Research Article Empirical Models for Estimating Global ...downloads.hindawi.com/journals/jse/2014/897970.pdf · of daily global solar radiation on a horizontal surface, (MJm 2 day

Research ArticleEmpirical Models for Estimating Global Solar Radiation overthe Ashanti Region of Ghana

Emmanuel Quansah Leonard K Amekudzi Kwasi Preko Jeffrey Aryee Osei R BoakyeDziewornu Boli and Mubarick R Salifu

Department of Physics Kwame Nkrumah University of Science and Technology Kumasi Ghana

Correspondence should be addressed to Emmanuel Quansah ekq 2yahoocom

Received 28 August 2013 Revised 19 November 2013 Accepted 20 November 2013 Published 16 January 2014

Academic Editor Xin Wang

Copyright copy 2014 Emmanuel Quansah et al 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

The performances of both sunshine and air temperature dependent models for the estimation of global solar radiation (GSR) overGhana and other tropical regions were evaluated and a comparison assessment of the models was carried out using measuredGSR at Owabi (6∘451015840010158401015840N 1∘431015840010158401015840W) in the Ashanti region of Ghana Furthermore an empirical model which also uses sunshinehours and air temperature measurements from the study site and its environs was proposed The results showed that all themodels could predict very well the pattern of the measured monthly daily mean GSR for the entire period of the study Howevermost of the selected models overestimated the measured GSR except in April and November where the empirical model usingair temperature measurements underestimated the measured GSR Nevertheless a very good agreement was found between themeasured radiations and the proposed models with a coefficient of determination within the range 088ndash096 The results revealedthat the proposed models using sunshine hours and air temperature had the smallest values of MBE MPE and RMSE of minus0010200585 and 00338 and minus02973 17075 and 09859 respectively

1 Introduction

Solar radiation is the primary source of the Earthrsquos energyproviding about 9997 of the heat energy required forchemophysical processes in the atmosphere ocean land andother water bodies [1] Solar radiation plays an important roleas a renewable energy source as solar radiationmeasurementscould be used to estimate potential power levels that canbe generated from photovoltaic cells and also necessary fordetermining cooling loads for buildings [2] Solar radiationthus has many useful applications in architectural designevapotranspiration estimates agriculture and atmosphericland ocean andhydrologicmodels [3 4]The acquisition andthe development of database on the long term solar radiationwill facilitate the evaluation of solar energy potential as aninput to the countryrsquos energy budget and other modelingapplications mentioned earlier The development of solartechnology in the country will minimise its overrelianceon wood fuel consumption estimated at 18 million tons

per annum especially in the rural communities ([5] andreferences therein) Studies carried out on solar irradiancemeasurements in some parts of the country suggest that thereis a potential for solar energy to be used on commercialscale and in this vein the Ghana Grid Company (GRIDco)has begun producing electrical energy from a solar farmestablished in the northern part of Ghana [6ndash8]

The immediate short term to the long term solutions toaddress the problems of inadequate infrastructure in the areaof solar energy data acquisitions have been the applicationof empirical models that rely on the correlation betweenthe parameters obtained from measured meteorological data[4 9] In this regard several empirical formulae have beendeveloped to predict the global solar radiation using variousmeteorological variables such as sunshine hours cloud coverrelative humidity maximum temperature and water vapourpressure [4 9ndash12] However the reliability and usability ofthesemodels depend largely on the strength of the correlationbetween the estimated and measured variables

Hindawi Publishing CorporationJournal of Solar EnergyVolume 2014 Article ID 897970 6 pageshttpdxdoiorg1011552014897970

2 Journal of Solar Energy

Figure 1 Locations of the KNUST surface observation sites in theAshanti region of Ghana

The aim of this paper is to assess the suitability of bothsunshine and temperature dependent empirical models forthe estimation of global solar radiation in Ghana

2 Materials and Methods

The measurement of the hourly global solar radiation wascarried out at Owabi in the Ashanti region of Ghana6750∘N 1716∘W and 77m asl The site is located near theOwabi dam surrounded by forest (see Figure 1) In this paperdata analysed span between the months of February andDecember 2011The global solar radiation data wasmeasuredwith a pyranometer with a spectral range between 5 and42120583m The pyranometer was mounted on an automaticweather station that also provided data on temperature rel-ative humidity atmospheric pressure rainfall downwellingradiation soil matrix potential soil heat flux and windspeed in horizontal and vertical directions The sunshinehours data was obtained from the synoptic station of theGhana Meteorological Agency at the Kumasi airport about20 km from the study site The air temperature data used tocalculate the global solar radiationwasmeasured on site usingthe ventilation resistant thermometers placed 2m above theground All the data used in this paper had been takenthrough quality checks and controls usingmethods explainedby Allen et al [15]

21 Empirical Model Based on Sunshine Hours Most empiri-cal models used to predict global solar radiation are based onthe Angstrom-Prescott model [16] given as

119866

119901

119866

119900

= 119886 + 119887 (

119899

119873

) (1)

where 119866119901(MJmminus2 dayminus1) is the predicted monthly mean

of daily global solar radiation on a horizontal surface 119866119900

(MJmminus2 dayminus1) is the monthly mean extraterrestrial solarradiation on horizontal surface 119899 is the monthly meandaily number of hours of sunshine and 119873 is the maximummonthly mean daily sunshine (MJmminus2 dayminus1) The constants119886 and 119887 are the location specific empirical coefficientsobtained from measured solar radiation data The monthly

average daily extraterrestrial irradiance 119866119900(KWhmminus2 dayminus1)

is estimated using

119866

119900=

24 times 3600

120587

119868

119900(

120587

180

120596

119904sin120593 sin 120575 + cos120593 sin120596

119904) (2)

where 119868119900is the solar constant (1367Wmminus2) 120593 is latitude

(degree) 120575 is the solar declination for the month (degree)and 120596

119904is the mean sunrise hour angle for the given month

(degree) The values of 120575 and 120596119904can be calculated using (3)

and (4) respectively where all the parameters have their usualmeanings and 119896 is the Julian days starting from 1st of January

120575 = 2345 sin [360 (119896 + 284)365

] (3)

120596

119904= cosminus1 (minus tan120593 tan 120575) (4)

The units in KWhmminus2 dayminus1 may be converted intoMJmminus2 dayminus1 using a factor of 36 proposed by Hargreavesand Samani [14]

22 Empirical Model Based on Air Temperature Hargreavesand Samani [14] were among the first to also suggest that theclearness index 119877 = 119866119866

119900could be estimated using (5) given

as119866

119901

119866

119900

= 120572Δ119879

05

(5)

where 119866119901and 119866

119900(MJmminus2 dayminus1) are as described by (1)

Δ119879(119870) = 119879max minus 119879min with 119879max as the mean value of thedaily maximum temperature while 119879min is the mean valueof the daily minimum temperature and 120572 is a dimensionlessempirical parameter fixed at 016 for interior regions and 019for coastal regions [2] In order to account for the influenceof altitude on 120572 Allen [17] proposed an estimator for 120572 using

120572 = 120572

119886(

119875

119875

119900

)

05

(6)

where 119875 and 119875119900are the average atmospheric pressures at the

altitude of the place and at sea level respectively and 120572119886was

fixed at 017 for interior regions and 020 for coastal areas Ina later date Chandel et al [13] proposed a model (7) basedon (5) and (6) as

119866

119901

119866

119900

= 79120593

minus1

(Δ119879 sin120593( 119875119875

119900

))

05

(7)

where120572119886from (6) has been expressed as a function of latitude

120593 in

120572

119886= 79120593

minus1

(sin120593)05 (8)

In this study we evaluated seven models five of which werebased on the Angstrom-Prescott relation [16] and two on theHargreaves and Samani [14] modelsThese models with theirvalues of the regression coefficients 119886 and 119887 (Tables 1 and 2)have been proposed in the literature to be suitable for theestimation of global solar radiation on a horizontal surfacein the tropics [8 18]

Journal of Solar Energy 3

Table 1 Summary of the regression constants used by differentauthors in the tropics as well as that proposed by this paper basedon sunshine hours

Author a b Region ofapplication

Turton (1987) [20] 030 040 TropicsFagbenle (1990) [21] 028 039 TropicsOtu-Danquah (1990)[22] 027 045 Ghana (everywhere)

Jackson and Akuffo(1992) [23] 025 045 Kumasi Ghana

Augustine andNnabuchi (2009b)[18]

029 042 Tropics

Proposed model 022 043 Kumasi Ghana

23 Model Evaluation Schemes Theperformances of the pre-dictions of each model as against the measured values of themonthly means of daily solar radiations were assessed usingfundamental error analysis schemes described by Muzathiket al [9] and Maghrabi [19] According to [9 19] themean percentage error (MPE) mean bias error (MBE) androot mean square error (RMSE) are given by the followingequations

MPE = 1

119873

119873

sum

119894=1

(

119866

119894119898minus 119866

119894119901

119866

119894119898

times 100)

MBE = 1

119873

119873

sum

119894=1

(119866

119894119901minus 119866

119894119898)

RMSE = radic 119868

119873

[

119873

sum

119894=1

(119866

119894119901minus 119866

119894119898)

2

]

(9)

where 119866119894119898

is the 119894th measured value 119866119894119901is the 119894th estimated

or predicted value and119873 is the total number of observationsThe MPE indicates the percentage deviation of the predictedand measured monthly average daily global solar radiationdataTheMBE provides a clue to whether a givenmodel has atendency to under- or overpredict withMBE values closest tozero being desirable The RMSE on the other hand indicatesthe level of scatter that a model produces thus providing aterm-by-term comparison of the actual deviation betweenthe predicted and observed values with a lower RMSE valuereflecting a better model in terms of its absolute deviationThe equations with the highest values of 119877 and 1198772 and leastvalues of MBE RMSE and MPE are suitable for predictingglobal solar radiation [9 19]

3 Results and Discussion

Based on the Angstrom-Prescott model given in (1) it wasobserved that the clearness index was related to the fractionof sunshine hours by the constants 119886 = 022 and 119887 =

043 over the study area With these derived approximated

Table 2 Summary of the regression constants used by differentauthors in the tropics as well as that proposed by this paper basedon air temperature measurements

Author a b Model formHargreaves andSamani (1982) [14] 0153 minus0033 119877 = 119886(Δ119879)

05

+ 119887

Chandel et al (2005)[13] 0264 minus0155 119877 = 119886 ln(Δ119879) + 119887

Proposed 0311 minus0293 119877 = 119886 ln(Δ119879) + 119887

16

14

12

10

Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

MeasuredCalculated

GSR

(MJ m

minus2

dayminus

1)

Months of the year 2011

(a)

16

14

12

10

10 11 12 13 14 15 16 17

Measured GSR (MJ mminus2 dayminus1)Cal

cula

ted

GSR

(MJ m

minus2

dayminus

1)

R2= 09098

(b)

Figure 2 Comparison between the measured GSR and the calcu-lated GSR using our proposed model

constants we proposed a model based on the Angstrom-Prescott model (1) and used it to calculate the monthly meandaily global solar radiation (GSR) for the study period andcompared it with the measured values (Figure 2) The resultsshowed that our proposed model was able to predict thevariability of the monthly mean daily global solar radiation(Figure 2(a)) with a very high coefficient of determination of09098 (Figure 2(b))

The monthly comparison studies showed a very goodagreement between the proposed model and the measure-mentswith aMBEofminus030 tominus001 In addition the proposedmodel compared favourably well with the other empiricalmodels used in the study In most cases the proposedmodels predicted the pattern of the measured solar radiationvery well especially the decrease in radiation between themonths of May and August (Figure 2) The decrease inradiation could be attributed to the fact that these monthsconstitute the rainy season and hence the presence of cloudsand rain droplets in the atmosphere prevented the surfacefrom receiving more radiation However the other empirical


Table 3 Summary of the model evaluations using sunshine hours

Model form 119877 119877

2 MBE (MJmminus2 dayminus1) MPE () RMSE (MJmminus2 dayminus1)Proposed 09538 09098 minus00102 00585 00338Turton (1987) [20] 09581 09179 24926 minus143170 82670Fagbenle (1990) [21] 09578 09174 16177 minus92919 53654Otu-Danquah (1990) [22] 09561 09142 21885 minus125706 72586Jackson and Akuffo (1992) [23] 09553 09125 14688 minus84365 48715Augustine and Nnabuchi (2009b) [18] 09575 09168 24430 minus140319 81024

Table 4 Summary of the model evaluations using air temperature

Author 119877 119877

2 MBE (MJmminus2 dayminus1) MPE () RMSE (MJmminus2 dayminus1)Proposed 09126 08328 minus02973 17075 09859Hargreaves and Samani (1982) [14] 08822 07782 11709 minus67255 38835Chandel et al (2005) [13] 09149 08370 09409 minus54044 31206

MeasuredPredictedTurtonFagbenle

DanquahJacksonAugustine

20

19

18

17

16

15

14

13

12

10

11

FebJan Mar Apr May Jun Jul Aug Sep Oct Nov Dec

GSR

(MJ m

minus2

dayminus

1)


Figure 3 Measured and calculated GSR using the empirical modelsproposed in the literature as well as our proposedmodel (predicted)

models overestimated themeasured global radiation betweenMay and August (Figure 3) Nevertheless the coefficient ofdetermination foundbetween themeasured radiation and theproposed models was within acceptable values (see Table 3for summary)

31 Determination of Global Solar Radiation fromAir Temper-ature Measurements Using the air temperature values fromthe study area a model was developed based on that ofChandel et al [13] (Table 2) Similarly our proposed modelcould predict the pattern of the measured monthly meandaily global solar radiation but underestimated thembetweenthe months of AprilndashJune and October-November while itoverestimated the measured radiation for the months of

16

14

12

10


MeasuredCalculated

GSR

(MJ m

minus2

dayminus

1)


(a)

16

14

12

10

10 11 12 13 14 15 16 17


cula

ted

GSR

(MJ m

minus2

dayminus

1)

R2= 08328

(b)

Figure 4 Comparison between the measured GSR and the calcu-lated GSR using our proposed model (calculated)

August September and December (Figure 4(a)) The corre-lation between themeasured and the predicted radiation gavea coefficient of determination (1198772) of 08328 (Figure 4(b))

In addition a comparison between the measured valuesand those calculated using the proposed models by Harg-reaves and Samani [14] andChandel et al [13] herein denotedas 119866(H-H) and 119866(Chen) respectively (Figure 5) revealed that

they predicted the pattern of the measured radiation verywell However they overestimated the measured radiation inall the months except the months of April and Novemberwhere the measured radiation were underestimated Table 4gives the summary of the correlation between the measuredGSR and those calculated using 119866

(H-H) and 119866(Chen)


MeasuredCalculated

H-HChen

18

17

16

15

14

13

12

10

11


GSR

(MJ m

minus2

dayminus

1)


Figure 5 Comparison between measured GSR and the GSRcalculated using the models by Chandel et al [13] and Hargreavesand Samani [14] as well as our proposed model (calculated)

Summary of the model evaluations is given in Tables 3and 4 for sunshine hours and air temperatures respectivelyThe results showed that in both model evaluation methodsour proposed model compared to the other models dis-played the smallest MBE MPE and RMSE This makes theproposed model most suitable for estimating global solarradiation In the case of calculatedGSR using sunshine hoursour model was followed by those proposed by Jackson andAkuffo [23] Fagbenle [21]Out-Danquah [22] Augustine andNnabuchi [18] and Turton [20] respectively in the orderof performances (Table 3) While for the GSR calculatedusing air temperature our proposed model was followed bythose of Chandel et al [13] and Hargreaves and Samani [14]respectively in the order of performances (Table 4)

4 Conclusions

The performances of both sunshine and temperature depen-dentmodels for the estimation of global solar radiation (GSR)over Ghana and other tropical regions were evaluated and acomparison assessment of the models were carried out usingmeasured GSR at Owabi in the Ashanti region of GhanaFurthermore we proposed two empirical models which alsouse sunshine hours and temperature measurements fromthe study site and its environs The results showed that themodels could predict very well the variability of themeasuredmonthly daily mean global solar radiation for the entireperiod of the study This could be attributed to the fact thatthe models used meteorological input data (sunshine hoursand air temperatures) that also respond to the variability inatmospheric conditions such as rainfall cloud cover and theseasonal changes that affect the amount of solar radiationreaching the Earthrsquos surface Tables 3 and 4 provide thesummary of the model evaluation results

The results revealed that our proposed model usingsunshine hours had the smallest values of MBE MPE andRMSE of minus00102 00585 and 00338 respectively (Table 3)while the proposed model using air temperature had MBEMPE and RMSE values of minus02973 17075 and 09859respectively (Table 4) However due to the fact that thesunshine hours data was measured from about 20 km fromthe study site there is the possibility of discrepancies withinthe global solar radiation calculated from our sunshine inputmodel arising as a result of the difference in environmentalconditions of the two areas (Owabi and Kumasi airport)

The comparison studies between the measured globalsolar radiation and the calculated global solar radiation sug-gest that both models can be employed to estimate monthlymean daily global solar radiation However the constants 119886and 119887 aswell as othermeteorological input data for themodelswere found to be site specific and therefore these modelsmust be used with care for global solar radiation estimationCurrently long term solar radiation measurements are beingundertaken in other parts of Ghana that would be used inthe near future to estimate the global solar radiation moreaccurately for effective use as a solar energy potential over theentire country

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors wish to acknowledge Mr Elvis Kofi Agyapongwho provided the field site technical supportThe installationand maintenance of the automatic weather station at Owabiwere funded by the EU project Quantifying Weather Impacton Health in Developing Countries (QWeCI funded bythe European Commissionrsquos Seventh Framework ResearchProgramme under theGrant agreement 243964)The authorsare also grateful to the reviewers for their comments andsuggestions that contributed to improve this paper

References

[1] E O Ogolo ldquoEvaluating the performance of some predictivemodels for estimating global solar radiation across varyingclimatic conditions in Nigeriardquo India Journal of Radio amp SpacePhysics vol 39 no 3 pp 121ndash131 2010

[2] K K Gopinathan ldquoSolar sky radiation estimation techniquesrdquoSolar Energy vol 49 no 1 pp 9ndash11 1992

[3] S V Tahas D Ristoiu andC Cosma ldquoTrends of the global solarradiation and air temperature in Cluj-Napoca Romania (1984ndash2008)rdquo Romanian Journal in Physics vol 56 no 5-6 pp 784ndash789 2011

[4] E O Falayi and A B Rabiu ldquoEstimation of global solar radia-tion using cloud cover and surface temperature in some selectedcities in Nigeriardquo Archives of Physics Research vol 2 no 3 pp99ndash109 2011

[5] E Quansah K Preko and L K Amekudzi ldquoFirst performanceassessment of blends of jatropha palm oil and soya bean


biodiesel with kerosene as fuel for domestic purposes in rural-Ghanardquo International Journal of Energy and Environment vol2 no 2 pp 331ndash336 2011

[6] F O Akuffo ldquoSolar and wind energy resources assessment-finalreportrdquo Preliminary Data Analysis and Evaluation Vol 1-2 aConsultant ReportTheMinistry of Energy Accra Ghana 1991

[7] K O Afriyie ldquoPerformance of Sayighrsquos universal formula inthe estimation of global solar radiation in Ghanardquo Tech RepInternational Centre forTheoretical Physics Trieste Italy 1995

[8] F S Arku ldquoThe modelled solar radiation pattern of Ghanaits prospects for alternative energy sourcerdquo Journal of AfricanStudies and Development vol 3 no 3 pp 45ndash64 2011

[9] A M Muzathik W B W Nik M Z Ibrahim K B SamoK Sopian and M A Alghoul ldquoDaily global solar radiationestimate based on sunshine hoursrdquo International Journal ofMechanical and Materials Engineering vol 6 no 1 pp 75ndash802011

[10] A A Trabea andM AM Shaltout ldquoCorrelation of global solarradiation with meteorological parameters over Egyptrdquo Renew-able Energy vol 21 no 2 pp 297ndash308 2000

[11] E B Pereira F R Martins S L Abreu et al ldquoCross validationof satellite radiation models during SWERA project in Brazilrdquoin Proceedings of the ISES Solar World Congress pp 14ndash19Goteborg Sweden June 2003

[12] M J Ahmad and G N Tiwari ldquoSolar radiation models-areviewrdquo International Journal of Energy Research vol 35 no 4pp 271ndash290 2011

[13] S S Chandel R K Aggarwal and A N Pandey ldquoNew correla-tion to estimate global solar radiation on horizontal surfacesusing sunshine hour and temperature data for indian sitesrdquoJournal of Solar Energy Engineering vol 127 no 3 pp 417ndash4202005

[14] G H Hargreaves and Z A Samani ldquoEstimating potentialevapotranspirationrdquo Journal of the Irrigation and DrainageDivision vol 108 no 3 pp 225ndash230 1982

[15] R G Allen L S Pereira D Raes and M Smith ldquoCrop evap-otranspiration guidelines for computing crop water require-mentsrdquo Irrigation andDrainage Paper 56 Food andAgricultureOrganisation of the United Nations (FAO) Rome Italy 1998

[16] J A Prescott ldquoEvaporation from water surface in relation tosolar radiationrdquo Transactions of the Royal Society of Australiavol 46 pp 114ndash118 1940

[17] R Allen ldquoEvaluation of procedures for estimating meanmonthly solar radiations from air temperaturerdquo Tech RepFood and Agricultural Organisation of the United Nations(FAO) Rome Italy 1995

[18] C Augustine and M N Nnabuchi ldquoCorrelation between sun-shine hours and global solar radiation inWarri Nigeriardquo PacificJournal of Science and Technology vol 10 no 2 pp 574ndash5792009

[19] A H Maghrabi ldquoParameterization of a simple model to esti-mate monthly global solar radiation based on meteorologicalvariables and evaluation of existing solar radiation models forTabouk Saudi Arabiardquo Energy Conversion and Managementvol 50 no 11 pp 2754ndash2760 2009

[20] S M Turton ldquoThe relationship between total irradiation andsunshine duration in the humid tropicsrdquo Solar Energy vol 38no 5 pp 353ndash354 1987

[21] R O Fagbenle ldquoEstimation of total solar radiation in Nigeriausing meteorological datardquo Nigerian Journal of RenewableEnergy vol 1 pp 1ndash10 1990

[22] K A Otu-Danquah ldquoAssociate Programme Officer GhanaEnergy Commission PMB Ministries AccraGhanardquo PrivateConversation 1990

[23] E A Jackson and F O Akuffo ldquoCorrelations between monthlyaverage daily global irradiation and relative duration of sun-shine at Kumasirdquo Energy Conversion and Management vol 33no 1 pp 13ndash22 1992

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of


Journal ofPetroleum Engineering


Industrial EngineeringJournal of


Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of


Journal of


Renewable Energy

Submit your manuscripts athttpwwwhindawicom


StructuresJournal of


RotatingMachinery


EnergyJournal of


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy


Nuclear InstallationsScience and Technology of


Solar EnergyJournal of


Wind EnergyJournal of


Nuclear EnergyInternational Journal of


High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Figure 1 Locations of the KNUST surface observation sites in theAshanti region of Ghana

The aim of this paper is to assess the suitability of bothsunshine and temperature dependent empirical models forthe estimation of global solar radiation in Ghana

2 Materials and Methods

The measurement of the hourly global solar radiation wascarried out at Owabi in the Ashanti region of Ghana6750∘N 1716∘W and 77m asl The site is located near theOwabi dam surrounded by forest (see Figure 1) In this paperdata analysed span between the months of February andDecember 2011The global solar radiation data wasmeasuredwith a pyranometer with a spectral range between 5 and42120583m The pyranometer was mounted on an automaticweather station that also provided data on temperature rel-ative humidity atmospheric pressure rainfall downwellingradiation soil matrix potential soil heat flux and windspeed in horizontal and vertical directions The sunshinehours data was obtained from the synoptic station of theGhana Meteorological Agency at the Kumasi airport about20 km from the study site The air temperature data used tocalculate the global solar radiationwasmeasured on site usingthe ventilation resistant thermometers placed 2m above theground All the data used in this paper had been takenthrough quality checks and controls usingmethods explainedby Allen et al [15]

21 Empirical Model Based on Sunshine Hours Most empiri-cal models used to predict global solar radiation are based onthe Angstrom-Prescott model [16] given as

119866

119901

119866

119900

= 119886 + 119887 (

119899

119873

) (1)

where 119866119901(MJmminus2 dayminus1) is the predicted monthly mean

of daily global solar radiation on a horizontal surface 119866119900

(MJmminus2 dayminus1) is the monthly mean extraterrestrial solarradiation on horizontal surface 119899 is the monthly meandaily number of hours of sunshine and 119873 is the maximummonthly mean daily sunshine (MJmminus2 dayminus1) The constants119886 and 119887 are the location specific empirical coefficientsobtained from measured solar radiation data The monthly

average daily extraterrestrial irradiance 119866119900(KWhmminus2 dayminus1)

is estimated using

119866

119900=

24 times 3600

120587

119868

119900(

120587

180

120596

119904sin120593 sin 120575 + cos120593 sin120596

119904) (2)

where 119868119900is the solar constant (1367Wmminus2) 120593 is latitude

(degree) 120575 is the solar declination for the month (degree)and 120596

119904is the mean sunrise hour angle for the given month

(degree) The values of 120575 and 120596119904can be calculated using (3)

and (4) respectively where all the parameters have their usualmeanings and 119896 is the Julian days starting from 1st of January

120575 = 2345 sin [360 (119896 + 284)365

] (3)

120596

119904= cosminus1 (minus tan120593 tan 120575) (4)

The units in KWhmminus2 dayminus1 may be converted intoMJmminus2 dayminus1 using a factor of 36 proposed by Hargreavesand Samani [14]

22 Empirical Model Based on Air Temperature Hargreavesand Samani [14] were among the first to also suggest that theclearness index 119877 = 119866119866

119900could be estimated using (5) given

as119866

119901

119866

119900

= 120572Δ119879

05

(5)

where 119866119901and 119866

119900(MJmminus2 dayminus1) are as described by (1)

Δ119879(119870) = 119879max minus 119879min with 119879max as the mean value of thedaily maximum temperature while 119879min is the mean valueof the daily minimum temperature and 120572 is a dimensionlessempirical parameter fixed at 016 for interior regions and 019for coastal regions [2] In order to account for the influenceof altitude on 120572 Allen [17] proposed an estimator for 120572 using

120572 = 120572

119886(

119875

119875

119900

)

05

(6)

where 119875 and 119875119900are the average atmospheric pressures at the

altitude of the place and at sea level respectively and 120572119886was

fixed at 017 for interior regions and 020 for coastal areas Ina later date Chandel et al [13] proposed a model (7) basedon (5) and (6) as

119866

119901

119866

119900

= 79120593

minus1

(Δ119879 sin120593( 119875119875

119900

))

05

(7)

where120572119886from (6) has been expressed as a function of latitude

120593 in

120572

119886= 79120593

minus1

(sin120593)05 (8)

In this study we evaluated seven models five of which werebased on the Angstrom-Prescott relation [16] and two on theHargreaves and Samani [14] modelsThese models with theirvalues of the regression coefficients 119886 and 119887 (Tables 1 and 2)have been proposed in the literature to be suitable for theestimation of global solar radiation on a horizontal surfacein the tropics [8 18]







029 042 Tropics



MPE = 1

119873

119873

sum

119894=1

(

119866

119894119898minus 119866

119894119901

119866

119894119898

times 100)

MBE = 1

119873

119873

sum

119894=1

(119866

119894119901minus 119866

119894119898)

RMSE = radic 119868

119873

[

119873

sum

119894=1

(119866

119894119901minus 119866

119894119898)

2

]

(9)

where 119866119894119898








05

+ 119887



16

14

12

10


MeasuredCalculated

GSR

(MJ m

minus2

dayminus

1)


(a)

16

14

12

10

10 11 12 13 14 15 16 17


cula

ted

GSR

(MJ m

minus2

dayminus

1)

R2= 09098

(b)






Model form 119877 119877



Author 119877 119877




20

19

18

17

16

15

14

13

12

10

11


GSR

(MJ m

minus2

dayminus

1)





16

14

12

10


MeasuredCalculated

GSR

(MJ m

minus2

dayminus

1)


(a)

16

14

12

10

10 11 12 13 14 15 16 17


cula

ted

GSR

(MJ m

minus2

dayminus

1)

R2= 08328

(b)







MeasuredCalculated

H-HChen

18

17

16

15

14

13

12

10

11


GSR

(MJ m

minus2

dayminus

1)




4 Conclusions






Acknowledgments


References






























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of























029 042 Tropics



MPE = 1

119873

119873

sum

119894=1

(

119866

119894119898minus 119866

119894119901

119866

119894119898

times 100)

MBE = 1

119873

119873

sum

119894=1

(119866

119894119901minus 119866

119894119898)

RMSE = radic 119868

119873

[

119873

sum

119894=1

(119866

119894119901minus 119866

119894119898)

2

]

(9)

where 119866119894119898








05

+ 119887



16

14

12

10


MeasuredCalculated

GSR

(MJ m

minus2

dayminus

1)


(a)

16

14

12

10

10 11 12 13 14 15 16 17


cula

ted

GSR

(MJ m

minus2

dayminus

1)

R2= 09098

(b)






Model form 119877 119877



Author 119877 119877




20

19

18

17

16

15

14

13

12

10

11


GSR

(MJ m

minus2

dayminus

1)





16

14

12

10


MeasuredCalculated

GSR

(MJ m

minus2

dayminus

1)


(a)

16

14

12

10

10 11 12 13 14 15 16 17


cula

ted

GSR

(MJ m

minus2

dayminus

1)

R2= 08328

(b)







MeasuredCalculated

H-HChen

18

17

16

15

14

13

12

10

11


GSR

(MJ m

minus2

dayminus

1)




4 Conclusions






Acknowledgments


References






























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



















Model form 119877 119877



Author 119877 119877




20

19

18

17

16

15

14

13

12

10

11


GSR

(MJ m

minus2

dayminus

1)





16

14

12

10


MeasuredCalculated

GSR

(MJ m

minus2

dayminus

1)


(a)

16

14

12

10

10 11 12 13 14 15 16 17


cula

ted

GSR

(MJ m

minus2

dayminus

1)

R2= 08328

(b)







MeasuredCalculated

H-HChen

18

17

16

15

14

13

12

10

11


GSR

(MJ m

minus2

dayminus

1)




4 Conclusions






Acknowledgments


References






























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















MeasuredCalculated

H-HChen

18

17

16

15

14

13

12

10

11


GSR

(MJ m

minus2

dayminus

1)




4 Conclusions






Acknowledgments


References






























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of









































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of





















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of

















Documents

Research Article Empirical Models for Estimating Global ...downloads.hindawi.com/journals/jse/2014/897970.pdf · of daily global solar radiation on a horizontal surface, (MJm 2 day