G Mansell ldquoCorrelationshipsbetween clearness index and relative sunshine duration forSudanrdquo Renewable Energy vol 17 no 4 pp 473ndash498 1999
[18] M Hussain L Rahman and M M Rahman ldquoTechnical notetechniques to obtain improved predictions of global radiationfrom sunshine durationrdquo Renewable Energy vol 18 no 2 pp263ndash275 1999
[19] M T Y Tadros ldquoUses of sunshine duration to estimate theglobal solar radiation over eight meteorological stations inEgyptrdquo Renewable Energy vol 21 no 2 pp 231ndash246 2000
[20] I T Togrul and E Onat ldquoStudy for estimating solar radiationin Elazig using geographical and meteorological datardquo EnergyConversion and Management vol 40 no 14 pp 1577ndash15841999
[21] R Chen K Ersi J Yang S Lu and W Zhao ldquoValidation offive global radiationmodels withmeasured daily data in ChinardquoEnergy Conversion andManagement vol 45 no 11-12 pp 1759ndash1769 2004
[22] C Ertekin and O Yaldiz ldquoComparison of some existing modelsfor estimating global solar radiation for Antalya (Turkey)rdquo
Energy Conversion and Management vol 41 no 4 pp 311ndash3302000
[23] J C Ododo J A Agbakwuru and F A Ogbu ldquoCorrelation ofsolar radiationwith cloud cover and relative sunshine durationrdquoEnergy Conversion and Management vol 37 no 10 pp 1555ndash1559 1996
[24] M Yorukoglu and A N Celik ldquoA critical review on the esti-mation of daily global solar radiation from sunshine durationrdquoEnergy Conversion andManagement vol 47 no 15-16 pp 2441ndash2450 2006
[25] Y Abdalla ldquoNew correlation of global solar radiation withmeteorological parameters for Bahrainrdquo International Journalof Solar Energy vol 16 pp 111ndash120 1994
[26] K K Gopinathan ldquoA new model for estimating total solarradiation in Dohardquo Energy Conversion andManagemen vol 28pp 6ndash72 1988
[27] 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
[28] R G Allen ldquoSelf-calibrating method for estimating solar radi-ation from air temperaturerdquo Journal of Hydrologic Engineeringvol 2 no 2 pp 56ndash67 1997
[29] G H Hargreaves and R G Allen ldquoHistory and evaluation ofhargreaves evapotranspiration equationrdquo Journal of Irrigationand Drainage Engineering vol 129 no 1 pp 53ndash63 2003
[30] Z Samani G H Hargreaves V Tran and S Bawazir ldquoEstimat-ing solar radiation from temperature with spatial and temporalcalibrationrdquo Journal of Irrigation and Drainage Engineering vol137 no 11 pp 692ndash696 2011
[31] J O Ojosu and L K Komolafe ldquoModels for estimating solarradiation availability in South Western Nigeriardquo Solar Energyvol 16 pp 69ndash77 1987
[32] G H Hargreaves and Z A Samani ldquoReference crop evapotran-spiration from temperaturerdquoTransactions of theASAE vol 1 pp96ndash99 1985
[33] J I Prieto J C Martınez-Garcıa and D Garcıa ldquoCorrela-tion between global solar irradiation and air temperature inAsturias Spainrdquo Solar Energy vol 83 no 7 pp 1076ndash1085 2009
[34] M Paulescu L Fara and E Tulcan-Paulescu ldquoModels forobtaining daily global solar irradiation from air temperaturedatardquo Atmospheric Research vol 79 no 3-4 pp 227ndash240 2006
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
ISRN Renewable Energy 7
0
02
04
06
08
1
0 02 04 06 08 1
January
SSSS0
HH
0
(a)
February
0
02
04
06
08
1
SSSS0
0 02 04 06 08 1
HH
0
(b)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
March
HH
0
(c)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
April
HH
0
(d)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
May
HH
0
(e)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
June
HH
0
(f)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
July
HH
0
(g)
August
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(h)
September
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(i)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
Experimental dataQuadratic fit
October
HH
0
(j)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
Experimental dataQuadratic fit
November
HH
0
(k)
Experimental dataQuadratic fit
December
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(l)
Figure 6 Scatter diagram of quadratic model
8 ISRN Renewable Energy
0
02
04
06
08
1
0 02 04 06 08 1
January
SSSS0
HH
0
(a)
February
0
02
04
06
08
1
SSSS0
0 02 04 06 08 1
HH
0
(b)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
March
HH
0
(c)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
April
HH
0
(d)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
May
HH
0
(e)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
June
HH
0
(f)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
July
HH
0
(g)
August
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(h)
September
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(i)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
Experimental dataLogarithmic fit
October
HH
0
(j)
Experimental dataLogarithmic fit
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
November
HH
0
(k)
Experimental dataLogarithmic fit
December
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(l)
Figure 7 Scatter diagram of logarithmic model
ISRN Renewable Energy 9
0
02
04
06
08
1
0 02 04 06 08 1
January
SSSS0
HH
0
(a)
February
0
02
04
06
08
1
SSSS0
0 02 04 06 08 1
HH
0
(b)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
March
HH
0
(c)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
April
HH
0
(d)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
May
HH
0
(e)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
June
HH
0
(f)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
July
HH
0
(g)
August
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(h)
September
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(i)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
October
Experimental dataExponential fit
HH
0
(j)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
November
Experimental dataExponential fit
HH
0
(k)
Experimental dataExponential fit
December
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(l)
Figure 8 Scatter diagram of exponential model
10 ISRN Renewable Energy
Table 6 Comparison between measured and estimated monthly global solar radiation (Whm2)
Measured Linear 119890 () Quadratic 119890 () Logarithmic 119890 () Exponential 119890 ()January 3871 387975 minus0226 392454 minus1383 405448 minus474 381238 1514February 4842 476892 1509 474643 1974 522917 minus7996 469399 3057March 5926 583664 1508 586369 1051 617679 minus4232 573538 3217April 7339 734601 minus0096 739331 minus074 77792 minus5998 726109 1062May 7745 774506 minus0001 780996 minus0839 820351 minus592 761716 1651June 7812 782641 minus0184 793014 minus1512 823929 minus547 769928 1443July 7503 749263 0138 748443 0248 79856 minus6432 743793 0867August 7090 722491 minus1903 737784 minus406 757691 minus6868 719104 minus1425September 6036 602421 0195 605437 minus0304 63717 minus5562 589847 2278October 4824 482102 0062 486969 minus0947 512876 minus6318 473796 1784November 4030 402613 0096 39782 1285 422429 minus4821 396304 1662December 3437 342706 0289 362654 minus5515 372876 minus8489 334942 2548
Table 7 Annual validation of different models
119886 119887 119888 119889 CC RMSE MBELinear 0420 0363 0785 00453 minus00012Quadratic 0403 0446 minus00737 0787 00451 minus00007Logarithmic 0701 0106 0627 00792 00281Exponential 0264 0198 0763 00511 minus00182Abdalla 0519 0357 minus00018 minus000126 0898 00429 minus000059Ojosu et al 0449 0358 minus000445 minus000619 0892 00443 minus000068Hargreaves et al 0261 0115 0431 00883 minus000073
Table 8 Comparison between measured and estimated annualglobal solar radiation (Whm2)
Measured value Model Estimated values 119890 ()Linear 585245 0316
Quadratic 585743 0231Logarithmic 610862 minus4047
5871 Exponential 584795 0393Abdalla 584603 0425
Ojosu et al 583350 0639Hargreaves et al 588797 minus0289
models usually give the best performance if we take intoaccount the statistical test while for the model based on themeteorological parameters Abdalla and Ojosu et alrsquos modelsgive the best accuracy with a CC of 0898 and 0892 andRMSE of 00429 and 00443 while Hargreaves et alrsquos modelunderestimates the global solar radiation
The comparison between the estimated and measuredannual average values of the global solar radiation arepresented in Table 8 the annual percentage error is rangedbetween minus4047 and 0639 So it is clear that the linearquadratic models Abdalla and Ojosu are also the suitablemodels to estimate the annual global solar radiation on ahorizontal surface in Ghardaıa region
6 Conclusion
Several empirical models have been tested to estimate theglobal solar radiation on a horizontal surface using the
sunshine duration and the meteorological parameters Thegoal of this paper is the validation of seven models to predictthe monthly and the annual global solar radiation withina dataset of Ghardaia area and thus select the suitablemodel The models were compared on the basis of statisticaltests
Depending on the obtained results we can conclude thatthe linear and the quadratic models are the most accuratefor estimating the monthly global solar radiation on ahorizontal surface according to the statistical tests (CC 0956RMSE 0018 and MBE 4310minus5) the percentage error neverexceeds plusmn5 which indicate an excellent fitting between theglobal solar radiation and sunshine duration On the basisof annual estimation of global solar radiation and for themodels based on the sunshine duration always the linearand the quadratic models provide the best accuracy (CC0787 RMSE 00451 andMBE minus00007) whereas formodelsusing the meteorological parameters in addition to sunshineduration we found that Abdalla and Ojosursquos models are themost suitable with a CC of 0898 and 0892 respectively andthe relative error ranges between minus0289 and 0639
References
[1] K Gairaa and S Benkaciali ldquoAnalysis of solar radiation mea-surements in Ghardaia area south Algeriardquo Energy Procediavol 6 pp 122ndash129 2011
[2] J L Desouza R M Nicaciob and M A L Mouraa ldquoGlobalsolar radiation measurements in Maceio Brazilrdquo RenewableEnergy vol 30 pp 1203ndash1220 2009
ISRN Renewable Energy 11
[3] J P Duffie and W A Beckman Solar Engineering of ThermalProcess John Wiley amp Sons New York NY USA 1991
[4] M Iqbal An Introduction to Solar Radiation Academic PressToronto Canada 1983
[5] International Energy Agency (IEA) ldquoValidation of models forestimating solar radiation on horizontal surfacesrdquo Atmosphereamp Environment service Canada 1988
[6] J A Prescott ldquoEvaporation from a water surface in relation tosolar radiationrdquo Philosophical Transactions of the Royal Societyvol 64 pp 114ndash120 1990
[7] C C Y Ma and M Iqbal ldquoStatistical comparison of solar radi-ation correlations Monthly average global and diffuse radiationon horizontal surfacesrdquo Solar Energy vol 33 no 2 pp 143ndash1481984
[8] J Almorox and C Hontoria ldquoGlobal solar radiation estimationusing sunshine duration in Spainrdquo Energy Conversion andManagement vol 45 no 9-10 pp 1529ndash1535 2004
[9] I T Togrul H Togrul and D Evin ldquoEstimation of monthlyglobal solar radiation from sunshine duration measurement inElazigrdquo Renewable Energy vol 19 no 4 pp 587ndash595 2000
[10] I T Togrul and E Onat ldquoA comparison of estimated andmeasured values of solar radiation in Elazig TurkeyrdquoRenewableEnergy vol 20 no 2 pp 243ndash252 2000
[11] A K Katiyar A Kumar K P Chanchal and B Das ldquoAcomparative study of monthly mean daily clear sky radiationover Indiardquo International Journal of Energy and Environmentvol 1 pp 177ndash182 2010
[12] G Oturanc A Hepbasli and A Genc ldquoStatistical analysis forsolar radiation datardquo Energy Sources vol 25 no 11 pp 1089ndash1097 2003
[13] M Benghanem and A A Joraid ldquoA multiple correlationbetween different solar parameters in Medina Saudi ArabiardquoRenewable Energy vol 32 no 14 pp 2424ndash2435 2007
[14] D B Ampratwum and A S S Dorvlo ldquoEstimation of solarradiation from the number of sunshine hoursrdquo Applied Energyvol 63 no 3 pp 161ndash167 1999
[15] Z Sen ldquoAngstrom equation parameter estimation by unre-stricted methodrdquo Solar Energy vol 71 no 2 pp 95ndash107 2001
[16] B T Nguyen and T L Pryor ldquoThe relationship between globalsolar radiation and sunshine duration in Vietnamrdquo RenewableEnergy vol 11 no 1 pp 47ndash60 1997
[17] N A Elagib S H Alvi and M G Mansell ldquoCorrelationshipsbetween clearness index and relative sunshine duration forSudanrdquo Renewable Energy vol 17 no 4 pp 473ndash498 1999
[18] M Hussain L Rahman and M M Rahman ldquoTechnical notetechniques to obtain improved predictions of global radiationfrom sunshine durationrdquo Renewable Energy vol 18 no 2 pp263ndash275 1999
[19] M T Y Tadros ldquoUses of sunshine duration to estimate theglobal solar radiation over eight meteorological stations inEgyptrdquo Renewable Energy vol 21 no 2 pp 231ndash246 2000
[20] I T Togrul and E Onat ldquoStudy for estimating solar radiationin Elazig using geographical and meteorological datardquo EnergyConversion and Management vol 40 no 14 pp 1577ndash15841999
[21] R Chen K Ersi J Yang S Lu and W Zhao ldquoValidation offive global radiationmodels withmeasured daily data in ChinardquoEnergy Conversion andManagement vol 45 no 11-12 pp 1759ndash1769 2004
[22] C Ertekin and O Yaldiz ldquoComparison of some existing modelsfor estimating global solar radiation for Antalya (Turkey)rdquo
Energy Conversion and Management vol 41 no 4 pp 311ndash3302000
[23] J C Ododo J A Agbakwuru and F A Ogbu ldquoCorrelation ofsolar radiationwith cloud cover and relative sunshine durationrdquoEnergy Conversion and Management vol 37 no 10 pp 1555ndash1559 1996
[24] M Yorukoglu and A N Celik ldquoA critical review on the esti-mation of daily global solar radiation from sunshine durationrdquoEnergy Conversion andManagement vol 47 no 15-16 pp 2441ndash2450 2006
[25] Y Abdalla ldquoNew correlation of global solar radiation withmeteorological parameters for Bahrainrdquo International Journalof Solar Energy vol 16 pp 111ndash120 1994
[26] K K Gopinathan ldquoA new model for estimating total solarradiation in Dohardquo Energy Conversion andManagemen vol 28pp 6ndash72 1988
[27] 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
[28] R G Allen ldquoSelf-calibrating method for estimating solar radi-ation from air temperaturerdquo Journal of Hydrologic Engineeringvol 2 no 2 pp 56ndash67 1997
[29] G H Hargreaves and R G Allen ldquoHistory and evaluation ofhargreaves evapotranspiration equationrdquo Journal of Irrigationand Drainage Engineering vol 129 no 1 pp 53ndash63 2003
[30] Z Samani G H Hargreaves V Tran and S Bawazir ldquoEstimat-ing solar radiation from temperature with spatial and temporalcalibrationrdquo Journal of Irrigation and Drainage Engineering vol137 no 11 pp 692ndash696 2011
[31] J O Ojosu and L K Komolafe ldquoModels for estimating solarradiation availability in South Western Nigeriardquo Solar Energyvol 16 pp 69ndash77 1987
[32] G H Hargreaves and Z A Samani ldquoReference crop evapotran-spiration from temperaturerdquoTransactions of theASAE vol 1 pp96ndash99 1985
[33] J I Prieto J C Martınez-Garcıa and D Garcıa ldquoCorrela-tion between global solar irradiation and air temperature inAsturias Spainrdquo Solar Energy vol 83 no 7 pp 1076ndash1085 2009
[34] M Paulescu L Fara and E Tulcan-Paulescu ldquoModels forobtaining daily global solar irradiation from air temperaturedatardquo Atmospheric Research vol 79 no 3-4 pp 227ndash240 2006
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 ISRN Renewable Energy
0
02
04
06
08
1
0 02 04 06 08 1
January
SSSS0
HH
0
(a)
February
0
02
04
06
08
1
SSSS0
0 02 04 06 08 1
HH
0
(b)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
March
HH
0
(c)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
April
HH
0
(d)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
May
HH
0
(e)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
June
HH
0
(f)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
July
HH
0
(g)
August
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(h)
September
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(i)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
Experimental dataLogarithmic fit
October
HH
0
(j)
Experimental dataLogarithmic fit
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
November
HH
0
(k)
Experimental dataLogarithmic fit
December
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(l)
Figure 7 Scatter diagram of logarithmic model
ISRN Renewable Energy 9
0
02
04
06
08
1
0 02 04 06 08 1
January
SSSS0
HH
0
(a)
February
0
02
04
06
08
1
SSSS0
0 02 04 06 08 1
HH
0
(b)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
March
HH
0
(c)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
April
HH
0
(d)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
May
HH
0
(e)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
June
HH
0
(f)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
July
HH
0
(g)
August
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(h)
September
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(i)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
October
Experimental dataExponential fit
HH
0
(j)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
November
Experimental dataExponential fit
HH
0
(k)
Experimental dataExponential fit
December
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(l)
Figure 8 Scatter diagram of exponential model
10 ISRN Renewable Energy
Table 6 Comparison between measured and estimated monthly global solar radiation (Whm2)
Measured Linear 119890 () Quadratic 119890 () Logarithmic 119890 () Exponential 119890 ()January 3871 387975 minus0226 392454 minus1383 405448 minus474 381238 1514February 4842 476892 1509 474643 1974 522917 minus7996 469399 3057March 5926 583664 1508 586369 1051 617679 minus4232 573538 3217April 7339 734601 minus0096 739331 minus074 77792 minus5998 726109 1062May 7745 774506 minus0001 780996 minus0839 820351 minus592 761716 1651June 7812 782641 minus0184 793014 minus1512 823929 minus547 769928 1443July 7503 749263 0138 748443 0248 79856 minus6432 743793 0867August 7090 722491 minus1903 737784 minus406 757691 minus6868 719104 minus1425September 6036 602421 0195 605437 minus0304 63717 minus5562 589847 2278October 4824 482102 0062 486969 minus0947 512876 minus6318 473796 1784November 4030 402613 0096 39782 1285 422429 minus4821 396304 1662December 3437 342706 0289 362654 minus5515 372876 minus8489 334942 2548
Table 7 Annual validation of different models
119886 119887 119888 119889 CC RMSE MBELinear 0420 0363 0785 00453 minus00012Quadratic 0403 0446 minus00737 0787 00451 minus00007Logarithmic 0701 0106 0627 00792 00281Exponential 0264 0198 0763 00511 minus00182Abdalla 0519 0357 minus00018 minus000126 0898 00429 minus000059Ojosu et al 0449 0358 minus000445 minus000619 0892 00443 minus000068Hargreaves et al 0261 0115 0431 00883 minus000073
Table 8 Comparison between measured and estimated annualglobal solar radiation (Whm2)
Measured value Model Estimated values 119890 ()Linear 585245 0316
Quadratic 585743 0231Logarithmic 610862 minus4047
5871 Exponential 584795 0393Abdalla 584603 0425
Ojosu et al 583350 0639Hargreaves et al 588797 minus0289
models usually give the best performance if we take intoaccount the statistical test while for the model based on themeteorological parameters Abdalla and Ojosu et alrsquos modelsgive the best accuracy with a CC of 0898 and 0892 andRMSE of 00429 and 00443 while Hargreaves et alrsquos modelunderestimates the global solar radiation
The comparison between the estimated and measuredannual average values of the global solar radiation arepresented in Table 8 the annual percentage error is rangedbetween minus4047 and 0639 So it is clear that the linearquadratic models Abdalla and Ojosu are also the suitablemodels to estimate the annual global solar radiation on ahorizontal surface in Ghardaıa region
6 Conclusion
Several empirical models have been tested to estimate theglobal solar radiation on a horizontal surface using the
sunshine duration and the meteorological parameters Thegoal of this paper is the validation of seven models to predictthe monthly and the annual global solar radiation withina dataset of Ghardaia area and thus select the suitablemodel The models were compared on the basis of statisticaltests
Depending on the obtained results we can conclude thatthe linear and the quadratic models are the most accuratefor estimating the monthly global solar radiation on ahorizontal surface according to the statistical tests (CC 0956RMSE 0018 and MBE 4310minus5) the percentage error neverexceeds plusmn5 which indicate an excellent fitting between theglobal solar radiation and sunshine duration On the basisof annual estimation of global solar radiation and for themodels based on the sunshine duration always the linearand the quadratic models provide the best accuracy (CC0787 RMSE 00451 andMBE minus00007) whereas formodelsusing the meteorological parameters in addition to sunshineduration we found that Abdalla and Ojosursquos models are themost suitable with a CC of 0898 and 0892 respectively andthe relative error ranges between minus0289 and 0639
References
[1] K Gairaa and S Benkaciali ldquoAnalysis of solar radiation mea-surements in Ghardaia area south Algeriardquo Energy Procediavol 6 pp 122ndash129 2011
[2] J L Desouza R M Nicaciob and M A L Mouraa ldquoGlobalsolar radiation measurements in Maceio Brazilrdquo RenewableEnergy vol 30 pp 1203ndash1220 2009
ISRN Renewable Energy 11
[3] J P Duffie and W A Beckman Solar Engineering of ThermalProcess John Wiley amp Sons New York NY USA 1991
[4] M Iqbal An Introduction to Solar Radiation Academic PressToronto Canada 1983
[5] International Energy Agency (IEA) ldquoValidation of models forestimating solar radiation on horizontal surfacesrdquo Atmosphereamp Environment service Canada 1988
[6] J A Prescott ldquoEvaporation from a water surface in relation tosolar radiationrdquo Philosophical Transactions of the Royal Societyvol 64 pp 114ndash120 1990
[7] C C Y Ma and M Iqbal ldquoStatistical comparison of solar radi-ation correlations Monthly average global and diffuse radiationon horizontal surfacesrdquo Solar Energy vol 33 no 2 pp 143ndash1481984
[8] J Almorox and C Hontoria ldquoGlobal solar radiation estimationusing sunshine duration in Spainrdquo Energy Conversion andManagement vol 45 no 9-10 pp 1529ndash1535 2004
[9] I T Togrul H Togrul and D Evin ldquoEstimation of monthlyglobal solar radiation from sunshine duration measurement inElazigrdquo Renewable Energy vol 19 no 4 pp 587ndash595 2000
[10] I T Togrul and E Onat ldquoA comparison of estimated andmeasured values of solar radiation in Elazig TurkeyrdquoRenewableEnergy vol 20 no 2 pp 243ndash252 2000
[11] A K Katiyar A Kumar K P Chanchal and B Das ldquoAcomparative study of monthly mean daily clear sky radiationover Indiardquo International Journal of Energy and Environmentvol 1 pp 177ndash182 2010
[12] G Oturanc A Hepbasli and A Genc ldquoStatistical analysis forsolar radiation datardquo Energy Sources vol 25 no 11 pp 1089ndash1097 2003
[13] M Benghanem and A A Joraid ldquoA multiple correlationbetween different solar parameters in Medina Saudi ArabiardquoRenewable Energy vol 32 no 14 pp 2424ndash2435 2007
[14] D B Ampratwum and A S S Dorvlo ldquoEstimation of solarradiation from the number of sunshine hoursrdquo Applied Energyvol 63 no 3 pp 161ndash167 1999
[15] Z Sen ldquoAngstrom equation parameter estimation by unre-stricted methodrdquo Solar Energy vol 71 no 2 pp 95ndash107 2001
[16] B T Nguyen and T L Pryor ldquoThe relationship between globalsolar radiation and sunshine duration in Vietnamrdquo RenewableEnergy vol 11 no 1 pp 47ndash60 1997
[17] N A Elagib S H Alvi and M G Mansell ldquoCorrelationshipsbetween clearness index and relative sunshine duration forSudanrdquo Renewable Energy vol 17 no 4 pp 473ndash498 1999
[18] M Hussain L Rahman and M M Rahman ldquoTechnical notetechniques to obtain improved predictions of global radiationfrom sunshine durationrdquo Renewable Energy vol 18 no 2 pp263ndash275 1999
[19] M T Y Tadros ldquoUses of sunshine duration to estimate theglobal solar radiation over eight meteorological stations inEgyptrdquo Renewable Energy vol 21 no 2 pp 231ndash246 2000
[20] I T Togrul and E Onat ldquoStudy for estimating solar radiationin Elazig using geographical and meteorological datardquo EnergyConversion and Management vol 40 no 14 pp 1577ndash15841999
[21] R Chen K Ersi J Yang S Lu and W Zhao ldquoValidation offive global radiationmodels withmeasured daily data in ChinardquoEnergy Conversion andManagement vol 45 no 11-12 pp 1759ndash1769 2004
[22] C Ertekin and O Yaldiz ldquoComparison of some existing modelsfor estimating global solar radiation for Antalya (Turkey)rdquo
Energy Conversion and Management vol 41 no 4 pp 311ndash3302000
[23] J C Ododo J A Agbakwuru and F A Ogbu ldquoCorrelation ofsolar radiationwith cloud cover and relative sunshine durationrdquoEnergy Conversion and Management vol 37 no 10 pp 1555ndash1559 1996
[24] M Yorukoglu and A N Celik ldquoA critical review on the esti-mation of daily global solar radiation from sunshine durationrdquoEnergy Conversion andManagement vol 47 no 15-16 pp 2441ndash2450 2006
[25] Y Abdalla ldquoNew correlation of global solar radiation withmeteorological parameters for Bahrainrdquo International Journalof Solar Energy vol 16 pp 111ndash120 1994
[26] K K Gopinathan ldquoA new model for estimating total solarradiation in Dohardquo Energy Conversion andManagemen vol 28pp 6ndash72 1988
[27] 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
[28] R G Allen ldquoSelf-calibrating method for estimating solar radi-ation from air temperaturerdquo Journal of Hydrologic Engineeringvol 2 no 2 pp 56ndash67 1997
[29] G H Hargreaves and R G Allen ldquoHistory and evaluation ofhargreaves evapotranspiration equationrdquo Journal of Irrigationand Drainage Engineering vol 129 no 1 pp 53ndash63 2003
[30] Z Samani G H Hargreaves V Tran and S Bawazir ldquoEstimat-ing solar radiation from temperature with spatial and temporalcalibrationrdquo Journal of Irrigation and Drainage Engineering vol137 no 11 pp 692ndash696 2011
[31] J O Ojosu and L K Komolafe ldquoModels for estimating solarradiation availability in South Western Nigeriardquo Solar Energyvol 16 pp 69ndash77 1987
[32] G H Hargreaves and Z A Samani ldquoReference crop evapotran-spiration from temperaturerdquoTransactions of theASAE vol 1 pp96ndash99 1985
[33] J I Prieto J C Martınez-Garcıa and D Garcıa ldquoCorrela-tion between global solar irradiation and air temperature inAsturias Spainrdquo Solar Energy vol 83 no 7 pp 1076ndash1085 2009
[34] M Paulescu L Fara and E Tulcan-Paulescu ldquoModels forobtaining daily global solar irradiation from air temperaturedatardquo Atmospheric Research vol 79 no 3-4 pp 227ndash240 2006
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
ISRN Renewable Energy 9
0
02
04
06
08
1
0 02 04 06 08 1
January
SSSS0
HH
0
(a)
February
0
02
04
06
08
1
SSSS0
0 02 04 06 08 1
HH
0
(b)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
March
HH
0
(c)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
April
HH
0
(d)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
May
HH
0
(e)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
June
HH
0
(f)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
July
HH
0
(g)
August
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(h)
September
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(i)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
October
Experimental dataExponential fit
HH
0
(j)
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
November
Experimental dataExponential fit
HH
0
(k)
Experimental dataExponential fit
December
0
02
04
06
08
1
0 02 04 06 08 1SSSS0
HH
0
(l)
Figure 8 Scatter diagram of exponential model
10 ISRN Renewable Energy
Table 6 Comparison between measured and estimated monthly global solar radiation (Whm2)
Measured Linear 119890 () Quadratic 119890 () Logarithmic 119890 () Exponential 119890 ()January 3871 387975 minus0226 392454 minus1383 405448 minus474 381238 1514February 4842 476892 1509 474643 1974 522917 minus7996 469399 3057March 5926 583664 1508 586369 1051 617679 minus4232 573538 3217April 7339 734601 minus0096 739331 minus074 77792 minus5998 726109 1062May 7745 774506 minus0001 780996 minus0839 820351 minus592 761716 1651June 7812 782641 minus0184 793014 minus1512 823929 minus547 769928 1443July 7503 749263 0138 748443 0248 79856 minus6432 743793 0867August 7090 722491 minus1903 737784 minus406 757691 minus6868 719104 minus1425September 6036 602421 0195 605437 minus0304 63717 minus5562 589847 2278October 4824 482102 0062 486969 minus0947 512876 minus6318 473796 1784November 4030 402613 0096 39782 1285 422429 minus4821 396304 1662December 3437 342706 0289 362654 minus5515 372876 minus8489 334942 2548
Table 7 Annual validation of different models
119886 119887 119888 119889 CC RMSE MBELinear 0420 0363 0785 00453 minus00012Quadratic 0403 0446 minus00737 0787 00451 minus00007Logarithmic 0701 0106 0627 00792 00281Exponential 0264 0198 0763 00511 minus00182Abdalla 0519 0357 minus00018 minus000126 0898 00429 minus000059Ojosu et al 0449 0358 minus000445 minus000619 0892 00443 minus000068Hargreaves et al 0261 0115 0431 00883 minus000073
Table 8 Comparison between measured and estimated annualglobal solar radiation (Whm2)
Measured value Model Estimated values 119890 ()Linear 585245 0316
Quadratic 585743 0231Logarithmic 610862 minus4047
5871 Exponential 584795 0393Abdalla 584603 0425
Ojosu et al 583350 0639Hargreaves et al 588797 minus0289
models usually give the best performance if we take intoaccount the statistical test while for the model based on themeteorological parameters Abdalla and Ojosu et alrsquos modelsgive the best accuracy with a CC of 0898 and 0892 andRMSE of 00429 and 00443 while Hargreaves et alrsquos modelunderestimates the global solar radiation
The comparison between the estimated and measuredannual average values of the global solar radiation arepresented in Table 8 the annual percentage error is rangedbetween minus4047 and 0639 So it is clear that the linearquadratic models Abdalla and Ojosu are also the suitablemodels to estimate the annual global solar radiation on ahorizontal surface in Ghardaıa region
6 Conclusion
Several empirical models have been tested to estimate theglobal solar radiation on a horizontal surface using the
sunshine duration and the meteorological parameters Thegoal of this paper is the validation of seven models to predictthe monthly and the annual global solar radiation withina dataset of Ghardaia area and thus select the suitablemodel The models were compared on the basis of statisticaltests
Depending on the obtained results we can conclude thatthe linear and the quadratic models are the most accuratefor estimating the monthly global solar radiation on ahorizontal surface according to the statistical tests (CC 0956RMSE 0018 and MBE 4310minus5) the percentage error neverexceeds plusmn5 which indicate an excellent fitting between theglobal solar radiation and sunshine duration On the basisof annual estimation of global solar radiation and for themodels based on the sunshine duration always the linearand the quadratic models provide the best accuracy (CC0787 RMSE 00451 andMBE minus00007) whereas formodelsusing the meteorological parameters in addition to sunshineduration we found that Abdalla and Ojosursquos models are themost suitable with a CC of 0898 and 0892 respectively andthe relative error ranges between minus0289 and 0639
References
[1] K Gairaa and S Benkaciali ldquoAnalysis of solar radiation mea-surements in Ghardaia area south Algeriardquo Energy Procediavol 6 pp 122ndash129 2011
[2] J L Desouza R M Nicaciob and M A L Mouraa ldquoGlobalsolar radiation measurements in Maceio Brazilrdquo RenewableEnergy vol 30 pp 1203ndash1220 2009
ISRN Renewable Energy 11
[3] J P Duffie and W A Beckman Solar Engineering of ThermalProcess John Wiley amp Sons New York NY USA 1991
[4] M Iqbal An Introduction to Solar Radiation Academic PressToronto Canada 1983
[5] International Energy Agency (IEA) ldquoValidation of models forestimating solar radiation on horizontal surfacesrdquo Atmosphereamp Environment service Canada 1988
[6] J A Prescott ldquoEvaporation from a water surface in relation tosolar radiationrdquo Philosophical Transactions of the Royal Societyvol 64 pp 114ndash120 1990
[7] C C Y Ma and M Iqbal ldquoStatistical comparison of solar radi-ation correlations Monthly average global and diffuse radiationon horizontal surfacesrdquo Solar Energy vol 33 no 2 pp 143ndash1481984
[8] J Almorox and C Hontoria ldquoGlobal solar radiation estimationusing sunshine duration in Spainrdquo Energy Conversion andManagement vol 45 no 9-10 pp 1529ndash1535 2004
[9] I T Togrul H Togrul and D Evin ldquoEstimation of monthlyglobal solar radiation from sunshine duration measurement inElazigrdquo Renewable Energy vol 19 no 4 pp 587ndash595 2000
[10] I T Togrul and E Onat ldquoA comparison of estimated andmeasured values of solar radiation in Elazig TurkeyrdquoRenewableEnergy vol 20 no 2 pp 243ndash252 2000
[11] A K Katiyar A Kumar K P Chanchal and B Das ldquoAcomparative study of monthly mean daily clear sky radiationover Indiardquo International Journal of Energy and Environmentvol 1 pp 177ndash182 2010
[12] G Oturanc A Hepbasli and A Genc ldquoStatistical analysis forsolar radiation datardquo Energy Sources vol 25 no 11 pp 1089ndash1097 2003
[13] M Benghanem and A A Joraid ldquoA multiple correlationbetween different solar parameters in Medina Saudi ArabiardquoRenewable Energy vol 32 no 14 pp 2424ndash2435 2007
[14] D B Ampratwum and A S S Dorvlo ldquoEstimation of solarradiation from the number of sunshine hoursrdquo Applied Energyvol 63 no 3 pp 161ndash167 1999
[15] Z Sen ldquoAngstrom equation parameter estimation by unre-stricted methodrdquo Solar Energy vol 71 no 2 pp 95ndash107 2001
[16] B T Nguyen and T L Pryor ldquoThe relationship between globalsolar radiation and sunshine duration in Vietnamrdquo RenewableEnergy vol 11 no 1 pp 47ndash60 1997
[17] N A Elagib S H Alvi and M G Mansell ldquoCorrelationshipsbetween clearness index and relative sunshine duration forSudanrdquo Renewable Energy vol 17 no 4 pp 473ndash498 1999
[18] M Hussain L Rahman and M M Rahman ldquoTechnical notetechniques to obtain improved predictions of global radiationfrom sunshine durationrdquo Renewable Energy vol 18 no 2 pp263ndash275 1999
[19] M T Y Tadros ldquoUses of sunshine duration to estimate theglobal solar radiation over eight meteorological stations inEgyptrdquo Renewable Energy vol 21 no 2 pp 231ndash246 2000
[20] I T Togrul and E Onat ldquoStudy for estimating solar radiationin Elazig using geographical and meteorological datardquo EnergyConversion and Management vol 40 no 14 pp 1577ndash15841999
[21] R Chen K Ersi J Yang S Lu and W Zhao ldquoValidation offive global radiationmodels withmeasured daily data in ChinardquoEnergy Conversion andManagement vol 45 no 11-12 pp 1759ndash1769 2004
[22] C Ertekin and O Yaldiz ldquoComparison of some existing modelsfor estimating global solar radiation for Antalya (Turkey)rdquo
Energy Conversion and Management vol 41 no 4 pp 311ndash3302000
[23] J C Ododo J A Agbakwuru and F A Ogbu ldquoCorrelation ofsolar radiationwith cloud cover and relative sunshine durationrdquoEnergy Conversion and Management vol 37 no 10 pp 1555ndash1559 1996
[24] M Yorukoglu and A N Celik ldquoA critical review on the esti-mation of daily global solar radiation from sunshine durationrdquoEnergy Conversion andManagement vol 47 no 15-16 pp 2441ndash2450 2006
[25] Y Abdalla ldquoNew correlation of global solar radiation withmeteorological parameters for Bahrainrdquo International Journalof Solar Energy vol 16 pp 111ndash120 1994
[26] K K Gopinathan ldquoA new model for estimating total solarradiation in Dohardquo Energy Conversion andManagemen vol 28pp 6ndash72 1988
[27] 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
[28] R G Allen ldquoSelf-calibrating method for estimating solar radi-ation from air temperaturerdquo Journal of Hydrologic Engineeringvol 2 no 2 pp 56ndash67 1997
[29] G H Hargreaves and R G Allen ldquoHistory and evaluation ofhargreaves evapotranspiration equationrdquo Journal of Irrigationand Drainage Engineering vol 129 no 1 pp 53ndash63 2003
[30] Z Samani G H Hargreaves V Tran and S Bawazir ldquoEstimat-ing solar radiation from temperature with spatial and temporalcalibrationrdquo Journal of Irrigation and Drainage Engineering vol137 no 11 pp 692ndash696 2011
[31] J O Ojosu and L K Komolafe ldquoModels for estimating solarradiation availability in South Western Nigeriardquo Solar Energyvol 16 pp 69ndash77 1987
[32] G H Hargreaves and Z A Samani ldquoReference crop evapotran-spiration from temperaturerdquoTransactions of theASAE vol 1 pp96ndash99 1985
[33] J I Prieto J C Martınez-Garcıa and D Garcıa ldquoCorrela-tion between global solar irradiation and air temperature inAsturias Spainrdquo Solar Energy vol 83 no 7 pp 1076ndash1085 2009
[34] M Paulescu L Fara and E Tulcan-Paulescu ldquoModels forobtaining daily global solar irradiation from air temperaturedatardquo Atmospheric Research vol 79 no 3-4 pp 227ndash240 2006
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
10 ISRN Renewable Energy
Table 6 Comparison between measured and estimated monthly global solar radiation (Whm2)
Measured Linear 119890 () Quadratic 119890 () Logarithmic 119890 () Exponential 119890 ()January 3871 387975 minus0226 392454 minus1383 405448 minus474 381238 1514February 4842 476892 1509 474643 1974 522917 minus7996 469399 3057March 5926 583664 1508 586369 1051 617679 minus4232 573538 3217April 7339 734601 minus0096 739331 minus074 77792 minus5998 726109 1062May 7745 774506 minus0001 780996 minus0839 820351 minus592 761716 1651June 7812 782641 minus0184 793014 minus1512 823929 minus547 769928 1443July 7503 749263 0138 748443 0248 79856 minus6432 743793 0867August 7090 722491 minus1903 737784 minus406 757691 minus6868 719104 minus1425September 6036 602421 0195 605437 minus0304 63717 minus5562 589847 2278October 4824 482102 0062 486969 minus0947 512876 minus6318 473796 1784November 4030 402613 0096 39782 1285 422429 minus4821 396304 1662December 3437 342706 0289 362654 minus5515 372876 minus8489 334942 2548
Table 7 Annual validation of different models
119886 119887 119888 119889 CC RMSE MBELinear 0420 0363 0785 00453 minus00012Quadratic 0403 0446 minus00737 0787 00451 minus00007Logarithmic 0701 0106 0627 00792 00281Exponential 0264 0198 0763 00511 minus00182Abdalla 0519 0357 minus00018 minus000126 0898 00429 minus000059Ojosu et al 0449 0358 minus000445 minus000619 0892 00443 minus000068Hargreaves et al 0261 0115 0431 00883 minus000073
Table 8 Comparison between measured and estimated annualglobal solar radiation (Whm2)
Measured value Model Estimated values 119890 ()Linear 585245 0316
Quadratic 585743 0231Logarithmic 610862 minus4047
5871 Exponential 584795 0393Abdalla 584603 0425
Ojosu et al 583350 0639Hargreaves et al 588797 minus0289
models usually give the best performance if we take intoaccount the statistical test while for the model based on themeteorological parameters Abdalla and Ojosu et alrsquos modelsgive the best accuracy with a CC of 0898 and 0892 andRMSE of 00429 and 00443 while Hargreaves et alrsquos modelunderestimates the global solar radiation
The comparison between the estimated and measuredannual average values of the global solar radiation arepresented in Table 8 the annual percentage error is rangedbetween minus4047 and 0639 So it is clear that the linearquadratic models Abdalla and Ojosu are also the suitablemodels to estimate the annual global solar radiation on ahorizontal surface in Ghardaıa region
6 Conclusion
Several empirical models have been tested to estimate theglobal solar radiation on a horizontal surface using the
sunshine duration and the meteorological parameters Thegoal of this paper is the validation of seven models to predictthe monthly and the annual global solar radiation withina dataset of Ghardaia area and thus select the suitablemodel The models were compared on the basis of statisticaltests
Depending on the obtained results we can conclude thatthe linear and the quadratic models are the most accuratefor estimating the monthly global solar radiation on ahorizontal surface according to the statistical tests (CC 0956RMSE 0018 and MBE 4310minus5) the percentage error neverexceeds plusmn5 which indicate an excellent fitting between theglobal solar radiation and sunshine duration On the basisof annual estimation of global solar radiation and for themodels based on the sunshine duration always the linearand the quadratic models provide the best accuracy (CC0787 RMSE 00451 andMBE minus00007) whereas formodelsusing the meteorological parameters in addition to sunshineduration we found that Abdalla and Ojosursquos models are themost suitable with a CC of 0898 and 0892 respectively andthe relative error ranges between minus0289 and 0639
References
[1] K Gairaa and S Benkaciali ldquoAnalysis of solar radiation mea-surements in Ghardaia area south Algeriardquo Energy Procediavol 6 pp 122ndash129 2011
[2] J L Desouza R M Nicaciob and M A L Mouraa ldquoGlobalsolar radiation measurements in Maceio Brazilrdquo RenewableEnergy vol 30 pp 1203ndash1220 2009
ISRN Renewable Energy 11
[3] J P Duffie and W A Beckman Solar Engineering of ThermalProcess John Wiley amp Sons New York NY USA 1991
[4] M Iqbal An Introduction to Solar Radiation Academic PressToronto Canada 1983
[5] International Energy Agency (IEA) ldquoValidation of models forestimating solar radiation on horizontal surfacesrdquo Atmosphereamp Environment service Canada 1988
[6] J A Prescott ldquoEvaporation from a water surface in relation tosolar radiationrdquo Philosophical Transactions of the Royal Societyvol 64 pp 114ndash120 1990
[7] C C Y Ma and M Iqbal ldquoStatistical comparison of solar radi-ation correlations Monthly average global and diffuse radiationon horizontal surfacesrdquo Solar Energy vol 33 no 2 pp 143ndash1481984
[8] J Almorox and C Hontoria ldquoGlobal solar radiation estimationusing sunshine duration in Spainrdquo Energy Conversion andManagement vol 45 no 9-10 pp 1529ndash1535 2004
[9] I T Togrul H Togrul and D Evin ldquoEstimation of monthlyglobal solar radiation from sunshine duration measurement inElazigrdquo Renewable Energy vol 19 no 4 pp 587ndash595 2000
[10] I T Togrul and E Onat ldquoA comparison of estimated andmeasured values of solar radiation in Elazig TurkeyrdquoRenewableEnergy vol 20 no 2 pp 243ndash252 2000
[11] A K Katiyar A Kumar K P Chanchal and B Das ldquoAcomparative study of monthly mean daily clear sky radiationover Indiardquo International Journal of Energy and Environmentvol 1 pp 177ndash182 2010
[12] G Oturanc A Hepbasli and A Genc ldquoStatistical analysis forsolar radiation datardquo Energy Sources vol 25 no 11 pp 1089ndash1097 2003
[13] M Benghanem and A A Joraid ldquoA multiple correlationbetween different solar parameters in Medina Saudi ArabiardquoRenewable Energy vol 32 no 14 pp 2424ndash2435 2007
[14] D B Ampratwum and A S S Dorvlo ldquoEstimation of solarradiation from the number of sunshine hoursrdquo Applied Energyvol 63 no 3 pp 161ndash167 1999
[15] Z Sen ldquoAngstrom equation parameter estimation by unre-stricted methodrdquo Solar Energy vol 71 no 2 pp 95ndash107 2001
[16] B T Nguyen and T L Pryor ldquoThe relationship between globalsolar radiation and sunshine duration in Vietnamrdquo RenewableEnergy vol 11 no 1 pp 47ndash60 1997
[17] N A Elagib S H Alvi and M G Mansell ldquoCorrelationshipsbetween clearness index and relative sunshine duration forSudanrdquo Renewable Energy vol 17 no 4 pp 473ndash498 1999
[18] M Hussain L Rahman and M M Rahman ldquoTechnical notetechniques to obtain improved predictions of global radiationfrom sunshine durationrdquo Renewable Energy vol 18 no 2 pp263ndash275 1999
[19] M T Y Tadros ldquoUses of sunshine duration to estimate theglobal solar radiation over eight meteorological stations inEgyptrdquo Renewable Energy vol 21 no 2 pp 231ndash246 2000
[20] I T Togrul and E Onat ldquoStudy for estimating solar radiationin Elazig using geographical and meteorological datardquo EnergyConversion and Management vol 40 no 14 pp 1577ndash15841999
[21] R Chen K Ersi J Yang S Lu and W Zhao ldquoValidation offive global radiationmodels withmeasured daily data in ChinardquoEnergy Conversion andManagement vol 45 no 11-12 pp 1759ndash1769 2004
[22] C Ertekin and O Yaldiz ldquoComparison of some existing modelsfor estimating global solar radiation for Antalya (Turkey)rdquo
Energy Conversion and Management vol 41 no 4 pp 311ndash3302000
[23] J C Ododo J A Agbakwuru and F A Ogbu ldquoCorrelation ofsolar radiationwith cloud cover and relative sunshine durationrdquoEnergy Conversion and Management vol 37 no 10 pp 1555ndash1559 1996
[24] M Yorukoglu and A N Celik ldquoA critical review on the esti-mation of daily global solar radiation from sunshine durationrdquoEnergy Conversion andManagement vol 47 no 15-16 pp 2441ndash2450 2006
[25] Y Abdalla ldquoNew correlation of global solar radiation withmeteorological parameters for Bahrainrdquo International Journalof Solar Energy vol 16 pp 111ndash120 1994
[26] K K Gopinathan ldquoA new model for estimating total solarradiation in Dohardquo Energy Conversion andManagemen vol 28pp 6ndash72 1988
[27] 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
[28] R G Allen ldquoSelf-calibrating method for estimating solar radi-ation from air temperaturerdquo Journal of Hydrologic Engineeringvol 2 no 2 pp 56ndash67 1997
[29] G H Hargreaves and R G Allen ldquoHistory and evaluation ofhargreaves evapotranspiration equationrdquo Journal of Irrigationand Drainage Engineering vol 129 no 1 pp 53ndash63 2003
[30] Z Samani G H Hargreaves V Tran and S Bawazir ldquoEstimat-ing solar radiation from temperature with spatial and temporalcalibrationrdquo Journal of Irrigation and Drainage Engineering vol137 no 11 pp 692ndash696 2011
[31] J O Ojosu and L K Komolafe ldquoModels for estimating solarradiation availability in South Western Nigeriardquo Solar Energyvol 16 pp 69ndash77 1987
[32] G H Hargreaves and Z A Samani ldquoReference crop evapotran-spiration from temperaturerdquoTransactions of theASAE vol 1 pp96ndash99 1985
[33] J I Prieto J C Martınez-Garcıa and D Garcıa ldquoCorrela-tion between global solar irradiation and air temperature inAsturias Spainrdquo Solar Energy vol 83 no 7 pp 1076ndash1085 2009
[34] M Paulescu L Fara and E Tulcan-Paulescu ldquoModels forobtaining daily global solar irradiation from air temperaturedatardquo Atmospheric Research vol 79 no 3-4 pp 227ndash240 2006
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
ISRN Renewable Energy 11
[3] J P Duffie and W A Beckman Solar Engineering of ThermalProcess John Wiley amp Sons New York NY USA 1991
[4] M Iqbal An Introduction to Solar Radiation Academic PressToronto Canada 1983
[5] International Energy Agency (IEA) ldquoValidation of models forestimating solar radiation on horizontal surfacesrdquo Atmosphereamp Environment service Canada 1988
[6] J A Prescott ldquoEvaporation from a water surface in relation tosolar radiationrdquo Philosophical Transactions of the Royal Societyvol 64 pp 114ndash120 1990
[7] C C Y Ma and M Iqbal ldquoStatistical comparison of solar radi-ation correlations Monthly average global and diffuse radiationon horizontal surfacesrdquo Solar Energy vol 33 no 2 pp 143ndash1481984
[8] J Almorox and C Hontoria ldquoGlobal solar radiation estimationusing sunshine duration in Spainrdquo Energy Conversion andManagement vol 45 no 9-10 pp 1529ndash1535 2004
[9] I T Togrul H Togrul and D Evin ldquoEstimation of monthlyglobal solar radiation from sunshine duration measurement inElazigrdquo Renewable Energy vol 19 no 4 pp 587ndash595 2000
[10] I T Togrul and E Onat ldquoA comparison of estimated andmeasured values of solar radiation in Elazig TurkeyrdquoRenewableEnergy vol 20 no 2 pp 243ndash252 2000
[11] A K Katiyar A Kumar K P Chanchal and B Das ldquoAcomparative study of monthly mean daily clear sky radiationover Indiardquo International Journal of Energy and Environmentvol 1 pp 177ndash182 2010
[12] G Oturanc A Hepbasli and A Genc ldquoStatistical analysis forsolar radiation datardquo Energy Sources vol 25 no 11 pp 1089ndash1097 2003
[13] M Benghanem and A A Joraid ldquoA multiple correlationbetween different solar parameters in Medina Saudi ArabiardquoRenewable Energy vol 32 no 14 pp 2424ndash2435 2007
[14] D B Ampratwum and A S S Dorvlo ldquoEstimation of solarradiation from the number of sunshine hoursrdquo Applied Energyvol 63 no 3 pp 161ndash167 1999
[15] Z Sen ldquoAngstrom equation parameter estimation by unre-stricted methodrdquo Solar Energy vol 71 no 2 pp 95ndash107 2001
[16] B T Nguyen and T L Pryor ldquoThe relationship between globalsolar radiation and sunshine duration in Vietnamrdquo RenewableEnergy vol 11 no 1 pp 47ndash60 1997
[17] N A Elagib S H Alvi and M G Mansell ldquoCorrelationshipsbetween clearness index and relative sunshine duration forSudanrdquo Renewable Energy vol 17 no 4 pp 473ndash498 1999
[18] M Hussain L Rahman and M M Rahman ldquoTechnical notetechniques to obtain improved predictions of global radiationfrom sunshine durationrdquo Renewable Energy vol 18 no 2 pp263ndash275 1999
[19] M T Y Tadros ldquoUses of sunshine duration to estimate theglobal solar radiation over eight meteorological stations inEgyptrdquo Renewable Energy vol 21 no 2 pp 231ndash246 2000
[20] I T Togrul and E Onat ldquoStudy for estimating solar radiationin Elazig using geographical and meteorological datardquo EnergyConversion and Management vol 40 no 14 pp 1577ndash15841999
[21] R Chen K Ersi J Yang S Lu and W Zhao ldquoValidation offive global radiationmodels withmeasured daily data in ChinardquoEnergy Conversion andManagement vol 45 no 11-12 pp 1759ndash1769 2004
[22] C Ertekin and O Yaldiz ldquoComparison of some existing modelsfor estimating global solar radiation for Antalya (Turkey)rdquo
Energy Conversion and Management vol 41 no 4 pp 311ndash3302000
[23] J C Ododo J A Agbakwuru and F A Ogbu ldquoCorrelation ofsolar radiationwith cloud cover and relative sunshine durationrdquoEnergy Conversion and Management vol 37 no 10 pp 1555ndash1559 1996
[24] M Yorukoglu and A N Celik ldquoA critical review on the esti-mation of daily global solar radiation from sunshine durationrdquoEnergy Conversion andManagement vol 47 no 15-16 pp 2441ndash2450 2006
[25] Y Abdalla ldquoNew correlation of global solar radiation withmeteorological parameters for Bahrainrdquo International Journalof Solar Energy vol 16 pp 111ndash120 1994
[26] K K Gopinathan ldquoA new model for estimating total solarradiation in Dohardquo Energy Conversion andManagemen vol 28pp 6ndash72 1988
[27] 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
[28] R G Allen ldquoSelf-calibrating method for estimating solar radi-ation from air temperaturerdquo Journal of Hydrologic Engineeringvol 2 no 2 pp 56ndash67 1997
[29] G H Hargreaves and R G Allen ldquoHistory and evaluation ofhargreaves evapotranspiration equationrdquo Journal of Irrigationand Drainage Engineering vol 129 no 1 pp 53ndash63 2003
[30] Z Samani G H Hargreaves V Tran and S Bawazir ldquoEstimat-ing solar radiation from temperature with spatial and temporalcalibrationrdquo Journal of Irrigation and Drainage Engineering vol137 no 11 pp 692ndash696 2011
[31] J O Ojosu and L K Komolafe ldquoModels for estimating solarradiation availability in South Western Nigeriardquo Solar Energyvol 16 pp 69ndash77 1987
[32] G H Hargreaves and Z A Samani ldquoReference crop evapotran-spiration from temperaturerdquoTransactions of theASAE vol 1 pp96ndash99 1985
[33] J I Prieto J C Martınez-Garcıa and D Garcıa ldquoCorrela-tion between global solar irradiation and air temperature inAsturias Spainrdquo Solar Energy vol 83 no 7 pp 1076ndash1085 2009
[34] M Paulescu L Fara and E Tulcan-Paulescu ldquoModels forobtaining daily global solar irradiation from air temperaturedatardquo Atmospheric Research vol 79 no 3-4 pp 227ndash240 2006
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