a review of solar radiation models—part i

Hindawi Publishing CorporationJournal of Renewable EnergyVolume 2013 Article ID 168048 11 pageshttpdxdoiorg1011552013168048

Review ArticleA Review of Solar RadiationModelsmdashPart I

A K Katiyar and C K Pandey

Department of Applied Sciences amp Humanities Institute of Engineering amp Technology Gautam Buddh Technical UniversityLucknow 226021 India

Correspondence should be addressed to C K Pandey chanchalpandey44yahoocom

Received 31 August 2012 Accepted 29 November 2012

Academic Editor Jayanta Deb Mondol

Copyright copy 2013 A K Katiyar and C K Pandey is is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Energy is considered as a key source for the future and plays a pivotal role in its socioeconomic development by raising the standardof living and the quality of life not only for India but also for the world In view of the scarce fossil fuel reserves solar energyis one of the important sources of renewable energy used in India because of the suitable climate conditions It receives about548517Whm2 day of solar insolation with an annual total of about 19 74 6612Whm2 Except for the monsoon months solarradiation incidence is very encouraging from the application point of view For the efficient functioning and better performanceof solar energy device the information of solar radiation and its components at particular location is very essential for designingthe solar energy devices erefore over the years several empirical correlations have been developed in order to estimate themore appropriate solar radiation in India as well as around the world Here we present a review of different solar radiation modelswhich predict global solar radiation and discussed the long-term plan to meet future energy demand with renewable energy dueto economy growth

1 Introduction

e growing demand in urban and rural areas for energy hasnecessitated the nding of alternative sources of energy Withthe change in the rural scenario and agricultural practicesand the advent of gadgets like televisions mobile phonesand computers the demand of energy has increased by amultitude In India commercial energy consumption makesup about 65 of the total energy consumption is includescoal with the largest share of 55 followed by oil at 31natural gas at 11 and hydroenergy at 3 Noncommercialenergy sources (like rewood cow dung agricultural wastesetc) make 30 over the total energy consumption [1]Being a tropical country India has unlimited potential forproducing renewable energy resources During the past 25years there has a signicant growth of the renewable energytechnology and today it considered by many countries asan important technology for the future Many countrieshave already established or are in the process of establishingsupport programs to encourage the adoption of this newtechnology e Government of India has also given a majorllip to the adoption of renewable energy by launching

the JNNSM (Jawaharlal Nehru National Solar Mission) asone of the eight national missions on climate change inNovember 2009 is mission aims to establish India as aglobal leader in solar energy by creating the policy conditionsfor its diffusion across the country as quickly as possiblee immediate aim of the mission is to focus on setting upan enabling environment for solar technology penetrationin the country both at centralized and decentralized levelse mission targets to set up 1100MW (megawatt) of gridsolar power 7 million sqm of solar collectors and 200MWof off-grid solar applications in the rst phase (by 2013) Bythe year 2022 it aims for establishing 20 000MW of gridsolar power 20million sqmof solar collectors and 2000MWof off-grid solar applications However the true success ofthis mission depends solely on the active participation ofevery member of the society e Department of Energy andClimate Change of the UK (United Kingdom) has recentlyoutlined a comprehensive long-term plan which maps outthe strategy for generating 30 of UKrsquos electricity fromrenewable energy sources by 2020 up from 55 today It alsoaims to generate 12 of heat and 10 of transport energyfrom renewable energy In the US California has proposed

2 Journal of Renewable Energy

an enhanced RPS (renewable portfolio standards) target of33 by 2020mdashup from the 2010 target of 20 Mexico pro-poses to more than double the share of electricity generatedfrom renewable from the existing 33 to 76 by 2012us a consensus is being developed that the utilization ofrenewable energy can be a tool for curbing carbon emissions

To overcome the dependency on conventional fuelsresearchers and many organizations are working on alter-native fuels which should be commercially viable easy touse less pollutant and must be abundant in nature Inthis direction renewable energies like Solar Energy TidalEnergy Wind Energy Biofuels and so forth are suitablethan conventional sources of energy ese nonconventionalforms are not only renewable but also maintain ecology andenvironment as they are eco-friendly and do not contributein global warming and production of green house gases andso forth

It is well known that solar energy is the source of lifeon earth It heats its atmosphere and its lands generatesits winds drives the water cycle warms its oceans growsits plants feeds its animals and even (over the long haul)produces its fossil fuels is energy can be converted intoheat and cold driving force and electricity Since solarradiation is vital to solar energy system design everywherewhere adequate observations are missing [2] ereforeinformation on solar radiation and its components at agiven location is very essential e best database would bethe long-term measured data at the site of the proposedsolar system However the limited coverage of radiationmeasuring networks dictates the need for developing solarradiation models [3] emain objective of the present studyis to review solar radiation (global radiation)models for Indiaand some of its provinces

2 ReviewModels

It is generally accepted that models for solar radiationprediction are necessary because in most cases the densityand number of solar radiation measuring stations cannotdescribe the necessary variability [4] It is understandablethen that new models and improvements to existing mod-eling techniques are continually proposed which intend toimprove estimates of solar radiation values with the use ofmore readily available meteorological variables [5ndash7]

21 Estimation of Global Solar Radiation Using Angstrom-Type Models Angstrom [8] proposed the rst theoreticalmodel for estimating global solar radiation based on sunshineduration Page [9] and Prescott [10] reconsidered this modelin order to make it possible to calculate monthly average ofthe daily global radiation 119867119867 (MJm2 day) on a horizontalsurface from monthly average daily total insolation on anextraterrestrial horizontal surface as per the following rela-tion

1198671198671198671198670

= 119886119886 119886 11988611988610076531007653119878119878119878119878010076691007669 (1)

where119867119867 is the monthly average global radiation on horizon-tal surface 119878119878 is the monthly average daily bright sunshinehours 1198781198780 is the maximum possible monthly average dailysunshine hours or the day length 119886119886 and 119886119886 are constantsand1198671198670 is the monthly average daily extraterrestrial radiation(MJm2 day) which can be expressed as [11]

1198671198670 =24120587120587119868119868sc 100771710077171 119886 033 cos 10076521007652

360119863119863119899119899365

1007668100766810076681007668

times 10077161007716cos 119871119871 cos 119871119871 s119871119871 119871119871119904119904 1198862120587120587119871119871119904119904360

s119871119871 119871119871 s119871119871 11987111987110077321007732 (2)

where 119871119871119904119904 is sunset hour angle in degree and dened as

119871119871119904119904 = cosminus1 (minus ta119871 119871119871 ta119871 119871119871) (3)

119868119868sc is the solar constant 119871119871 is the latitude of location underconsideration119863119863119899119899 is the day of year starting fromrst Januaryand 119871119871 is declination angle as given below

119871119871 = 2345 s119871119871 10077181007718360 10076491007649284 119886 11986311986311989911989910076651007665

36510077341007734 (4)

For a givenmonth the maximum possible sunshine durationcan be computed by the following equation [12]

1198781198780 =215

cosminus1 (minus ta119871 119871119871 ta119871 119871119871) (5)

e regression models that have been proposed in theliterature are given below

Model 1 Page [9] has given the coecients of modiedAngstrom model as the following

1198671198671198671198670

= 023 119886 0481198781198781198781198780 (6)

Model 2 Kholagi et al [13] obtained the following linearequations from the data measured at three different stationsin Yemen

1198671198671198671198670

= 0191 119886 05711198781198781198781198780 (7a)

1198671198671198671198670

= 0297 119886 04321198781198781198781198780 (7b)

1198671198671198671198670

= 0262 119886 04541198781198781198781198780 (7c)

Model 3 Benson et al [14] have obtained regression con-stants in to two intervals of a year depending on the climaticparameters

1198671198671198671198670

= 018 119886 0601198781198781198781198780

for JanndashMarch and OctndashDec

(8a)

1198671198671198671198670

= 024 119886 0531198781198781198781198780

for rest of the month (8b)

Journal of Renewable Energy 3

Model 4 H P Garg and S N Garg [15] obtained thefollowing equations from the experimental data of elevenstations in India

1198671198671198671198670

= 03156 + 045201198781198781198781198780

(9)

Model 5 Bahel et al [16] proposed the following relation-ship

1198671198671198671198670

= 0175 + 05521198781198781198781198780

(10)

Model 6 Jain [17] has proposed the following regressionconstants based on Angstrom-type correlation using theaverage daily global solar radiation and the sunshine data of31 Italian locations

1198671198671198671198670

= 0177 + 06921198781198781198781198780

(11)

Model 7 Alsaad [18] suggested the following relation toestimate the global radiation for Amman Jordan

1198671198671198671198670

= 0174 + 06151198781198781198781198780

(12)

Model 8 S Jain and P C Jain [19] suggested the followingcorrelation constants to estimate the global radiation overeight Zambian locations

1198671198671198671198670

= 0240 + 05131198781198781198781198780

(13)

Model 9 Luhanga and Andringa [20] proposed model asfollows

1198671198671198671198670

= 0241 + 04881198781198781198781198780

(14)

Model 10 Raja and Twidell [21 22] provided the followingequations using the data from ve main observatories inPakistan and by taking into account the effect of latitudeΦ

1198671198671198671198670

= 0335 + 03671198781198781198781198780

(15a)

1198671198671198671198670

= 0388 cosΦ + 03671198781198781198781198780

(15b)

Model 11 Jain [23] proposed the following relations forthree locations (Salisbury Bulawayo and Macerata) on themeasured data of Italy

1198671198671198671198670

= 0313 + 04741198781198781198781198780

(16a)

1198671198671198671198670

= 0307 + 04881198781198781198781198780

(16b)

1198671198671198671198670

= 0309 + 05991198781198781198781198780

(16c)

Model 12 Louche et al [24] suggested the regression con-stants to estimate global solar radiation as a function of theratio of sunshine duration

1198671198671198671198670

= 0309 + 05991198781198781198781198780

(17)

Model 13 Lewis [25] proposed the following linear equationto estimate global radiation for locations in the state ofTennessee USA

1198671198671198671198670

= 014 + 0571198781198781198781198780

(18)

Model 14 Gopinathan and Soler [26] suggested linear equa-tion for locations with latitudes between 60N and 70N

1198671198671198671198670

= 01538 + 078741198781198781198781198780

(19a)

1198671198671198671198670

= 01961 + 072121198781198781198781198780

(19b)

Model 15 Veeran and Kumar [27] proposed the followinglinear equation for two tropical locations in India

1198671198671198671198670

= 034 + 0321198781198781198781198780

(20a)

1198671198671198671198670

= 027 + 0651198781198781198781198780

(20b)

Model 16 Tiris et al [28] also proposed the regressionconstants using the ve-year (19881992) data for Gebze

1198671198671198671198670

= 02262 + 04181198781198781198781198780

(21)

Model 17 Said et al [29] obtained the following equation toestimate monthly average daily global solar radiation

1198671198671198671198670

= 0215 + 05271198781198781198781198780

(22)

Model 18 Ulgen and Ozbalta [30] suggested the followingregression constants for Bornova Izmir Turkey

1198671198671198671198670

= 02424 + 050141198781198781198781198780

(23)

Model 19 Chegaar and Chibani [31] have proposed thefollowing linear relationship between 1198671198671198671198671198670 and 1198781198781198671198781198780 forestimating global solar radiation on horizontal surface

1198671198671198671198670

= 02424 + 050141198781198781198781198780

(24a)

1198671198671198671198670

= 02424 + 050141198781198781198781198780

(24b)

1198671198671198671198670

= 02424 + 050141198781198781198781198780

(24c)


Model 20 I T Toğural and H Toğural [32] suggested therelation for the estimation of global solar radiation in Turkey

1198671198671198671198670

= 0318 + 04491198781198781198781198780

(25a)

e results of regression analyses applied for winter (Jan-uaryndashMarch and OctoberndashDecember intervals) and summer(AprilndashSeptember) are given below

1198671198671198671198670

= 02947 + 046691198781198781198781198780

for winter (25b)

1198671198671198671198670

= 05103 + 016281198781198781198781198780

for summer (25c)

1198671198671198671198670

= 02948 + 05342119878119878119878119878nh

for winter (25d)

1198671198671198671198670

= 05067 + 01937119878119878119878119878nh

for summer (25e)

1198671198671198671198670

= 01739 ln119878119878119878119878nh

+ 06782 for winter (25f)

1198671198671198671198670

= 01124 ln119878119878119878119878nh

+ 06822 for winter (25g)

Model 21 Ulgen and Hepbasli [33] proposed the linearrelation equation for Ankara Istanbul and Izmir in Turkey

1198671198671198671198670

= 02671 + 047541198781198781198781198780

(26)

Model 22 Ahmad and Ulfat [34] also suggested the linearregression constants for Karachi Pakistan

1198671198671198671198670

= 0324 + 04051198781198781198781198780

(27)

Model 23 Jin et al [35] proposed the following relation

1198671198671198671198670

= 01332 + 064711198781198781198781198780

(28)

Model 24 El-Sabaii and Trabea [36] reported the followingrst-order Angstrom-type correlations for Egypt using themeasured data for ve Egyptian locations (Al-Arish RafahMatruh Tanta and Aswan)

1198671198671198671198670

= 03647 + 035051198781198781198781198780

(29)

Model 25 Aras et al [37] proposed the following linearequation for twelve provinces in the Central Anatolia Regionof Turkey

1198671198671198671198670

= 03078 + 041661198781198781198781198780

(30)

Model 26 Rensheng et al [38] suggested the linear equationto estimate global solar radiation as follows

1198671198671198671198670

= 0176 + 05631198781198781198781198780

(31)

Model 27 Katiyar and Pandey [39] reported the followingrst-order Angstrom-type correlations for four locations(Jodhpur Calcutta Bombay and Pune India) respectivelyfor the estimation of global solar radiation using the long-range measured data of ve years (2001ndash2005)

1198671198671198671198670

= 02276 + 051051198781198781198781198780

(32a)

1198671198671198671198670

= 02623 + 039521198781198781198781198780

(32b)

1198671198671198671198670

= 02229 + 051231198781198781198781198780

(32c)

1198671198671198671198670

= 02286 + 053091198781198781198781198780

(32d)

urther in order to develop the rst-order correlationapplicable to all Indian locations the authors combined theentire measured data of all the four locations together andanalyze to obtain the following correlation

1198671198671198671198670

= 02281 + 050931198781198781198781198780

(32e)

Over the years the following authors study the constants ofAngstrom equation

Model 28 Rietveld [40] examined several published valuesof 119886119886 and 119887119887 and noted that 119886119886 is related linearly and 119887119887hyperbolically to the appropriate yearly average value of1198781198781198781198781198780 such that

119886119886 = 010 + 0241198781198781198781198780

(33a)

119887119887 = 038 + 0081198781198781198781198780

(33b)

e Rietveld model [40] can be simplied to a constant-coefficient Angstrom-Prescott equation

1198671198671198671198670

= 018 + 0621198781198781198781198780

(34)

Model 29 Gariepty [41] has reported that the empiricalcoefficients 119886119886 and 119887119887 are dependent on mean air temperature(119879119879) and the precipitation (119875119875)

119886119886 = 03791 119886 00041119879119879 119886 00176119875119875 (35a)

119887119887 = 04810 119886 00043119879119879 119886 00097119875119875 (35b)


Model 30 Kilic and Ozturk [42] determined that the coeffi-cients 119886119886 and 119887119887 are functions of the solar declination (120575120575) with120601120601 and 119885119885 given by the following equations

119886119886 119886 119886119886119886119886119886 119886 119886119886119886119886119886119886119886119886119885119885 119886 119886119886119886119886119886 119886119886119886 10076491007649120601120601 119886 12057512057510076651007665 (36a)

119887119887 119886 119886119886119887119886119886 119886 119886119886119886119887119887 119886119886119886 10076491007649120601120601 119886 12057512057510076651007665 119886 (36b)

22 Estimation of Global Solar Radiation Using Higher OrderCorrelations Page [9] pointed out that linear-type equa-tion based on climatologically means cannot necessarily beexpected to be applicable extreme values for a particularday as it overestimates the total radiation on cloudless daysthat is when 119878119878119878119878119878119886 119886 119886 and on overcast days that is when119878119878119878119878119878119886 119886 119886 is fact was later conrmed by Benson et al[14] and Michalsky [43] who considered the relationshipon the basis of individual daily records e former studyshows a signicant downward curvature of the data pointswith discontinuity of 119867119867119878119867119867119886 at 119878119878119878119878119878119886 119886 119886 hence a quadraticform for the relationship between daily globalextraterrestrialradiation and actualmaximum possible hours of sunshinegreater than zero was employed as

119867119867119867119867119886

119886 119886119886 119886 11988711988710076531007653119878119878119878119878119886

10076691007669 119886 11988811988810076531007653119878119878119878119878119886

100766910076692119886 (37)

Higher order correlations (higher than quadratic) also havethe same property as quadratic correlations In general ahigher order correlation is written as

119867119867119867119867119886

119886 119886119886 119886 11988711988710076531007653119878119878119878119878119886

10076691007669 119886 11988811988810076531007653119878119878119878119878119886

100766910076692119886 11988911988910076531007653

119878119878119878119878119886

10076691007669119886 (38)

where 119886119886 to 119889119889 are regression coefficients

Model 31 Oumlelman et al [44] have developed second-orderpolynomial equation to estimate global solar radiation

119867119867119867119867119886

119886 119886119886119886119886119887 119886 119886119886119887119886119887 10076531007653119878119878119878119878119886

10076691007669 119886 11988611988611988611988611988610076531007653119878119878119878119878119886

100766910076692119886 (39)

Model 32 Bahel et al [45] also developed the following third-order correlation based on the measured data of global andbright sunshine hours for 48 stations around the world

119867119867119867119867119886

119886 119886119886119886119887 119886 119886119886119886119886 10076531007653119878119878119878119878119886

10076691007669 119886 11988611988611988711988610076531007653119878119878119878119878119886

100766910076692119886 119886119886119886410076531007653

119878119878119878119878119886

10076691007669119886119886

(40)

Model 33 Akinoğlu and Ecevit [46] suggested the second-order polynomials to estimate the global solar radiation forTurkey

119867119867119867119867119886

119886 1198861198861198864119887 119886 1198861198861198864119887 10076531007653119878119878119878119878119886

10076691007669 119886 119886119886211988611988610076531007653119878119878119878119878119886

100766910076692119886 (41)

Model 34 Samuel [47] proposed the ratio of global toextraterrestrial radiation as a function of the ratio of sunshinehours for third-order polynomials

119867119867119867119867119886

119886 119886 1198861198861198864 119886 21198861198872 10076531007653119878119878119878119878119886

10076691007669

119886 11988611988611988611988610076531007653119878119878119878119878119886

100766910076692119886 21198862410076531007653

119878119878119878119878119886

10076691007669119886119886

(42)

Model 35 Taşdemiroğlu and Sever [48] also developed thefollowing second-order polynomials to estimate global solarradiation for six locations of Turkey as follows

119867119867119867119867119886

119886 11988611988622119887 119886 1198861198861198861198864 10076531007653119878119878119878119878119886

10076691007669 119886 11988611988611988611988611988610076531007653119878119878119878119878119886

100766910076692119886 (43)

Model 36 Lewis [25] also proposed the following third-orderequation to estimate global radiation for locations in the stateof Tennessee USA as follows

119867119867119867119867119886

119886 119886119886119886119886 119886 1198861198861198864 10076531007653119878119878119878119878119886

10076691007669 119886 11988611988611988611988610076531007653119878119878119878119878119886

100766910076692119886 411988611988711988610076531007653

119878119878119878119878119886

10076691007669119886119886 (44)

Model 37 Yildiz and Oz [49] developed the followingsecond-order polynomials using the measured data of vestations located in different places of Turkey

119867119867119867119867119886

119886 1198861198862119886119886119886 119886 1198861198861198862119886119887 10076531007653119878119878119878119878119886

10076691007669 119886 11988611988611988611988611988611988610076531007653119878119878119878119878119886

100766910076692119886 (45)

Model 38 Aksoy [50] developed the quadratic equation toestimate global solar radiation for Turkey as follows

119867119867119867119867119886

119886 1198861198861198864119886 119886 119886119886119887119887119886 10076531007653119878119878119878119878119886

10076691007669 119886 11988611988611988611988611988610076531007653119878119878119878119878119886

100766910076692119886 (46)

Model 39 Said et al [29] obtained the following second-order equation to estimate monthly average daily global solarradiation on a horizontal surface at Tripoli Libya

119867119867119867119867119886

119886 119886119886119886 119886 1198861198861198861198864 10076531007653119878119878119878119878119886

10076691007669 119886 119886119886211988711988710076531007653119878119878119878119878119886

100766910076692119886 (47)

Model 40 Ulgen and Ozbalta [30] suggested the follow-ing second-order regression constants for Bornova IzmirTurkey

119867119867119867119867119886

119886 119886119886119886119886119887119886 119886 119886119886119886119886119887119886 10076531007653119878119878119878119878119886

10076691007669 119886 1198861198861198861198862210076531007653119878119878119878119878119886

100766910076692119886 (48)

Model 41 Ertekin and Yaldiz [51] have proposed the follow-ing third-order polynomial equations for Antalya Turkey

119867119867119867119867119886

119886 119886 211988642119886119887 119886 1198861198861198861198864119887 10076531007653119878119878119878119878119886

10076691007669

119886 119886119887119886119886411988710076531007653119878119878119878119878119886

100766910076692119886 11988611988611988611988711988611988710076531007653

119878119878119878119878119886

10076691007669119886119886

(49)


Model 42 Ulgen and Hepbasli [52] proposed the third-orderrelation for Izmir in Turkey as follows

1198671198671198671198670

= 02408 + 03625 10076531007653119878119878119878119878010076691007669

+ 04597100765310076531198781198781198781198780100766910076692minus 0370810076531007653

1198781198781198781198780100766910076693

(50)

Model 43 I T Toğural and H Toğural [32] suggestedthe third-order relation for the estimation of global solarradiation in Turkey as follows

1198671198671198671198670

= 01796 + 09813 10076531007653119878119878119878119878010076691007669

minus 02958100765310076531198781198781198781198780100766910076692minus 0265710076531007653

1198781198781198781198780100766910076693

(51a)

1198671198671198671198670

= 01587 + 13652 10076531007653119878119878119878119878nh

10076691007669

minus 0117510076531007653119878119878119878119878nh

100766910076692

for winter(51b)

1198671198671198671198670

= 0288 + 09874 10076531007653119878119878119878119878nh

10076691007669

minus 0696710076531007653119878119878119878119878nh

100766910076692

for summer(51c)

Model 44 Ulgen and Hepbasli [33] also proposed the third-order polynomial relation for Ankara Istanbul and Izmir inTurkey as follows

1198671198671198671198670

= 02854 + 02591 10076531007653119878119878119878119878010076691007669

+ 06171100765310076531198781198781198781198780100766910076692minus 0483410076531007653

1198781198781198781198780100766910076693

(52)

Model 45 Ahmad andUlfat [34] also suggested the quadraticequation for Karachi Pakistan

1198671198671198671198670

= 0348 + 0320 10076531007653119878119878119878119878010076691007669 + 007010076531007653

1198781198781198781198780100766910076692 (53)

Model 46 Tarhan and Sari [53] have proposed second andthird-order polynomialmodels to predict solar radiation overthe Central Black Sea Region of Turkey as follows

1198671198671198671198670

= 01874 + 08592 10076531007653119878119878119878119878010076691007669 minus 0476410076531007653

1198781198781198781198780100766910076692

1198671198671198671198670

= 01520 + 11334 10076531007653119878119878119878119878010076691007669

minus 11126 100765310076531198781198781198781198780100766910076692+ 0451610076531007653

1198781198781198781198780100766910076693

(54)

Model 47 Aras et al [37] also proposed the followingsecond- and third-order equations for twelve provinces in theCentral Anatolia Region of Turkey

1198671198671198671198670

= 03398 + 02868 10076531007653119878119878119878119878010076691007669 + 0118710076531007653

1198781198781198781198780100766910076692

1198671198671198671198670

= 04832 minus 06161 10076531007653119878119878119878119878010076691007669

+ 18932100765310076531198781198781198781198780100766910076692minus 1097510076531007653

1198781198781198781198780100766910076693

(55)

Model 48 Bakirchi [54] proposed third-order polynomialequation for Erzurum Turkey

1198671198671198671198670

= 06307 minus 07251 10076531007653119878119878119878119878010076691007669

+ 12089100765310076531198781198781198781198780100766910076692minus 0463310076531007653

1198781198781198781198780100766910076693

(56)

Model 49 Besides all the above empirical correlations dis-cussed a sixth order polynomial could also be tted byKatiyar et al [55] for sixteen Indian locations

1198671198671198671198670

= 1198861198866 + 1198871198876 10076531007653119878119878119878119878010076691007669 + 119888119888610076531007653

1198781198781198781198780100766910076692+ 119889119889610076531007653

1198781198781198781198780100766910076693

+ 1198901198906100765310076531198781198781198781198780100766910076694+ 119891119891610076531007653

1198781198781198781198780100766910076695+ 119892119892610076531007653

1198781198781198781198780100766910076696

(57)

where 1198861198866 1198871198876 1198881198886 1198891198896 1198901198906 1198911198916 and 1198921198926 are constants which arepresented in Table 1

Instead of polynomials regression analysis several inves-tigators reported the following multilinear regression equa-tion to predict global solar radiation

Model 50 Falayi et al [56] developed a number of multi lin-ear regression equations to predict the relationship betweenglobal solar radiations with one or more combinations of thefollowingweather parameters clearness index (1198671198671198671198671198670)meanof daily temperature (119879119879) ratio of maximum and minimumdaily temperature (120579120579120579 relative humidity (RH120579 and relativesunshine duration (1198781198781198671198781198780) for Iseyin igeria for ve years(1995ndash1999) using the Angstrom model as base

1198671198671198671198670

= 01874 + 08592 10076531007653119878119878119878119878010076691007669 minus 1567 (120579120579120579

+ 00033 (RH120579 minus 000806 (119879119879120579 (58)

Model 51 Al-Salihi et al [57] also developed multi linearregression equations for Baghdad Mosul and Rutba Iraqto predict the relationship between the ratio of global toextraterrestrial solar radiations with the combinations ofthe following weather parameters maximum temperatures


T 1 Regression coefficients of sixth order polynomial (57) for different cities of India

City 1198861198866 1198871198876 1198881198886 1198891198896 1198901198906 1198911198916 1198921198926

Trivandrum minus142 2021 minus11032 30756 minus46451 3626 minus11488Kodaikanal 33 minus549 3916 minus13792 25794 minus24391 9149Madras minus579 6079 minus25941 58039 minus71799 46596 minus12403GoaPanji minus59 996 minus5919 17255 minus26374 2031 minus6216Vishakhapatnam 32 minus316 1324 minus2603 2581 minus1216 206Pune 75 minus1265 8306 minus25871 41314 minus32705 10179Mumbai minus06 171 minus1076 336 minus5437 4374 minus1383Nagpur 87 minus1268 7441 minus21751 33763 minus26609 8383Bhaunagar 45 minus723 4606 minus14039 22179 minus17483 5429Ahmedabad minus407 557 minus29135 75484 minus103149 7127 minus19636Kolkata 1202 minus16155 88557 minus252845 396988 minus32525 108713Shilong 441 minus933 7867 minus31602 65343 minus66926 26853Jodhpur minus95485 837627 minus304722 5884925 minus636355 365339 minus869949Kanpur minus44039 450882 minus1882215 4114577 minus497959 3169214 minus829902Lucknow minus788 659775 minus228376 418576 minus428474 232305 minus52128New Delhi minus63266 666944 minus2903816 6687289 minus8594592 5846858 minus1645391

(119879119879max) sunshine duration (1198781198781198781198781198780) and relative humidity (RH)as follows

1198671198671198671198670

= 1078 + 0071 10076531007653119878119878119878119878010076691007669 + 00026 10076491007649119879119879max10076651007665

minus 000078 (RH) for Baghdad(59a)

1198671198671198671198670

= 886 + 0301 10076531007653119878119878119878119878010076691007669 + 00035 10076491007649119879119879max10076651007665

+ 000157 (RH) for Mosul(59b)

1198671198671198671198670

= 1507 + 0104 10076531007653119878119878119878119878010076691007669 + 000139 10076491007649119879119879max10076651007665

minus 000112 (RH) for Rutba(59c)

23 Estimation of Global Solar Radiation Based on AmbientTemperature

Model 52 Bristow and Campbell [58] suggested the follow-ing relationship for daily values of global solar radiation (119867119867)as a function of daily extraterrestrial solar radiation (1198671198670) andtemperature difference (Δ119879119879) as

1198671198671198671198670

= 119860119860 100771410077141 minus exp 10076501007650minus119861119861Δ1198791198791198621198621007666100766610077301007730 (60)

where Δ119879119879 = 119879119879max minus 119879119879min and 119860119860 119861119861 and 119862119862 are the empiricalcoefficients e values of 119860119860 119861119861 and 119862119862 in Bristow andCampbellrsquos model were taken to be 07 0004ndash001 and 24respectively

Model 53 Allen [59] estimated mean monthly global solarradiation as a function of 1198671198670 mean monthly maximumtemperature (119879119879119872119872) and mean monthly minimum (119879119879119898119898) as

1198671198671198671198670

= 11987011987011990311990310076491007649119879119879119872119872 minus 1198791198791198981198981007665100766505 (61a)

where119870119870119903119903 is dened as

119870119870119903119903 = 119870119870ra100765310076531198751198751198751198750

1007669100766905 (61b)

Following Lunde [60] 119870119870ra = 017 and 1198751198751198781198751198750 may be denedas

1198751198751198751198750

= exp (minus00001184 ℎ) (61c)

where 119875119875 and 1198751198750 are the values of local and standard atmo-spheric pressure respectively and ℎ is the altitude of the placein meters

Model 54 Pandey and Katiyar [61] proposed the followingrst- to third-order euations for the pairs of (1198671198671198781198671198670) and(1205791205791198781205791205790) at Jodhpur Ahmedabad Calcutta Bombay and Punestations India

1198671198671198671198670

= 02889 + 01562 lowast 10076531007653120579120579120579120579010076691007669

1198671198671198671198670

= minus1148 + 1901 lowast 10076531007653120579120579120579120579010076691007669 minus 05109 lowast 10076531007653

1205791205791205791205790100766910076692

1198671198671198671198670

= minus 5159 + 9126 lowast 10076531007653120579120579120579120579010076691007669 minus 4766 lowast 10076531007653

1205791205791205791205790100766910076692

+ 08201 lowast 100765310076531205791205791205791205790100766910076693

(62)

where 120579120579 and 1205791205790 are the maximum and minimum air temper-atures respectively

Inspite of these Ertekin et al estimated monthly averagedaily global radiation on horizontal surface for Antalya andturkey [62ndash64] Further his group compared all the existingsolar radiation models with their results [65] ey havefurther given spatial and temporal modeling of global solarradiation dynamics as a function of sunshine duration for


Turkey [66] and thereaer they have produced good resultsby assessing regional spatial-temporal dynamics of globalsolar radiation models over Turkey [67]

3 Result and Discussion

Being a clean eco-friendly domestic energy source renew-able energy will be the essential components of futuresustainable energy sources For development of suitabletheoretical model the information of solar radiation at agiven location is needed erefore we have studied the61 models from 1960 to 2010 for the ratio of global toextraterrestrial radiation as a function of the ratio of sunshineduration (linear model) higher order relationship between1198671198671198671198671198670 and 1198781198781198671198781198780 (second- third- and six-order relation)and based on ambient air temperature ere are 30 modelsderived from the Angstrom-type regression equation esemodels are also known as linearmodels because the empiricalcoefficients 119886119886 and 119887119887 were obtained from the results of therst-order regression analysis Angstrom [8] recommendedvalues of 025 and 075 respectively for the constants 119886119886 and119887119887 based on data from Stockholm It is obvious that 119886119886 119886 119887119887 1198861 because on clear days 1199041199041198671199041199040 is supposed to be equal to 1However because of the inherence in sunshine recordersmeasurements of 1199041199041198671199041199040 will never be equal to 1 So the constant119886119886 usually has values in the interval 01ndash03 and the sum119886119886 119886 119887119887 ranges from 06 to 09 Tiris et al [28] tested the(21) on the basis of statistical error tests and recommended(21) to estimate the monthly average daily global radiationfor the Gebze location in Turkey Said et al [29] comparedseven models (Rietveld [40] Dogniaux and Lemoine [68]H F Garg and S N Garg [69] Gariepty [41] Glover andMcCulloch [70] Hay [71] and Black [72]) for Tripoli andobserved that the Dogniaux and Rietveld results follow themeasured data closely over the whole year period Garg andGarg model has an excellent t for the experimental datafor the months June July August and September but itdeviates considerably for the period January to May Blackmodel was found the least accurate of all of thesemodels withnoted overestimation of global radiation for all the monthsof the years Glover and Hey results follow closely those ofDogniaux and Rietveld respectively I T Toğural and HToğural [32] developed many equations using the ratios of1198781198781198671198781198780 and 119878119878119867119878119878nh to estimate the global radiation in Turkey Itwas seen that the equations which include the summer andwinter periods gave better than the others in all the developedequations It is predictable results that the performances ofthe equations are different for the whole Turkey and for thecities Equations (25a) (25b) (25c) (25d) (25e) (25f) (51a)(51b) and (51c) gave the best results in all of the developedequations Finally these results clearly indicate that relianceon the RMSE and MBE used separately can lead to a wrongdecision in selecting the bestmodel froma suited of candidatemodels and that the use of the RMSE andMBE in isolation isnot an adequate indicator of model performance ereforethe t-statistic should be used in conjunction with these twoindicators to better evaluate a modelrsquos performance Ahmadand Ulfat [34] suggested that (27) and (53) can be used with

February April June August October December

3

6

9

12

15

18

21

24

27

Months

CampbellAllen

First

Second

ird

MeasuredG

lob

al s

ola

r ra

dia

tio

n (

kW

hm2

day

)

mdash

F 1 Measured and estimated global solar radiation forJodhpur India

condence for Karachi Pakistan with the percentage errorfor all the months being below 5 El-Sabaii and Trabea [36]reported the rst-orderAngstrom-type correlations using themeasured data for ve Egyptian locations (Al-Arish RafahMatruh Tanta and Aswan) for Egypt (29) can be used forestimating global radiation for any location of Egypt withabsolute values of the MPE less than 6

Katiyar and Pandey [39] compared our own model [39]with the theoretical estimates of Angstrom [8] Bahel et al[16] and El-Sabaii and Trabea [36] models along with themeasured data for Jodhpur Calcutta Bombay and PuneComparison of all stations shows that equation (32e) predictsmore accurate results thanAngstrom [8] Bahel et al [16] andEl-Sabaii andTrabea [36]models For further validationKati-yar and Pandey model is compared with the measured datafor Matrough Arish and Cairo cities of Egypt Katiyar andPandey [39] also observed that the second- and third-orderAngstrom-type correlations do not signicantly improve theaccuracy of the estimated global solar radiation over rstorder

Using multi linear regression analysis Falayi et al [56]reported that (58) has the highest value of correlationcoefficient and correlation determination which gives goodresults

Since the air temperature is a worldwide measuredmeteorological parameter it rarely used in solar radiationtechniqueserefore we have compared the results with thetheoretical estimates of Pandey and Katiyar [61] Bristow andCampbell [58] and Allen [59] as well as with measured datathrough Figure 1

Comparison shows that Bristow and Campbellrsquos [58]model for Ahmedabad Calcutta and Pune shows higher


values of global radiation due to higher values of temperaturedeference while Allen [59] model gives satisfactory resultsHowever Pandey and Katiyar [61] model with their third-order correlation provide more accurate estimates than Bris-tow and Campbell and Allen models

4 Conclusions

In the absence and scarcity of trustworthy solar radiationdata the need for empirical model to predict and estimateglobal solar radiation seems inevitable Sunshine-basedmod-els are employed for estimation of global solar radiation fora location ese models given in this study will enable thesolar energy researcher to use the estimated data due tone agreement with the observed data Most of the modelsgiven to estimate the monthly average daily global solarradiation are of the modied Angstrom-type relation It isalso concluded that the rst-orderAngstrom-type correlationsupercedes over second and third orders not only for theaccuracy of estimated monthly average daily global radiationon horizontal surface but also requires less computationalwork Katiyar and Pandey model (32e) was found as the mostaccurate model for the estimation of monthly average dailyglobal radiation on horizontal surface for Indian locationEquation (32e) may also be extended for other locationswhich have the same values of the maximum clearness indexe temperature base model also indicates that Pandey andKatiyar model (Model 54) has good potential for use inestimating values of monthly average global solar radiationon horizontal surface for the locations where measurementsof the sunshine duration are not available

References

[1] S Singh and U Bajpai ldquoIntegrated energy planning for sustain-able development in rural-areas a case study fromEasternUttarPradeshrdquo International Journal of Energy and Environmentalvol 1 pp 1083ndash1096 2010

[2] G Loacutepez F J Batlles and J Tovar-Pescador ldquoA new sim-ple parameterization of daily clear-sky global solar radiationincluding horizon effectsrdquo Energy Conversion andManagementvol 48 no 1 pp 226ndash233 2007

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

[4] T Muneer S Younes and S Munawwar ldquoDiscourses onsolar radiation modelingrdquo Renewable and Sustainable EnergyReviews vol 11 no 4 pp 551ndash602 2007

[5] S Sa A Zeroual and M Hassani ldquoPrediction of global dailysolar radiation using higher order statisticsrdquo Renewable Energyvol 27 no 4 pp 647ndash666 2002

[6] M Donatelli G Bellocchi and F Fontana ldquoRadEst300 so-ware to estimate daily radiation data from commonly availablemeteorological variablesrdquo European Journal of Agronomy vol18 no 3-4 pp 363ndash367 2003

[7] S Younes and T Muneer ldquoImprovements in solar radiationmodels based on cloud datardquo Building Services EngineeringResearch and Technology vol 27 no 1 pp 41ndash54 2006

[8] AAngstrom ldquoSolar and terrestrial radiationrdquoQuarterly Journalof the RoyalMeteorological Society vol 50 no 210 pp 121ndash1261924

[9] J K Page ldquoe estimation ofmonthlymean values of daily totalshort wave radiation on-vertical and inclined surfaces from sunshine records for latitudes 400Nndash400 Srdquo in Proceedings of theUnited Nations Conference on New Sources of Energy vol 98no 4 pp 378ndash390 1961

[10] J A Prescott ldquoEvaporation from water surface in relationto solar radiationrdquo Transactions of the Royal Society of SouthAustralia vol 64 pp 114ndash118 1940

[11] S A Klein ldquoCalculation of monthly average insolation on tiltedsurfacesrdquo Solar Energy vol 19 no 4 pp 325ndash329 1977

[12] P I Cooper ldquoe absorption of radiation in solar stillsrdquo SolarEnergy vol 12 no 3 pp 333ndash346 1969

[13] A Khogali M R I Ramadan Z E H Ali and Y A FattahldquoGlobal and diffuse solar irradiance in Yemen (YAR)rdquo SolarEnergy vol 31 no 1 pp 55ndash62 1983

[14] R B Benson M V Paris J E Sherry and C G JustusldquoEstimation of daily andmonthly direct diffuse and global solarradiation from sunshine durationmeasurementsrdquo Solar Energyvol 32 no 4 pp 523ndash535 1984

[15] H PGarg and SNGarg ldquoCorrelation ofmonthly-average dailyglobal diffuse and beam radiation with bright sunshine hoursrdquoEnergy Conversion andManagement vol 25 no 4 pp 409ndash4171985

[16] V Bahel R Srinivasan and H Bakhsh ldquoSolar radiation forDhahran Saudi Arabiardquo Energy vol 11 no 10 pp 985ndash9891986

[17] P C Jain ldquoGlobal irradiation estimation for Italian locationsrdquoSolar and Wind Technology vol 3 no 4 pp 323ndash328 1986

[18] M A Alsaad ldquoCharacteristic distribution of global solar radia-tion for Amman Jordanrdquo Solar andWind Technology vol 7 no2-3 pp 261ndash266 1990

[19] S Jain and P C Jain ldquoA comparison of the Angstrom-typecorrelations and the estimation of monthly average daily globalirradiationrdquo Solar Energy vol 40 no 2 pp 93ndash98 1988

[20] P V C Luhanga and J Andringa ldquoCharacteristics of solarradiation at Sebele Gaborone Botswanardquo Solar Energy vol 44no 2 pp 77ndash81 1990

[21] I A Raja and J W Twidell ldquoDistribution of global insolationover Pakistanrdquo Solar Energy vol 44 no 2 pp 63ndash71 1990

[22] I A Raja and J W Twidell ldquoDiurnal variation of globalinsolation over ve locations in Pakistanrdquo Solar Energy vol 44no 2 pp 73ndash76 1990

[23] P C Jain ldquoA model for diffuse and global irradiation onhorizontal surfacesrdquo Solar Energy vol 45 no 5 pp 301ndash3081990

[24] A Louche G Notton P Poggi and G Simonnot ldquoCorrelationsfor direct normal and global horizontal irradiation on a FrenchMediterranean siterdquo Solar Energy vol 46 no 4 pp 261ndash2661991

[25] G Lewis ldquoAn empirical relation for estimating global irradi-ation for Tennessee USArdquo Energy Conversion and Manage-ment vol 33 no 12 pp 1097ndash1099 1992

[26] K K Gopinathan and A Soler ldquoA sunshine dependent globalinsolation model for latitudes between 60∘N and 70∘Nrdquo Renew-able Energy vol 2 no 4-5 pp 401ndash404 1992

[27] P K Veeran and S Kumar ldquoAnalysis of monthly average dailyglobal radiation and monthly average sunshine duration at two


tropical locationsrdquo Renewable Energy vol 3 no 8 pp 935ndash9391993

[28] M Tiris C Tiris and I E Ture ldquoCorrelations of monthly-average daily global diffuse and beam radiations with hoursof bright sunshine in Gebze Turkeyrdquo Energy Conversion andManagement vol 37 no 9 pp 1417ndash1421 1996

[29] R Said M Mansor and T Abuain ldquoEstimation of global anddiffuse radiation at Tripolirdquo Renewable Energy vol 14 no 1ndash4pp 221ndash227 1998

[30] K Ulgen and N Ozbalta ldquoMeasured and estimated global radi-ation on horizontal surface for Bornova Izmirrdquo in Proceedingsof the 12th Nationalermal Science and Technical Congress pp113ndash118 Izmir Turkey 2000

[31] M Chegaar and A Chibani ldquoGlobal solar radiation estimationin Algeriardquo Energy Conversion and Management vol 42 no 8pp 967ndash973 2001

[32] I T Toğrul and H Toğrul ldquoGlobal solar radiation overTurkey comparison of predicted and measured datardquo Renew-able Energy vol 25 no 1 pp 55ndash67 2002

[33] K Ulgen and A Hepbasli ldquoSolar radiation models Part 2comparison and developing new modelsrdquo Energy Sources vol26 no 5 pp 521ndash530 2004

[34] F Ahmad and I Ulfat ldquoEmpirical models for the correlationof monthly average daily global solar radiation with hours ofsunshine on a horizontal surface at Karachi Pakistanrdquo TurkishJournal of Physics vol 28 no 5 pp 301ndash307 2004

[35] Z Jin W Yezheng and Y Gang ldquoGeneral formula for estima-tion of monthly average daily global solar radiation in ChinardquoEnergy Conversion andManagement vol 46 no 2 pp 257ndash2682005

[36] A A El-Sabaii and A A Trabea ldquoEstimation of global solarradiation on horizontal surfaces over Egyptrdquo Egyptian Journalof Solids vol 28 pp 163ndash175 2005

[37] H Aras O Balli and A Hepbasli ldquoGlobal solar radiationpotential part 1 model developmentrdquo Energy Sources B vol 1no 3 pp 303ndash315 2006

[38] C Rensheng L Shihua K Ersi Y Jianping and J XibinldquoEstimating daily global radiation using two types of revisedmodels in Chinardquo Energy Conversion and Management vol 47no 7-8 pp 865ndash878 2006

[39] A K Katiyar and C K Pandey ldquoSimple correlation forestimating the global solar radiation on horizontal surfaces inIndiardquo Energy vol 35 no 12 pp 5043ndash5048 2010

[40] M R Rietveld ldquoA new method for estimating the regressioncoefficients in the formula relating solar radiation to sunshinerdquoAgricultural Meteorology vol 19 no 2-3 pp 243ndash252 1978

[41] J Gariepty ldquoEstimation of global solar radiationrdquo InternationalReport Service of meteorology Government of Quebec Que-bec Canada 1980

[42] A Kilic and A Ozturk Solar Energy Kipas DistributionIstanbul Turkey 1983

[43] J J Michalsky ldquoComparison of a National Weather ServiceFoster sunshine recorder and the World Meteorological Orga-nization standard for sunshine durationrdquo Solar Energy vol 48no 2 pp 133ndash141 1992

[44] H Oumlgelman A Ecevit and E Tasdemiroğlu ldquoA new methodfor estimating solar radiation from bright sunshine datardquo SolarEnergy vol 33 no 6 pp 619ndash625 1984

[45] V Bahel H Bakhsh and R Srinivasan ldquoA correlation forestimation of global solar radiationrdquo Energy vol 12 no 2 pp131ndash135 1987

[46] B G Akinoğlu and A Ecevit ldquoA further comparison anddiscussion of sunshine-based models to estimate global solarradiationrdquo Energy vol 15 no 10 pp 865ndash872 1990

[47] T D M A Samuel ldquoEstimation of global radiation for SriLankardquo Solar Energy vol 47 no 5 pp 333ndash337 1991

[48] E Taşdemiroğlu and R Sever ldquoAn improved correlationfor estimating solar radiation from bright sunshine data forTurkeyrdquo Energy vol 16 no 6 pp 787ndash790 1991

[49] M Yildiz and S Oz ldquoEvaluation of the solar energy potential ofTurkeyrdquo in Proceedings of the 6th National Energy Congress pp250ndash260 1994

[50] B Aksoy ldquoEstimated monthly average global radiation forTurkey and its comparison with observationsrdquo RenewableEnergy vol 10 no 4 pp 625ndash633 1997

[51] C Ertekin and O Yaldiz ldquoComparison of some existing modelsfor estimating global solar radiation for Antalya (Turkey)rdquoEnergy Conversion andManagement vol 41 no 4 pp 311ndash3302000

[52] K Ulgen and A Hepbasli ldquoEstimation of solar radiationparameters for Izmir Turkeyrdquo International Journal of EnergyResearch vol 26 no 9 pp 807ndash823 2002

[53] S Tarhan and A Sari ldquoModel selection for global and diffuseradiation over the Central Black Sea (CBS) region of TurkeyrdquoEnergy Conversion andManagement vol 46 no 4 pp 605ndash6132005

[54] K Bakirchi ldquoEstimation of global solar radiation on horizontalsurfacerdquo Journal of ermal Science and Technology vol 27 pp7ndash11 2007

[55] A K Katiyar V K Katiyar A Kumar and C K Pandey ldquoSixthorder empirical relationship for estimatingglobal solar radiationfrom sunshine hoursrdquo Jour PAS vol 15 pp 156ndash165 2008

[56] E O Falayi J O Adepitan and A B Rabiu ldquoEmpirical modelsfor the correlation of global solar radiation with meteorologicaldata for Iseyin Nigeriardquo International Journal of Physical Sci-ences vol 3 no 9 pp 210ndash216 2008

[57] M A Al-Salihi M M Kadam and J A Mohammed ldquoEstima-tion of global solar radiation onhorizontal surface using routinemeteorological measurements for different cities in Iraqrdquo AsianJournal of Scientic Research vol 3 pp 240ndash248 2010

[58] K L Bristow and G S Campbell ldquoOn the relationship betweenincoming solar radiation and daily maximum and minimumtemperaturerdquo Agricultural and Forest Meteorology vol 31 no2 pp 159ndash166 1984

[59] R G Allen ldquoSelf-calibrating method for estimating solar radi-ation from air temperaturerdquo Journal of Hydrologic Engineeringvol 2 no 2 pp 56ndash67 1997

[60] P J Lunde Solar ermal Engineering Space Heating and HotWater Systems Wiley New York NY USA 1979

[61] C K Pandey and A K Katiyar ldquoTemperature base correlationfor the estimation of global solar radiation on horizontalsurfacerdquo International Journal of Energy and Environmental vol1 no 4 pp 737ndash744 2010

[62] C Ertekin and O Yaldiz ldquoEstimation of monthly average dailyglobal radiation on horizontal surface for Antalya (Turkey)rdquoRenewable Energy vol 17 no 1 pp 95ndash102 1999

[63] H O Menges C Ertekin and M H Sonmete ldquoEvaluationof global solar radiation models for Konya Turkeyrdquo EnergyConversion andManagement vol 47 no 18-19 pp 3149ndash31732006

[64] M H Sonmete C Ertekin H OMengec H Hacıseferoğullarıand F Evrendilek ldquoA comparative analysis of solar radiation


models over Ankara Turkeyrdquo Environmental Monitoring Asses-ment vol 175 pp 251ndash277 2011

[65] C Ertekin and F Evrendilek ldquoSpatio-temporal modeling ofglobal solar radiation dynamics as a function of sunshineduration for Turkeyrdquo Agricultural and Forest Meteorology vol145 no 1-2 pp 36ndash47 2007

[66] F ev Evrendilek and C Ertekin ldquoStatistical modeling of spatio-temporal variability in monthly average daily solar radiationover Turkeyrdquo Sensors vol 7 no 11 pp 2763ndash2778 2007

[67] F ev Evrendilek and C Ertekin ldquoAssessing solar radiationmod-els using multiple variables over Turkeyrdquo Climate Dynamicsvol 31 no 2-3 pp 131ndash149 2008

[68] R ogniaux and M Lemoine ldquoClassication of radiation interms of different indices of atmospheric transparencyrdquo in Pro-ceedings of the International Daylighting Conference PhoenixAriz USA February 1983

[69] H F Garg and S N Garg ldquoGlobal solar radiation climate ofLibyardquo Energy Conversion and Management vol 23 p 4131983

[70] J Glover and J S C McCulloch ldquoe empirical relationbetween solar radiation and hours of sunshinerdquo QuarterlyJournal of the Royal Meteorological Society vol 84 pp 172ndash1751958

[71] J E Hay ldquoA revised method for determining the direct and dif-fuse components of the total shortwave radiationrdquo Atmospherevol 14 pp 278ndash287 1976

[72] J N Black ldquoe distribution of solar radiation over the earthrsquossurfacerdquo Archiv fuumlr Meteorologie Geophysik und Bioklimatolo-gie vol 7 pp 165ndash189 1956

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


an enhanced RPS (renewable portfolio standards) target of33 by 2020mdashup from the 2010 target of 20 Mexico pro-poses to more than double the share of electricity generatedfrom renewable from the existing 33 to 76 by 2012us a consensus is being developed that the utilization ofrenewable energy can be a tool for curbing carbon emissions

To overcome the dependency on conventional fuelsresearchers and many organizations are working on alter-native fuels which should be commercially viable easy touse less pollutant and must be abundant in nature Inthis direction renewable energies like Solar Energy TidalEnergy Wind Energy Biofuels and so forth are suitablethan conventional sources of energy ese nonconventionalforms are not only renewable but also maintain ecology andenvironment as they are eco-friendly and do not contributein global warming and production of green house gases andso forth

It is well known that solar energy is the source of lifeon earth It heats its atmosphere and its lands generatesits winds drives the water cycle warms its oceans growsits plants feeds its animals and even (over the long haul)produces its fossil fuels is energy can be converted intoheat and cold driving force and electricity Since solarradiation is vital to solar energy system design everywherewhere adequate observations are missing [2] ereforeinformation on solar radiation and its components at agiven location is very essential e best database would bethe long-term measured data at the site of the proposedsolar system However the limited coverage of radiationmeasuring networks dictates the need for developing solarradiation models [3] emain objective of the present studyis to review solar radiation (global radiation)models for Indiaand some of its provinces

2 ReviewModels

It is generally accepted that models for solar radiationprediction are necessary because in most cases the densityand number of solar radiation measuring stations cannotdescribe the necessary variability [4] It is understandablethen that new models and improvements to existing mod-eling techniques are continually proposed which intend toimprove estimates of solar radiation values with the use ofmore readily available meteorological variables [5ndash7]

21 Estimation of Global Solar Radiation Using Angstrom-Type Models Angstrom [8] proposed the rst theoreticalmodel for estimating global solar radiation based on sunshineduration Page [9] and Prescott [10] reconsidered this modelin order to make it possible to calculate monthly average ofthe daily global radiation 119867119867 (MJm2 day) on a horizontalsurface from monthly average daily total insolation on anextraterrestrial horizontal surface as per the following rela-tion

1198671198671198671198670

= 119886119886 119886 11988611988610076531007653119878119878119878119878010076691007669 (1)

where119867119867 is the monthly average global radiation on horizon-tal surface 119878119878 is the monthly average daily bright sunshinehours 1198781198780 is the maximum possible monthly average dailysunshine hours or the day length 119886119886 and 119886119886 are constantsand1198671198670 is the monthly average daily extraterrestrial radiation(MJm2 day) which can be expressed as [11]

1198671198670 =24120587120587119868119868sc 100771710077171 119886 033 cos 10076521007652

360119863119863119899119899365

1007668100766810076681007668

times 10077161007716cos 119871119871 cos 119871119871 s119871119871 119871119871119904119904 1198862120587120587119871119871119904119904360

s119871119871 119871119871 s119871119871 11987111987110077321007732 (2)

where 119871119871119904119904 is sunset hour angle in degree and dened as

119871119871119904119904 = cosminus1 (minus ta119871 119871119871 ta119871 119871119871) (3)

119868119868sc is the solar constant 119871119871 is the latitude of location underconsideration119863119863119899119899 is the day of year starting fromrst Januaryand 119871119871 is declination angle as given below

119871119871 = 2345 s119871119871 10077181007718360 10076491007649284 119886 11986311986311989911989910076651007665

36510077341007734 (4)

For a givenmonth the maximum possible sunshine durationcan be computed by the following equation [12]

1198781198780 =215

cosminus1 (minus ta119871 119871119871 ta119871 119871119871) (5)

e regression models that have been proposed in theliterature are given below

Model 1 Page [9] has given the coecients of modiedAngstrom model as the following

1198671198671198671198670

= 023 119886 0481198781198781198781198780 (6)

Model 2 Kholagi et al [13] obtained the following linearequations from the data measured at three different stationsin Yemen

1198671198671198671198670

= 0191 119886 05711198781198781198781198780 (7a)

1198671198671198671198670

= 0297 119886 04321198781198781198781198780 (7b)

1198671198671198671198670

= 0262 119886 04541198781198781198781198780 (7c)

Model 3 Benson et al [14] have obtained regression con-stants in to two intervals of a year depending on the climaticparameters

1198671198671198671198670

= 018 119886 0601198781198781198781198780

for JanndashMarch and OctndashDec

(8a)

1198671198671198671198670

= 024 119886 0531198781198781198781198780

for rest of the month (8b)



1198671198671198671198670

= 03156 + 045201198781198781198781198780

(9)


1198671198671198671198670

= 0175 + 05521198781198781198781198780

(10)


1198671198671198671198670

= 0177 + 06921198781198781198781198780

(11)


1198671198671198671198670

= 0174 + 06151198781198781198781198780

(12)


1198671198671198671198670

= 0240 + 05131198781198781198781198780

(13)


1198671198671198671198670

= 0241 + 04881198781198781198781198780

(14)


1198671198671198671198670

= 0335 + 03671198781198781198781198780

(15a)

1198671198671198671198670

= 0388 cosΦ + 03671198781198781198781198780

(15b)


1198671198671198671198670

= 0313 + 04741198781198781198781198780

(16a)

1198671198671198671198670

= 0307 + 04881198781198781198781198780

(16b)

1198671198671198671198670

= 0309 + 05991198781198781198781198780

(16c)


1198671198671198671198670

= 0309 + 05991198781198781198781198780

(17)


1198671198671198671198670

= 014 + 0571198781198781198781198780

(18)


1198671198671198671198670

= 01538 + 078741198781198781198781198780

(19a)

1198671198671198671198670

= 01961 + 072121198781198781198781198780

(19b)


1198671198671198671198670

= 034 + 0321198781198781198781198780

(20a)

1198671198671198671198670

= 027 + 0651198781198781198781198780

(20b)


1198671198671198671198670

= 02262 + 04181198781198781198781198780

(21)


1198671198671198671198670

= 0215 + 05271198781198781198781198780

(22)


1198671198671198671198670

= 02424 + 050141198781198781198781198780

(23)


1198671198671198671198670

= 02424 + 050141198781198781198781198780

(24a)

1198671198671198671198670

= 02424 + 050141198781198781198781198780

(24b)

1198671198671198671198670

= 02424 + 050141198781198781198781198780

(24c)



1198671198671198671198670

= 0318 + 04491198781198781198781198780

(25a)


1198671198671198671198670

= 02947 + 046691198781198781198781198780

for winter (25b)

1198671198671198671198670

= 05103 + 016281198781198781198781198780

for summer (25c)

1198671198671198671198670

= 02948 + 05342119878119878119878119878nh

for winter (25d)

1198671198671198671198670

= 05067 + 01937119878119878119878119878nh

for summer (25e)

1198671198671198671198670

= 01739 ln119878119878119878119878nh


1198671198671198671198670

= 01124 ln119878119878119878119878nh



1198671198671198671198670

= 02671 + 047541198781198781198781198780

(26)


1198671198671198671198670

= 0324 + 04051198781198781198781198780

(27)


1198671198671198671198670

= 01332 + 064711198781198781198781198780

(28)


1198671198671198671198670

= 03647 + 035051198781198781198781198780

(29)


1198671198671198671198670

= 03078 + 041661198781198781198781198780

(30)


1198671198671198671198670

= 0176 + 05631198781198781198781198780

(31)


1198671198671198671198670

= 02276 + 051051198781198781198781198780

(32a)

1198671198671198671198670

= 02623 + 039521198781198781198781198780

(32b)

1198671198671198671198670

= 02229 + 051231198781198781198781198780

(32c)

1198671198671198671198670

= 02286 + 053091198781198781198781198780

(32d)


1198671198671198671198670

= 02281 + 050931198781198781198781198780

(32e)



119886119886 = 010 + 0241198781198781198781198780

(33a)

119887119887 = 038 + 0081198781198781198781198780

(33b)


1198671198671198671198670

= 018 + 0621198781198781198781198780

(34)


119886119886 = 03791 119886 00041119879119879 119886 00176119875119875 (35a)

119887119887 = 04810 119886 00043119879119879 119886 00097119875119875 (35b)



119886119886 119886 119886119886119886119886119886 119886 119886119886119886119886119886119886119886119886119885119885 119886 119886119886119886119886119886 119886119886119886 10076491007649120601120601 119886 12057512057510076651007665 (36a)

119887119887 119886 119886119886119887119886119886 119886 119886119886119886119887119887 119886119886119886 10076491007649120601120601 119886 12057512057510076651007665 119886 (36b)


119867119867119867119867119886

119886 119886119886 119886 11988711988710076531007653119878119878119878119878119886

10076691007669 119886 11988811988810076531007653119878119878119878119878119886

100766910076692119886 (37)


119867119867119867119867119886

119886 119886119886 119886 11988711988710076531007653119878119878119878119878119886

10076691007669 119886 11988811988810076531007653119878119878119878119878119886

100766910076692119886 11988911988910076531007653

119878119878119878119878119886

10076691007669119886 (38)



119867119867119867119867119886

119886 119886119886119886119886119887 119886 119886119886119887119886119887 10076531007653119878119878119878119878119886

10076691007669 119886 11988611988611988611988611988610076531007653119878119878119878119878119886

100766910076692119886 (39)


119867119867119867119867119886

119886 119886119886119886119887 119886 119886119886119886119886 10076531007653119878119878119878119878119886

10076691007669 119886 11988611988611988711988610076531007653119878119878119878119878119886

100766910076692119886 119886119886119886410076531007653

119878119878119878119878119886

10076691007669119886119886

(40)


119867119867119867119867119886

119886 1198861198861198864119887 119886 1198861198861198864119887 10076531007653119878119878119878119878119886

10076691007669 119886 119886119886211988611988610076531007653119878119878119878119878119886

100766910076692119886 (41)


119867119867119867119867119886

119886 119886 1198861198861198864 119886 21198861198872 10076531007653119878119878119878119878119886

10076691007669

119886 11988611988611988611988610076531007653119878119878119878119878119886

100766910076692119886 21198862410076531007653

119878119878119878119878119886

10076691007669119886119886

(42)


119867119867119867119867119886

119886 11988611988622119887 119886 1198861198861198861198864 10076531007653119878119878119878119878119886

10076691007669 119886 11988611988611988611988611988610076531007653119878119878119878119878119886

100766910076692119886 (43)


119867119867119867119867119886

119886 119886119886119886119886 119886 1198861198861198864 10076531007653119878119878119878119878119886

10076691007669 119886 11988611988611988611988610076531007653119878119878119878119878119886

100766910076692119886 411988611988711988610076531007653

119878119878119878119878119886

10076691007669119886119886 (44)


119867119867119867119867119886

119886 1198861198862119886119886119886 119886 1198861198861198862119886119887 10076531007653119878119878119878119878119886

10076691007669 119886 11988611988611988611988611988611988610076531007653119878119878119878119878119886

100766910076692119886 (45)


119867119867119867119867119886

119886 1198861198861198864119886 119886 119886119886119887119887119886 10076531007653119878119878119878119878119886

10076691007669 119886 11988611988611988611988611988610076531007653119878119878119878119878119886

100766910076692119886 (46)


119867119867119867119867119886

119886 119886119886119886 119886 1198861198861198861198864 10076531007653119878119878119878119878119886

10076691007669 119886 119886119886211988711988710076531007653119878119878119878119878119886

100766910076692119886 (47)


119867119867119867119867119886

119886 119886119886119886119886119887119886 119886 119886119886119886119886119887119886 10076531007653119878119878119878119878119886

10076691007669 119886 1198861198861198861198862210076531007653119878119878119878119878119886

100766910076692119886 (48)


119867119867119867119867119886

119886 119886 211988642119886119887 119886 1198861198861198861198864119887 10076531007653119878119878119878119878119886

10076691007669

119886 119886119887119886119886411988710076531007653119878119878119878119878119886

100766910076692119886 11988611988611988611988711988611988710076531007653

119878119878119878119878119886

10076691007669119886119886

(49)



1198671198671198671198670

= 02408 + 03625 10076531007653119878119878119878119878010076691007669

+ 04597100765310076531198781198781198781198780100766910076692minus 0370810076531007653

1198781198781198781198780100766910076693

(50)


1198671198671198671198670

= 01796 + 09813 10076531007653119878119878119878119878010076691007669

minus 02958100765310076531198781198781198781198780100766910076692minus 0265710076531007653

1198781198781198781198780100766910076693

(51a)

1198671198671198671198670

= 01587 + 13652 10076531007653119878119878119878119878nh

10076691007669

minus 0117510076531007653119878119878119878119878nh

100766910076692

for winter(51b)

1198671198671198671198670

= 0288 + 09874 10076531007653119878119878119878119878nh

10076691007669

minus 0696710076531007653119878119878119878119878nh

100766910076692

for summer(51c)


1198671198671198671198670

= 02854 + 02591 10076531007653119878119878119878119878010076691007669

+ 06171100765310076531198781198781198781198780100766910076692minus 0483410076531007653

1198781198781198781198780100766910076693

(52)


1198671198671198671198670

= 0348 + 0320 10076531007653119878119878119878119878010076691007669 + 007010076531007653

1198781198781198781198780100766910076692 (53)


1198671198671198671198670

= 01874 + 08592 10076531007653119878119878119878119878010076691007669 minus 0476410076531007653

1198781198781198781198780100766910076692

1198671198671198671198670

= 01520 + 11334 10076531007653119878119878119878119878010076691007669

minus 11126 100765310076531198781198781198781198780100766910076692+ 0451610076531007653

1198781198781198781198780100766910076693

(54)


1198671198671198671198670

= 03398 + 02868 10076531007653119878119878119878119878010076691007669 + 0118710076531007653

1198781198781198781198780100766910076692

1198671198671198671198670

= 04832 minus 06161 10076531007653119878119878119878119878010076691007669

+ 18932100765310076531198781198781198781198780100766910076692minus 1097510076531007653

1198781198781198781198780100766910076693

(55)


1198671198671198671198670

= 06307 minus 07251 10076531007653119878119878119878119878010076691007669

+ 12089100765310076531198781198781198781198780100766910076692minus 0463310076531007653

1198781198781198781198780100766910076693

(56)


1198671198671198671198670

= 1198861198866 + 1198871198876 10076531007653119878119878119878119878010076691007669 + 119888119888610076531007653

1198781198781198781198780100766910076692+ 119889119889610076531007653

1198781198781198781198780100766910076693

+ 1198901198906100765310076531198781198781198781198780100766910076694+ 119891119891610076531007653

1198781198781198781198780100766910076695+ 119892119892610076531007653

1198781198781198781198780100766910076696

(57)




1198671198671198671198670

= 01874 + 08592 10076531007653119878119878119878119878010076691007669 minus 1567 (120579120579120579

+ 00033 (RH120579 minus 000806 (119879119879120579 (58)




City 1198861198866 1198871198876 1198881198886 1198891198896 1198901198906 1198911198916 1198921198926



1198671198671198671198670

= 1078 + 0071 10076531007653119878119878119878119878010076691007669 + 00026 10076491007649119879119879max10076651007665


1198671198671198671198670

= 886 + 0301 10076531007653119878119878119878119878010076691007669 + 00035 10076491007649119879119879max10076651007665

+ 000157 (RH) for Mosul(59b)

1198671198671198671198670

= 1507 + 0104 10076531007653119878119878119878119878010076691007669 + 000139 10076491007649119879119879max10076651007665




1198671198671198671198670

= 119860119860 100771410077141 minus exp 10076501007650minus119861119861Δ1198791198791198621198621007666100766610077301007730 (60)



1198671198671198671198670

= 11987011987011990311990310076491007649119879119879119872119872 minus 1198791198791198981198981007665100766505 (61a)

where119870119870119903119903 is dened as

119870119870119903119903 = 119870119870ra100765310076531198751198751198751198750

1007669100766905 (61b)


1198751198751198751198750

= exp (minus00001184 ℎ) (61c)



1198671198671198671198670

= 02889 + 01562 lowast 10076531007653120579120579120579120579010076691007669

1198671198671198671198670


1205791205791205791205790100766910076692

1198671198671198671198670


1205791205791205791205790100766910076692

+ 08201 lowast 100765310076531205791205791205791205790100766910076693

(62)








3

6

9

12

15

18

21

24

27

Months

CampbellAllen

First

Second

ird

MeasuredG

lob

al s

ola

r ra

dia

tio

n (

kW

hm2

day

)

mdash









4 Conclusions


References

















































































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



















1198671198671198671198670

= 03156 + 045201198781198781198781198780

(9)


1198671198671198671198670

= 0175 + 05521198781198781198781198780

(10)


1198671198671198671198670

= 0177 + 06921198781198781198781198780

(11)


1198671198671198671198670

= 0174 + 06151198781198781198781198780

(12)


1198671198671198671198670

= 0240 + 05131198781198781198781198780

(13)


1198671198671198671198670

= 0241 + 04881198781198781198781198780

(14)


1198671198671198671198670

= 0335 + 03671198781198781198781198780

(15a)

1198671198671198671198670

= 0388 cosΦ + 03671198781198781198781198780

(15b)


1198671198671198671198670

= 0313 + 04741198781198781198781198780

(16a)

1198671198671198671198670

= 0307 + 04881198781198781198781198780

(16b)

1198671198671198671198670

= 0309 + 05991198781198781198781198780

(16c)


1198671198671198671198670

= 0309 + 05991198781198781198781198780

(17)


1198671198671198671198670

= 014 + 0571198781198781198781198780

(18)


1198671198671198671198670

= 01538 + 078741198781198781198781198780

(19a)

1198671198671198671198670

= 01961 + 072121198781198781198781198780

(19b)


1198671198671198671198670

= 034 + 0321198781198781198781198780

(20a)

1198671198671198671198670

= 027 + 0651198781198781198781198780

(20b)


1198671198671198671198670

= 02262 + 04181198781198781198781198780

(21)


1198671198671198671198670

= 0215 + 05271198781198781198781198780

(22)


1198671198671198671198670

= 02424 + 050141198781198781198781198780

(23)


1198671198671198671198670

= 02424 + 050141198781198781198781198780

(24a)

1198671198671198671198670

= 02424 + 050141198781198781198781198780

(24b)

1198671198671198671198670

= 02424 + 050141198781198781198781198780

(24c)



1198671198671198671198670

= 0318 + 04491198781198781198781198780

(25a)


1198671198671198671198670

= 02947 + 046691198781198781198781198780

for winter (25b)

1198671198671198671198670

= 05103 + 016281198781198781198781198780

for summer (25c)

1198671198671198671198670

= 02948 + 05342119878119878119878119878nh

for winter (25d)

1198671198671198671198670

= 05067 + 01937119878119878119878119878nh

for summer (25e)

1198671198671198671198670

= 01739 ln119878119878119878119878nh


1198671198671198671198670

= 01124 ln119878119878119878119878nh



1198671198671198671198670

= 02671 + 047541198781198781198781198780

(26)


1198671198671198671198670

= 0324 + 04051198781198781198781198780

(27)


1198671198671198671198670

= 01332 + 064711198781198781198781198780

(28)


1198671198671198671198670

= 03647 + 035051198781198781198781198780

(29)


1198671198671198671198670

= 03078 + 041661198781198781198781198780

(30)


1198671198671198671198670

= 0176 + 05631198781198781198781198780

(31)


1198671198671198671198670

= 02276 + 051051198781198781198781198780

(32a)

1198671198671198671198670

= 02623 + 039521198781198781198781198780

(32b)

1198671198671198671198670

= 02229 + 051231198781198781198781198780

(32c)

1198671198671198671198670

= 02286 + 053091198781198781198781198780

(32d)


1198671198671198671198670

= 02281 + 050931198781198781198781198780

(32e)



119886119886 = 010 + 0241198781198781198781198780

(33a)

119887119887 = 038 + 0081198781198781198781198780

(33b)


1198671198671198671198670

= 018 + 0621198781198781198781198780

(34)


119886119886 = 03791 119886 00041119879119879 119886 00176119875119875 (35a)

119887119887 = 04810 119886 00043119879119879 119886 00097119875119875 (35b)



119886119886 119886 119886119886119886119886119886 119886 119886119886119886119886119886119886119886119886119885119885 119886 119886119886119886119886119886 119886119886119886 10076491007649120601120601 119886 12057512057510076651007665 (36a)

119887119887 119886 119886119886119887119886119886 119886 119886119886119886119887119887 119886119886119886 10076491007649120601120601 119886 12057512057510076651007665 119886 (36b)


119867119867119867119867119886

119886 119886119886 119886 11988711988710076531007653119878119878119878119878119886

10076691007669 119886 11988811988810076531007653119878119878119878119878119886

100766910076692119886 (37)


119867119867119867119867119886

119886 119886119886 119886 11988711988710076531007653119878119878119878119878119886

10076691007669 119886 11988811988810076531007653119878119878119878119878119886

100766910076692119886 11988911988910076531007653

119878119878119878119878119886

10076691007669119886 (38)



119867119867119867119867119886

119886 119886119886119886119886119887 119886 119886119886119887119886119887 10076531007653119878119878119878119878119886

10076691007669 119886 11988611988611988611988611988610076531007653119878119878119878119878119886

100766910076692119886 (39)


119867119867119867119867119886

119886 119886119886119886119887 119886 119886119886119886119886 10076531007653119878119878119878119878119886

10076691007669 119886 11988611988611988711988610076531007653119878119878119878119878119886

100766910076692119886 119886119886119886410076531007653

119878119878119878119878119886

10076691007669119886119886

(40)


119867119867119867119867119886

119886 1198861198861198864119887 119886 1198861198861198864119887 10076531007653119878119878119878119878119886

10076691007669 119886 119886119886211988611988610076531007653119878119878119878119878119886

100766910076692119886 (41)


119867119867119867119867119886

119886 119886 1198861198861198864 119886 21198861198872 10076531007653119878119878119878119878119886

10076691007669

119886 11988611988611988611988610076531007653119878119878119878119878119886

100766910076692119886 21198862410076531007653

119878119878119878119878119886

10076691007669119886119886

(42)


119867119867119867119867119886

119886 11988611988622119887 119886 1198861198861198861198864 10076531007653119878119878119878119878119886

10076691007669 119886 11988611988611988611988611988610076531007653119878119878119878119878119886

100766910076692119886 (43)


119867119867119867119867119886

119886 119886119886119886119886 119886 1198861198861198864 10076531007653119878119878119878119878119886

10076691007669 119886 11988611988611988611988610076531007653119878119878119878119878119886

100766910076692119886 411988611988711988610076531007653

119878119878119878119878119886

10076691007669119886119886 (44)


119867119867119867119867119886

119886 1198861198862119886119886119886 119886 1198861198861198862119886119887 10076531007653119878119878119878119878119886

10076691007669 119886 11988611988611988611988611988611988610076531007653119878119878119878119878119886

100766910076692119886 (45)


119867119867119867119867119886

119886 1198861198861198864119886 119886 119886119886119887119887119886 10076531007653119878119878119878119878119886

10076691007669 119886 11988611988611988611988611988610076531007653119878119878119878119878119886

100766910076692119886 (46)


119867119867119867119867119886

119886 119886119886119886 119886 1198861198861198861198864 10076531007653119878119878119878119878119886

10076691007669 119886 119886119886211988711988710076531007653119878119878119878119878119886

100766910076692119886 (47)


119867119867119867119867119886

119886 119886119886119886119886119887119886 119886 119886119886119886119886119887119886 10076531007653119878119878119878119878119886

10076691007669 119886 1198861198861198861198862210076531007653119878119878119878119878119886

100766910076692119886 (48)


119867119867119867119867119886

119886 119886 211988642119886119887 119886 1198861198861198861198864119887 10076531007653119878119878119878119878119886

10076691007669

119886 119886119887119886119886411988710076531007653119878119878119878119878119886

100766910076692119886 11988611988611988611988711988611988710076531007653

119878119878119878119878119886

10076691007669119886119886

(49)



1198671198671198671198670

= 02408 + 03625 10076531007653119878119878119878119878010076691007669

+ 04597100765310076531198781198781198781198780100766910076692minus 0370810076531007653

1198781198781198781198780100766910076693

(50)


1198671198671198671198670

= 01796 + 09813 10076531007653119878119878119878119878010076691007669

minus 02958100765310076531198781198781198781198780100766910076692minus 0265710076531007653

1198781198781198781198780100766910076693

(51a)

1198671198671198671198670

= 01587 + 13652 10076531007653119878119878119878119878nh

10076691007669

minus 0117510076531007653119878119878119878119878nh

100766910076692

for winter(51b)

1198671198671198671198670

= 0288 + 09874 10076531007653119878119878119878119878nh

10076691007669

minus 0696710076531007653119878119878119878119878nh

100766910076692

for summer(51c)


1198671198671198671198670

= 02854 + 02591 10076531007653119878119878119878119878010076691007669

+ 06171100765310076531198781198781198781198780100766910076692minus 0483410076531007653

1198781198781198781198780100766910076693

(52)


1198671198671198671198670

= 0348 + 0320 10076531007653119878119878119878119878010076691007669 + 007010076531007653

1198781198781198781198780100766910076692 (53)


1198671198671198671198670

= 01874 + 08592 10076531007653119878119878119878119878010076691007669 minus 0476410076531007653

1198781198781198781198780100766910076692

1198671198671198671198670

= 01520 + 11334 10076531007653119878119878119878119878010076691007669

minus 11126 100765310076531198781198781198781198780100766910076692+ 0451610076531007653

1198781198781198781198780100766910076693

(54)


1198671198671198671198670

= 03398 + 02868 10076531007653119878119878119878119878010076691007669 + 0118710076531007653

1198781198781198781198780100766910076692

1198671198671198671198670

= 04832 minus 06161 10076531007653119878119878119878119878010076691007669

+ 18932100765310076531198781198781198781198780100766910076692minus 1097510076531007653

1198781198781198781198780100766910076693

(55)


1198671198671198671198670

= 06307 minus 07251 10076531007653119878119878119878119878010076691007669

+ 12089100765310076531198781198781198781198780100766910076692minus 0463310076531007653

1198781198781198781198780100766910076693

(56)


1198671198671198671198670

= 1198861198866 + 1198871198876 10076531007653119878119878119878119878010076691007669 + 119888119888610076531007653

1198781198781198781198780100766910076692+ 119889119889610076531007653

1198781198781198781198780100766910076693

+ 1198901198906100765310076531198781198781198781198780100766910076694+ 119891119891610076531007653

1198781198781198781198780100766910076695+ 119892119892610076531007653

1198781198781198781198780100766910076696

(57)




1198671198671198671198670

= 01874 + 08592 10076531007653119878119878119878119878010076691007669 minus 1567 (120579120579120579

+ 00033 (RH120579 minus 000806 (119879119879120579 (58)




City 1198861198866 1198871198876 1198881198886 1198891198896 1198901198906 1198911198916 1198921198926



1198671198671198671198670

= 1078 + 0071 10076531007653119878119878119878119878010076691007669 + 00026 10076491007649119879119879max10076651007665


1198671198671198671198670

= 886 + 0301 10076531007653119878119878119878119878010076691007669 + 00035 10076491007649119879119879max10076651007665

+ 000157 (RH) for Mosul(59b)

1198671198671198671198670

= 1507 + 0104 10076531007653119878119878119878119878010076691007669 + 000139 10076491007649119879119879max10076651007665




1198671198671198671198670

= 119860119860 100771410077141 minus exp 10076501007650minus119861119861Δ1198791198791198621198621007666100766610077301007730 (60)



1198671198671198671198670

= 11987011987011990311990310076491007649119879119879119872119872 minus 1198791198791198981198981007665100766505 (61a)

where119870119870119903119903 is dened as

119870119870119903119903 = 119870119870ra100765310076531198751198751198751198750

1007669100766905 (61b)


1198751198751198751198750

= exp (minus00001184 ℎ) (61c)



1198671198671198671198670

= 02889 + 01562 lowast 10076531007653120579120579120579120579010076691007669

1198671198671198671198670


1205791205791205791205790100766910076692

1198671198671198671198670


1205791205791205791205790100766910076692

+ 08201 lowast 100765310076531205791205791205791205790100766910076693

(62)








3

6

9

12

15

18

21

24

27

Months

CampbellAllen

First

Second

ird

MeasuredG

lob

al s

ola

r ra

dia

tio

n (

kW

hm2

day

)

mdash









4 Conclusions


References

















































































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



















1198671198671198671198670

= 0318 + 04491198781198781198781198780

(25a)


1198671198671198671198670

= 02947 + 046691198781198781198781198780

for winter (25b)

1198671198671198671198670

= 05103 + 016281198781198781198781198780

for summer (25c)

1198671198671198671198670

= 02948 + 05342119878119878119878119878nh

for winter (25d)

1198671198671198671198670

= 05067 + 01937119878119878119878119878nh

for summer (25e)

1198671198671198671198670

= 01739 ln119878119878119878119878nh


1198671198671198671198670

= 01124 ln119878119878119878119878nh



1198671198671198671198670

= 02671 + 047541198781198781198781198780

(26)


1198671198671198671198670

= 0324 + 04051198781198781198781198780

(27)


1198671198671198671198670

= 01332 + 064711198781198781198781198780

(28)


1198671198671198671198670

= 03647 + 035051198781198781198781198780

(29)


1198671198671198671198670

= 03078 + 041661198781198781198781198780

(30)


1198671198671198671198670

= 0176 + 05631198781198781198781198780

(31)


1198671198671198671198670

= 02276 + 051051198781198781198781198780

(32a)

1198671198671198671198670

= 02623 + 039521198781198781198781198780

(32b)

1198671198671198671198670

= 02229 + 051231198781198781198781198780

(32c)

1198671198671198671198670

= 02286 + 053091198781198781198781198780

(32d)


1198671198671198671198670

= 02281 + 050931198781198781198781198780

(32e)



119886119886 = 010 + 0241198781198781198781198780

(33a)

119887119887 = 038 + 0081198781198781198781198780

(33b)


1198671198671198671198670

= 018 + 0621198781198781198781198780

(34)


119886119886 = 03791 119886 00041119879119879 119886 00176119875119875 (35a)

119887119887 = 04810 119886 00043119879119879 119886 00097119875119875 (35b)



119886119886 119886 119886119886119886119886119886 119886 119886119886119886119886119886119886119886119886119885119885 119886 119886119886119886119886119886 119886119886119886 10076491007649120601120601 119886 12057512057510076651007665 (36a)

119887119887 119886 119886119886119887119886119886 119886 119886119886119886119887119887 119886119886119886 10076491007649120601120601 119886 12057512057510076651007665 119886 (36b)


119867119867119867119867119886

119886 119886119886 119886 11988711988710076531007653119878119878119878119878119886

10076691007669 119886 11988811988810076531007653119878119878119878119878119886

100766910076692119886 (37)


119867119867119867119867119886

119886 119886119886 119886 11988711988710076531007653119878119878119878119878119886

10076691007669 119886 11988811988810076531007653119878119878119878119878119886

100766910076692119886 11988911988910076531007653

119878119878119878119878119886

10076691007669119886 (38)



119867119867119867119867119886

119886 119886119886119886119886119887 119886 119886119886119887119886119887 10076531007653119878119878119878119878119886

10076691007669 119886 11988611988611988611988611988610076531007653119878119878119878119878119886

100766910076692119886 (39)


119867119867119867119867119886

119886 119886119886119886119887 119886 119886119886119886119886 10076531007653119878119878119878119878119886

10076691007669 119886 11988611988611988711988610076531007653119878119878119878119878119886

100766910076692119886 119886119886119886410076531007653

119878119878119878119878119886

10076691007669119886119886

(40)


119867119867119867119867119886

119886 1198861198861198864119887 119886 1198861198861198864119887 10076531007653119878119878119878119878119886

10076691007669 119886 119886119886211988611988610076531007653119878119878119878119878119886

100766910076692119886 (41)


119867119867119867119867119886

119886 119886 1198861198861198864 119886 21198861198872 10076531007653119878119878119878119878119886

10076691007669

119886 11988611988611988611988610076531007653119878119878119878119878119886

100766910076692119886 21198862410076531007653

119878119878119878119878119886

10076691007669119886119886

(42)


119867119867119867119867119886

119886 11988611988622119887 119886 1198861198861198861198864 10076531007653119878119878119878119878119886

10076691007669 119886 11988611988611988611988611988610076531007653119878119878119878119878119886

100766910076692119886 (43)


119867119867119867119867119886

119886 119886119886119886119886 119886 1198861198861198864 10076531007653119878119878119878119878119886

10076691007669 119886 11988611988611988611988610076531007653119878119878119878119878119886

100766910076692119886 411988611988711988610076531007653

119878119878119878119878119886

10076691007669119886119886 (44)


119867119867119867119867119886

119886 1198861198862119886119886119886 119886 1198861198861198862119886119887 10076531007653119878119878119878119878119886

10076691007669 119886 11988611988611988611988611988611988610076531007653119878119878119878119878119886

100766910076692119886 (45)


119867119867119867119867119886

119886 1198861198861198864119886 119886 119886119886119887119887119886 10076531007653119878119878119878119878119886

10076691007669 119886 11988611988611988611988611988610076531007653119878119878119878119878119886

100766910076692119886 (46)


119867119867119867119867119886

119886 119886119886119886 119886 1198861198861198861198864 10076531007653119878119878119878119878119886

10076691007669 119886 119886119886211988711988710076531007653119878119878119878119878119886

100766910076692119886 (47)


119867119867119867119867119886

119886 119886119886119886119886119887119886 119886 119886119886119886119886119887119886 10076531007653119878119878119878119878119886

10076691007669 119886 1198861198861198861198862210076531007653119878119878119878119878119886

100766910076692119886 (48)


119867119867119867119867119886

119886 119886 211988642119886119887 119886 1198861198861198861198864119887 10076531007653119878119878119878119878119886

10076691007669

119886 119886119887119886119886411988710076531007653119878119878119878119878119886

100766910076692119886 11988611988611988611988711988611988710076531007653

119878119878119878119878119886

10076691007669119886119886

(49)



1198671198671198671198670

= 02408 + 03625 10076531007653119878119878119878119878010076691007669

+ 04597100765310076531198781198781198781198780100766910076692minus 0370810076531007653

1198781198781198781198780100766910076693

(50)


1198671198671198671198670

= 01796 + 09813 10076531007653119878119878119878119878010076691007669

minus 02958100765310076531198781198781198781198780100766910076692minus 0265710076531007653

1198781198781198781198780100766910076693

(51a)

1198671198671198671198670

= 01587 + 13652 10076531007653119878119878119878119878nh

10076691007669

minus 0117510076531007653119878119878119878119878nh

100766910076692

for winter(51b)

1198671198671198671198670

= 0288 + 09874 10076531007653119878119878119878119878nh

10076691007669

minus 0696710076531007653119878119878119878119878nh

100766910076692

for summer(51c)


1198671198671198671198670

= 02854 + 02591 10076531007653119878119878119878119878010076691007669

+ 06171100765310076531198781198781198781198780100766910076692minus 0483410076531007653

1198781198781198781198780100766910076693

(52)


1198671198671198671198670

= 0348 + 0320 10076531007653119878119878119878119878010076691007669 + 007010076531007653

1198781198781198781198780100766910076692 (53)


1198671198671198671198670

= 01874 + 08592 10076531007653119878119878119878119878010076691007669 minus 0476410076531007653

1198781198781198781198780100766910076692

1198671198671198671198670

= 01520 + 11334 10076531007653119878119878119878119878010076691007669

minus 11126 100765310076531198781198781198781198780100766910076692+ 0451610076531007653

1198781198781198781198780100766910076693

(54)


1198671198671198671198670

= 03398 + 02868 10076531007653119878119878119878119878010076691007669 + 0118710076531007653

1198781198781198781198780100766910076692

1198671198671198671198670

= 04832 minus 06161 10076531007653119878119878119878119878010076691007669

+ 18932100765310076531198781198781198781198780100766910076692minus 1097510076531007653

1198781198781198781198780100766910076693

(55)


1198671198671198671198670

= 06307 minus 07251 10076531007653119878119878119878119878010076691007669

+ 12089100765310076531198781198781198781198780100766910076692minus 0463310076531007653

1198781198781198781198780100766910076693

(56)


1198671198671198671198670

= 1198861198866 + 1198871198876 10076531007653119878119878119878119878010076691007669 + 119888119888610076531007653

1198781198781198781198780100766910076692+ 119889119889610076531007653

1198781198781198781198780100766910076693

+ 1198901198906100765310076531198781198781198781198780100766910076694+ 119891119891610076531007653

1198781198781198781198780100766910076695+ 119892119892610076531007653

1198781198781198781198780100766910076696

(57)




1198671198671198671198670

= 01874 + 08592 10076531007653119878119878119878119878010076691007669 minus 1567 (120579120579120579

+ 00033 (RH120579 minus 000806 (119879119879120579 (58)




City 1198861198866 1198871198876 1198881198886 1198891198896 1198901198906 1198911198916 1198921198926



1198671198671198671198670

= 1078 + 0071 10076531007653119878119878119878119878010076691007669 + 00026 10076491007649119879119879max10076651007665


1198671198671198671198670

= 886 + 0301 10076531007653119878119878119878119878010076691007669 + 00035 10076491007649119879119879max10076651007665

+ 000157 (RH) for Mosul(59b)

1198671198671198671198670

= 1507 + 0104 10076531007653119878119878119878119878010076691007669 + 000139 10076491007649119879119879max10076651007665




1198671198671198671198670

= 119860119860 100771410077141 minus exp 10076501007650minus119861119861Δ1198791198791198621198621007666100766610077301007730 (60)



1198671198671198671198670

= 11987011987011990311990310076491007649119879119879119872119872 minus 1198791198791198981198981007665100766505 (61a)

where119870119870119903119903 is dened as

119870119870119903119903 = 119870119870ra100765310076531198751198751198751198750

1007669100766905 (61b)


1198751198751198751198750

= exp (minus00001184 ℎ) (61c)



1198671198671198671198670

= 02889 + 01562 lowast 10076531007653120579120579120579120579010076691007669

1198671198671198671198670


1205791205791205791205790100766910076692

1198671198671198671198670


1205791205791205791205790100766910076692

+ 08201 lowast 100765310076531205791205791205791205790100766910076693

(62)








3

6

9

12

15

18

21

24

27

Months

CampbellAllen

First

Second

ird

MeasuredG

lob

al s

ola

r ra

dia

tio

n (

kW

hm2

day

)

mdash









4 Conclusions


References

















































































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



















119886119886 119886 119886119886119886119886119886 119886 119886119886119886119886119886119886119886119886119885119885 119886 119886119886119886119886119886 119886119886119886 10076491007649120601120601 119886 12057512057510076651007665 (36a)

119887119887 119886 119886119886119887119886119886 119886 119886119886119886119887119887 119886119886119886 10076491007649120601120601 119886 12057512057510076651007665 119886 (36b)


119867119867119867119867119886

119886 119886119886 119886 11988711988710076531007653119878119878119878119878119886

10076691007669 119886 11988811988810076531007653119878119878119878119878119886

100766910076692119886 (37)


119867119867119867119867119886

119886 119886119886 119886 11988711988710076531007653119878119878119878119878119886

10076691007669 119886 11988811988810076531007653119878119878119878119878119886

100766910076692119886 11988911988910076531007653

119878119878119878119878119886

10076691007669119886 (38)



119867119867119867119867119886

119886 119886119886119886119886119887 119886 119886119886119887119886119887 10076531007653119878119878119878119878119886

10076691007669 119886 11988611988611988611988611988610076531007653119878119878119878119878119886

100766910076692119886 (39)


119867119867119867119867119886

119886 119886119886119886119887 119886 119886119886119886119886 10076531007653119878119878119878119878119886

10076691007669 119886 11988611988611988711988610076531007653119878119878119878119878119886

100766910076692119886 119886119886119886410076531007653

119878119878119878119878119886

10076691007669119886119886

(40)


119867119867119867119867119886

119886 1198861198861198864119887 119886 1198861198861198864119887 10076531007653119878119878119878119878119886

10076691007669 119886 119886119886211988611988610076531007653119878119878119878119878119886

100766910076692119886 (41)


119867119867119867119867119886

119886 119886 1198861198861198864 119886 21198861198872 10076531007653119878119878119878119878119886

10076691007669

119886 11988611988611988611988610076531007653119878119878119878119878119886

100766910076692119886 21198862410076531007653

119878119878119878119878119886

10076691007669119886119886

(42)


119867119867119867119867119886

119886 11988611988622119887 119886 1198861198861198861198864 10076531007653119878119878119878119878119886

10076691007669 119886 11988611988611988611988611988610076531007653119878119878119878119878119886

100766910076692119886 (43)


119867119867119867119867119886

119886 119886119886119886119886 119886 1198861198861198864 10076531007653119878119878119878119878119886

10076691007669 119886 11988611988611988611988610076531007653119878119878119878119878119886

100766910076692119886 411988611988711988610076531007653

119878119878119878119878119886

10076691007669119886119886 (44)


119867119867119867119867119886

119886 1198861198862119886119886119886 119886 1198861198861198862119886119887 10076531007653119878119878119878119878119886

10076691007669 119886 11988611988611988611988611988611988610076531007653119878119878119878119878119886

100766910076692119886 (45)


119867119867119867119867119886

119886 1198861198861198864119886 119886 119886119886119887119887119886 10076531007653119878119878119878119878119886

10076691007669 119886 11988611988611988611988611988610076531007653119878119878119878119878119886

100766910076692119886 (46)


119867119867119867119867119886

119886 119886119886119886 119886 1198861198861198861198864 10076531007653119878119878119878119878119886

10076691007669 119886 119886119886211988711988710076531007653119878119878119878119878119886

100766910076692119886 (47)


119867119867119867119867119886

119886 119886119886119886119886119887119886 119886 119886119886119886119886119887119886 10076531007653119878119878119878119878119886

10076691007669 119886 1198861198861198861198862210076531007653119878119878119878119878119886

100766910076692119886 (48)


119867119867119867119867119886

119886 119886 211988642119886119887 119886 1198861198861198861198864119887 10076531007653119878119878119878119878119886

10076691007669

119886 119886119887119886119886411988710076531007653119878119878119878119878119886

100766910076692119886 11988611988611988611988711988611988710076531007653

119878119878119878119878119886

10076691007669119886119886

(49)



1198671198671198671198670

= 02408 + 03625 10076531007653119878119878119878119878010076691007669

+ 04597100765310076531198781198781198781198780100766910076692minus 0370810076531007653

1198781198781198781198780100766910076693

(50)


1198671198671198671198670

= 01796 + 09813 10076531007653119878119878119878119878010076691007669

minus 02958100765310076531198781198781198781198780100766910076692minus 0265710076531007653

1198781198781198781198780100766910076693

(51a)

1198671198671198671198670

= 01587 + 13652 10076531007653119878119878119878119878nh

10076691007669

minus 0117510076531007653119878119878119878119878nh

100766910076692

for winter(51b)

1198671198671198671198670

= 0288 + 09874 10076531007653119878119878119878119878nh

10076691007669

minus 0696710076531007653119878119878119878119878nh

100766910076692

for summer(51c)


1198671198671198671198670

= 02854 + 02591 10076531007653119878119878119878119878010076691007669

+ 06171100765310076531198781198781198781198780100766910076692minus 0483410076531007653

1198781198781198781198780100766910076693

(52)


1198671198671198671198670

= 0348 + 0320 10076531007653119878119878119878119878010076691007669 + 007010076531007653

1198781198781198781198780100766910076692 (53)


1198671198671198671198670

= 01874 + 08592 10076531007653119878119878119878119878010076691007669 minus 0476410076531007653

1198781198781198781198780100766910076692

1198671198671198671198670

= 01520 + 11334 10076531007653119878119878119878119878010076691007669

minus 11126 100765310076531198781198781198781198780100766910076692+ 0451610076531007653

1198781198781198781198780100766910076693

(54)


1198671198671198671198670

= 03398 + 02868 10076531007653119878119878119878119878010076691007669 + 0118710076531007653

1198781198781198781198780100766910076692

1198671198671198671198670

= 04832 minus 06161 10076531007653119878119878119878119878010076691007669

+ 18932100765310076531198781198781198781198780100766910076692minus 1097510076531007653

1198781198781198781198780100766910076693

(55)


1198671198671198671198670

= 06307 minus 07251 10076531007653119878119878119878119878010076691007669

+ 12089100765310076531198781198781198781198780100766910076692minus 0463310076531007653

1198781198781198781198780100766910076693

(56)


1198671198671198671198670

= 1198861198866 + 1198871198876 10076531007653119878119878119878119878010076691007669 + 119888119888610076531007653

1198781198781198781198780100766910076692+ 119889119889610076531007653

1198781198781198781198780100766910076693

+ 1198901198906100765310076531198781198781198781198780100766910076694+ 119891119891610076531007653

1198781198781198781198780100766910076695+ 119892119892610076531007653

1198781198781198781198780100766910076696

(57)




1198671198671198671198670

= 01874 + 08592 10076531007653119878119878119878119878010076691007669 minus 1567 (120579120579120579

+ 00033 (RH120579 minus 000806 (119879119879120579 (58)




City 1198861198866 1198871198876 1198881198886 1198891198896 1198901198906 1198911198916 1198921198926



1198671198671198671198670

= 1078 + 0071 10076531007653119878119878119878119878010076691007669 + 00026 10076491007649119879119879max10076651007665


1198671198671198671198670

= 886 + 0301 10076531007653119878119878119878119878010076691007669 + 00035 10076491007649119879119879max10076651007665

+ 000157 (RH) for Mosul(59b)

1198671198671198671198670

= 1507 + 0104 10076531007653119878119878119878119878010076691007669 + 000139 10076491007649119879119879max10076651007665




1198671198671198671198670

= 119860119860 100771410077141 minus exp 10076501007650minus119861119861Δ1198791198791198621198621007666100766610077301007730 (60)



1198671198671198671198670

= 11987011987011990311990310076491007649119879119879119872119872 minus 1198791198791198981198981007665100766505 (61a)

where119870119870119903119903 is dened as

119870119870119903119903 = 119870119870ra100765310076531198751198751198751198750

1007669100766905 (61b)


1198751198751198751198750

= exp (minus00001184 ℎ) (61c)



1198671198671198671198670

= 02889 + 01562 lowast 10076531007653120579120579120579120579010076691007669

1198671198671198671198670


1205791205791205791205790100766910076692

1198671198671198671198670


1205791205791205791205790100766910076692

+ 08201 lowast 100765310076531205791205791205791205790100766910076693

(62)








3

6

9

12

15

18

21

24

27

Months

CampbellAllen

First

Second

ird

MeasuredG

lob

al s

ola

r ra

dia

tio

n (

kW

hm2

day

)

mdash









4 Conclusions


References

















































































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



















1198671198671198671198670

= 02408 + 03625 10076531007653119878119878119878119878010076691007669

+ 04597100765310076531198781198781198781198780100766910076692minus 0370810076531007653

1198781198781198781198780100766910076693

(50)


1198671198671198671198670

= 01796 + 09813 10076531007653119878119878119878119878010076691007669

minus 02958100765310076531198781198781198781198780100766910076692minus 0265710076531007653

1198781198781198781198780100766910076693

(51a)

1198671198671198671198670

= 01587 + 13652 10076531007653119878119878119878119878nh

10076691007669

minus 0117510076531007653119878119878119878119878nh

100766910076692

for winter(51b)

1198671198671198671198670

= 0288 + 09874 10076531007653119878119878119878119878nh

10076691007669

minus 0696710076531007653119878119878119878119878nh

100766910076692

for summer(51c)


1198671198671198671198670

= 02854 + 02591 10076531007653119878119878119878119878010076691007669

+ 06171100765310076531198781198781198781198780100766910076692minus 0483410076531007653

1198781198781198781198780100766910076693

(52)


1198671198671198671198670

= 0348 + 0320 10076531007653119878119878119878119878010076691007669 + 007010076531007653

1198781198781198781198780100766910076692 (53)


1198671198671198671198670

= 01874 + 08592 10076531007653119878119878119878119878010076691007669 minus 0476410076531007653

1198781198781198781198780100766910076692

1198671198671198671198670

= 01520 + 11334 10076531007653119878119878119878119878010076691007669

minus 11126 100765310076531198781198781198781198780100766910076692+ 0451610076531007653

1198781198781198781198780100766910076693

(54)


1198671198671198671198670

= 03398 + 02868 10076531007653119878119878119878119878010076691007669 + 0118710076531007653

1198781198781198781198780100766910076692

1198671198671198671198670

= 04832 minus 06161 10076531007653119878119878119878119878010076691007669

+ 18932100765310076531198781198781198781198780100766910076692minus 1097510076531007653

1198781198781198781198780100766910076693

(55)


1198671198671198671198670

= 06307 minus 07251 10076531007653119878119878119878119878010076691007669

+ 12089100765310076531198781198781198781198780100766910076692minus 0463310076531007653

1198781198781198781198780100766910076693

(56)


1198671198671198671198670

= 1198861198866 + 1198871198876 10076531007653119878119878119878119878010076691007669 + 119888119888610076531007653

1198781198781198781198780100766910076692+ 119889119889610076531007653

1198781198781198781198780100766910076693

+ 1198901198906100765310076531198781198781198781198780100766910076694+ 119891119891610076531007653

1198781198781198781198780100766910076695+ 119892119892610076531007653

1198781198781198781198780100766910076696

(57)




1198671198671198671198670

= 01874 + 08592 10076531007653119878119878119878119878010076691007669 minus 1567 (120579120579120579

+ 00033 (RH120579 minus 000806 (119879119879120579 (58)




City 1198861198866 1198871198876 1198881198886 1198891198896 1198901198906 1198911198916 1198921198926



1198671198671198671198670

= 1078 + 0071 10076531007653119878119878119878119878010076691007669 + 00026 10076491007649119879119879max10076651007665


1198671198671198671198670

= 886 + 0301 10076531007653119878119878119878119878010076691007669 + 00035 10076491007649119879119879max10076651007665

+ 000157 (RH) for Mosul(59b)

1198671198671198671198670

= 1507 + 0104 10076531007653119878119878119878119878010076691007669 + 000139 10076491007649119879119879max10076651007665




1198671198671198671198670

= 119860119860 100771410077141 minus exp 10076501007650minus119861119861Δ1198791198791198621198621007666100766610077301007730 (60)



1198671198671198671198670

= 11987011987011990311990310076491007649119879119879119872119872 minus 1198791198791198981198981007665100766505 (61a)

where119870119870119903119903 is dened as

119870119870119903119903 = 119870119870ra100765310076531198751198751198751198750

1007669100766905 (61b)


1198751198751198751198750

= exp (minus00001184 ℎ) (61c)



1198671198671198671198670

= 02889 + 01562 lowast 10076531007653120579120579120579120579010076691007669

1198671198671198671198670


1205791205791205791205790100766910076692

1198671198671198671198670


1205791205791205791205790100766910076692

+ 08201 lowast 100765310076531205791205791205791205790100766910076693

(62)








3

6

9

12

15

18

21

24

27

Months

CampbellAllen

First

Second

ird

MeasuredG

lob

al s

ola

r ra

dia

tio

n (

kW

hm2

day

)

mdash









4 Conclusions


References

















































































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



















City 1198861198866 1198871198876 1198881198886 1198891198896 1198901198906 1198911198916 1198921198926



1198671198671198671198670

= 1078 + 0071 10076531007653119878119878119878119878010076691007669 + 00026 10076491007649119879119879max10076651007665


1198671198671198671198670

= 886 + 0301 10076531007653119878119878119878119878010076691007669 + 00035 10076491007649119879119879max10076651007665

+ 000157 (RH) for Mosul(59b)

1198671198671198671198670

= 1507 + 0104 10076531007653119878119878119878119878010076691007669 + 000139 10076491007649119879119879max10076651007665




1198671198671198671198670

= 119860119860 100771410077141 minus exp 10076501007650minus119861119861Δ1198791198791198621198621007666100766610077301007730 (60)



1198671198671198671198670

= 11987011987011990311990310076491007649119879119879119872119872 minus 1198791198791198981198981007665100766505 (61a)

where119870119870119903119903 is dened as

119870119870119903119903 = 119870119870ra100765310076531198751198751198751198750

1007669100766905 (61b)


1198751198751198751198750

= exp (minus00001184 ℎ) (61c)



1198671198671198671198670

= 02889 + 01562 lowast 10076531007653120579120579120579120579010076691007669

1198671198671198671198670


1205791205791205791205790100766910076692

1198671198671198671198670


1205791205791205791205790100766910076692

+ 08201 lowast 100765310076531205791205791205791205790100766910076693

(62)








3

6

9

12

15

18

21

24

27

Months

CampbellAllen

First

Second

ird

MeasuredG

lob

al s

ola

r ra

dia

tio

n (

kW

hm2

day

)

mdash









4 Conclusions


References

















































































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of






















3

6

9

12

15

18

21

24

27

Months

CampbellAllen

First

Second

ird

MeasuredG

lob

al s

ola

r ra

dia

tio

n (

kW

hm2

day

)

mdash









4 Conclusions


References

















































































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



















4 Conclusions


References

















































































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of






































































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of

















a review of solar radiation models—part i

Documents