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Energy

journal homepage:www.elsevier.com/locate/energy

Energy 51 (2013) 257-266

Introducing the best model for predicting the monthly mean global solar radiationover six major cities of Iran

H. Khorasanizadeh*

, K. MohammadiDepartment of Mechanical Engineering, University of Kashan, Kashan 87317-51167, Iran

A R T C L E N F O A B S T R A C T

Article history:

Received 20 August 2012Received in revised form31 October 2012Accepted 2 November 2012Available online 4 December 2012

Keywords:

Global solar radiation

Empirical modelsSunshine durationPredictionIran

In this study, by using long-term global solar radiation data and other meteorological parameters, 11empirical models taken from the literature were tested for prediction of monthly mean daily global solarradiation over six major cities of Iran, named Isfahan, Karaj, Mashhad, Shiraz, Tabriz and Tehran. Themodels are from 3 categories: (1) Only function of sunshine duration; (2) Function of sunshine durationas well as relative humidity and ambient temperature; (3) Independent of sunshine duration and functionof relative humidity, ambient temperature and its maximum and minimum. The models wereestablished using statistical regression technique and their accuracies evaluated using the statisticalindicators of mean percentage error (MPE), mean bias error (MBE) and root mean square error(RMSE); hence the best model in each category was recognized. Although, 5 out of the 6 nominatedcities fell in climatic classification of BSk, it was not possible to introduce a single model even for thecities having the same climate type. However, for all of the cities the best model was either fromcategories (1) or (2). In line with increased tendency toward installation of solar systems in Iran, theproposed models are useful for simulations and incorporation in design procedures.

2012 Elsevier Ltd. All rights reserved.

1. Introduction

Today, due to environmental pollution caused by gas emissions,such as carbon dioxide and sulfur dioxide, also increase in fuelcosts the use of renewable energies particularly solar energy hasincreased around the world. Amount of solar radiation in some

countries like Iran as a result of being in solar belt region is verystrong. Knowledge of accurate solar radiation information, espe-cially monthly mean daily global solar radiation on horizontalsurface, is very vital for solar researchers [1,2]. In many developedcountries the global solar radiation is recorded and the data areavailable for many regions of the country. Since the measuringequipment and their maintenance and calibrations are costly, in Iranthe data are recorded only in some areas. As a result, depen-dencyexists on prediction of the models to estimate monthly mean global

solar radiation based on different meteorological parame-ters.Many surveys have been conducted to develop models forprediction of monthly mean daily global solar radiation on hori-zontal surface by using various meteorological parameters [2-41].The models used in some studies are only function of sunshine

* Corresponding author. Tel.: 98 361 5912449; fax: 98 361 5912424.E-mail addresses: [email protected] (H. Khorasanizadeh), kasra278@

yahoo.com(K. Mohammadi).

0360-5442/$ - see front matter 2012 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.energy.2012.11.007

hours [2-26], among them is Angstrm-Prescott model, and othersare functions of multiple parameters. The studies done for devel-oping models to predict monthly mean global radiation in Iran arevery limited. Behrang et al. [22] used particle swarm optimizationtechnique (PSO) to establish, develop and test only sunshine-basedmodels for predicting monthly average daily global radiation for 17

Iranian cities for which long-term global solar radiation data wereavailable. For these cities the empirical coefficients for Angstrm-Prescott model based on PSO had more accuracy than those ob-tained using statistical regression technique (SRT). Sabziparvar and

Shetaee [39] and Sabziparvar [40] used various meteorologicalparameters to develop height-dependent formulas for the predic-tionof the global monthly average solar radiation for some arid andsemi-arid locations in west and east as well as some locations incentral arid deserts of Iran, respectively. Also in another studySabziparvar [41] revised some radiation models for some coastalsouth and north locations in Iran based on meteorological param-eters by taking into account relative humidity, ground albedo andSun-Earth distance. The models proposed in [39-41] are relativelycomplex and they have been validated only for limited sites. By

means of measured solar data as well as other meteorologicalparameters in some nominated stations, the main purposes of thisstudy are: 1) Establishing and testing 11 simple models in threedifferent categories for six major cities of Iran. 2) For each city,introducing the best model among all of the tested models by
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24 ~ 3600Ho 1/4

TC

21/4 15cos

258 H. Khorasanizadeh, K. Mohammadi / Energy 51 (2013) 257-266

Nomenclature

Gsc solar constant (equal to 1367 W/m2)

H monthly mean daily global radiation on horizontalsurface (MJ/m

2)

Ho monthly mean daily extraterrestrial horizontal

surface (MJ/m

2

)Hi,c, Hi,mith calculated and measured values of H (MJ/m2) Hc,avg,

Hm,avgaverage calculated and measured values of H (MJ/m2)

KT monthly mean daily clearness indexMBE mean bias error (MJ/m

2)

MPE mean percentage error (%)n monthly mean daily sunshine hours (h)nda y number of daysN monthly mean daily maximum possible sunshine

hours (h)RMSE root mean square error (MJ/m

2)

R2 coefficient of determinationRh monthly mean relative humidity (%)Tav g monthly mean ambient temperature (

C)

Ta x monthly mean maximum ambient temperature (C)

Ti n monthly mean minimum ambient temperature (C)

Greek letters

d solardeclinationangle(deg.)4 latitudeofthelocation (deg.)

us sunrise hour angle (deg.)

comparing the best models in different categories with each otheraccording to statistical indicators.

2. Models

11 models selected from the literature and classi fied in 3different categories are:

Category (1): In this category the ratio of monthly mean dailyglobal solar radiation on a horizontal surface to monthly meandaily solar extraterrestrial on a horizontal surface is only functionof relative sunshine duration; such that:

( / )H=Ho 1/ 4 f n N

Five simple models selected from this categoryare: Model 1 [3,4]:

( / )H=Ho 1/4 a b n N (1)

Model 2 [15]:

( / ) ( /)2H=Ho 1 / 4 a b n N c n N (2)Model 3 [17]:

( / ) ( /)2 ( /)3H=Ho 1/4 a b n N c n N d n N

(3)

M o d e l 4 [ 2 3 ] : ( /

) b

H=Ho 1/ 4 a n N(4)Model 5 [23]:

( ( / ) )H=Ho 1/4 aexp b n N (5)

Category (2): In this category the ratio of monthly mean dailyglobal solar radiation to monthly mean daily solar extraterrestrialon a horizontal surface is not only function of relative sunshineduration but also function of other meteorological parameters;such that:

( / )H=Ho 1/ 4 f n N;Tavg ;Rh

Three simple models selected from this category are:Model 6 [34]:

( / )H=Ho 1/4 a b n N cTavg (6)

Model 7 [34]:

( / )H=Ho 1/4 a b n N cRh (7)

Model 8 [31]:

( / )H=Ho 1/4 a b n N cTavgdRh (8)

Category (3): In this category the ratio of monthly mean dailyglobal solar radiation to monthly mean daily solar extraterrestrialon a horizontal surface is independent of relative sunshineduration but is function of monthly mean relative humidity,monthly mean temperature, monthly mean maximum temperatureand monthly mean minimum temperature; such that:

H=Ho 1/4 f(Tmax; Tmin; Tavg; Rh)

Three simple models selected from this category are:Model 9 [36]:

H=Ho 1/4 aTmax ~ Tminb (9)

Model 10 [37]:

H=Ho 1/4 aTmax ~ Tmin0:5b (10)

Model 11 [34]:

H=Ho 1/4 a bTavg cRh (11)

The monthly mean daily extraterrestrial solar radiation on ahorizontal surface is [42]:

Gsc (1 0:033cos 360nday3 6 5 )

x (cos 4cos dsin us 180sin 4sin d)

where d and us are the monthly mean daily solar declination andsunrise hour angle, respectively, as [42]:

1/4 23:45sin (n 365360) (13)

us 1/4 cos-1

tan 4tan d (14)

The monthly mean daily maximum possible sunshine duration is

[42]:

-1tan 4tan d


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H. Khorasanizadeh, K. Mohammadi / Energy 51 (2013) 257-266 259

(Hi,c Hi,m )

x1MBE

x i1

Hi,c Hi,m

Hi,m )100 (16)

x1MPE

x i 1

1X

x (Hi,c

Hi,m)

2

(18)

3. Meteorological data and location description

Iran is a vast country with 1,648,195 km2

areas and enjoysconsiderable climatic diversity. The temperature difference betweencoldest and hottest parts of the country in winter season issometimes about 50

C. Iran is one of the countries located in solar

belt region of the world with high amount of solar radiation andhigh number of sunshine hours. Positions of the 6 cities consideredin this study are shown on the map of Iran in Fig. 1 and informationfor their geographical locations is presented in Table 1. In order toestablish and evaluate the models for predicting monthly meanglobal radiation for these cities, long-term global solar radiationdata on horizontal surfaces have been used together with someother meteorological parameters provided by the Iranian meteo-rological organization (IMO). IMO has started working since 1955and today in many cities across the country has meteorologicalstations. However, global solar radiation on horizontal surface isbeing recorded only in 22 stations.

The data provided by IMO include long-term daily global radi-ation on horizontal surface as well as some other meteorologicalparameters such as monthly mean daily sunshine duration,monthly mean relative humidity, monthly mean ambient temper-

ature, monthly mean maximum ambient temperature and monthlymean minimum ambient temperature. In the data provided byIMO, there are differences in the number and distributions of yearsfor which data exist for the six considered cities. Also the datacollec-tions for these cities contain some missing and incorrectvalues. The missing values relate to some days, months andsometimes years that data have not been recorded and incorrectvalues relate to possible malfunction of instruments. To overcomethis problem and in order to arrive at accurate models thefollowing method was used.

1. A data collection for a month involving more than 5 daysmissing or incorrect values was fully withdrawn [43]. For theomitted months all of the meteorological parameters

mentioned earlier were excluded from the calculationprocedures.

2. Forfinding which global solar radiation values were not correct,the concept of monthly mean clearness index was used as abenchmark. For this purpose all values which were out of

Fig. 1.Location of the cities considered on the map of Iran.

Table 1

Geographical locations of the cities considered.

City Latitude (N) Longitude (

E) Elevation from

sea level (m)

Isfahan 3237 5140 1550.4Karaj 3555 5054 1312.5Mashhad 3616 5938 999.2Shiraz 2932 5636 1484.0

Tabriz 3850 4617 1361.0Tehran 3548 5129 1549.1

monthly mean clearness index range of (0.015


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Shiraz 1982-1992 120 1993-1994 &1999-2000 36Tabriz 1992-1994 & 1998-2002 75 2003-2005 36Tehran 1993-2000 90 2001-2003 & 2005 29


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(19)


Table 3

Sunshine and maximum possible sunshine hours and other meteorological parameters for the 6 cities considered.

City Parameter Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Isfahan n (h) 6.99 8.52 8.46 8.19 10.91 11.96 11.29 11.67 10.85 9.84 7.72 6.29N(h) 10.13 10.88 11.80 12.80 13.66 14.09 13.90 13.16 12.19 11.18 10.33 9.91Rh (%) 57.86 36.74 33.02 35.97 25.12 18.52 18.28 19.09 21.32 25.59 48.16 59.58Tavg (C) 4.18 6.60 11.75 16.55 21.17 27.15 29.85 28.48 24.18 18.60 9.77 5.25Tmax (C) 9.95 13.67 18.95 23.25 29.00 35.15 37.75 37.08 32.98 27.20 16.87 11.23

Tmin (

C)-

1.63-

0.47

4.60 9.90 13.37 19.18 21.95 19.85 15.35 10.00 2.70-

0.73

Karaj n (h) 5.96 6.15 6.37 7.49 8.93 10.93 11.10 11.04 10.20 9.00 7.60 5.70N(h) 9.89 10.74 11.77 12.91 13.88 14.36 14.14 13.31 12.21 11.07 10.11 9.64Rh (%) 66.39 63.21 55.75 48.92 46.69 39.05 32.50 32.17 32.95 44.80 32.00 65.90Tavg (C) 2.55 5.20 7.65 14.50 19.15 23.20 27.50 26.35 21.80 15.60 11.50 2.60Tmax (C) 6.85 9.70 12.85 20.20 25.55 30.95 35.60 34.25 29.10 22.10 17.70 6.80Tmin (C) -1.75 0.70 2.55 8.90 12.75 15.40 19.30 18.40 14.55 9.00 5.30 -1.60

Mashhad n (h) 4.77 5.32 4.95 7.29 9.64 11.23 11.99 12.10 10.47 8.26 6.55 5.41N(h) 9.84 10.71 11.76 12.93 13.92 14.42 14.19 13.34 12.22 11.05 10.07 9.58Rh (%) 73.60 69.52 72.77 56.91 43.85 36.85 36.26 35.26 39.44 48.88 63.62 66.48Tavg (C) 3.90 3.20 8.30 14.35 20.20 25.90 27.74 26.60 21.22 15.47 10.02 5.73Tmax (C) 9.00 8.60 13.23 20.68 27.10 33.15 34.82 34.52 29.12 22.90 16.52 11.73Tmin (C) -1.15 -2.25 3.35 8.08 13.25 18.60 20.70 18.70 13.32 7.98 3.53 -0.27

Shiraz n (h) 6.80 8.10 7.94 8.90 10.70 12.10 11.10 10.85 10.55 9.53 7.88 7.77N(h) 10.35 11.01 11.82 12.71 13.47 13.85 13.68 13.03 12.17 11.27 10.52 10.16Rh (%) 59.26 49.37 47.01 38.72 29.79 20.97 23.31 24.90 28.15 34.97 49.98 48.57Tavg (C) 6.33 8.75 11.13 18.70 23.03 27.53 30.10 28.33 25.40 19.10 11.13 8.43Tmax (C) 11.63 14.70 17.50 25.53 30.80 35.80 37.77 37.20 33.85 27.23 19.00 15.57Tmin (C) 6.33 8.75 11.13 18.70 23.03 27.53 30.10 29.33 25.40 19.10 12.13 8.43

Tabriz n (h) 4.21 5.35 6.34 7.04 8.78 11.60 11.39 11.51 10.32 8.05 5.53 5.61N(h) 9.64 10.59 11.74 13.01 14.09 14.64 14.39 13.46 12.24 10.97 9.89 9.36Rh (%) 70.36 61.63 49.06 51.06 48.12 38.53 38.25 34.68 37.49 41.37 63.82 69.26Tavg (C) 0.23 1.53 6.90 11.90 17.10 22.73 26.53 27.30 22.23 16.67 7.70 1.80Tmax (C) 4.07 5.90 12.07 17.40 22.80 29.33 33.07 33.73 28.70 23.00 12.27 6.20Tmin (C) -3.63 -2.77 1.73 6.30 11.40 16.10 20.03 20.87 15.73 10.27 3.17 -2.60

Tehran n (h) 4.46 4.10 6.00 6.21 8.95 10.96 10.73 10.59 9.82 8.64 5.48 4.52N(h) 9.89 10.74 11.77 12.91 13.87 14.36 14.14 13.31 12.21 11.08 10.12 9.65Rh (%) 64.53 60.80 50.90 47.59 39.04 29.43 31.60 32.03 31.05 38.76 61.13 69.62Tavg (C) 3.85 5.00 8.20 15.17 19.55 25.38 28.33 27.90 25.00 19.10 9.65 4.95Tmax (C) 7.75 8.70 12.50 19.90 25.33 31.50 34.20 34.03 31.60 25.20 14.15 8.60Tmin (C) -0.05 1.20 3.90 10.37 13.78 19.30 22.43 21.77 18.40 12.95 5.20 1.30

xR2 =

i=1Hi,c-Hc,avgHi,m-Hm,avg=1Hi,c-Hc,avg2i=1Hi,m-Hm,avg2E-

whereHi,c,Hi,m,Hc,a v g andHm,a v g are the ith calculated, measured,average calculated and average measured values, respectively, andxis the total number of observations.

Percentage deviation between the calculated and measured valuesis evaluated by MPE. Furthermore, MBE and RMSE indicate long-term and short-term performance of the models, respectively.Negative and positive values of MBE show underestimation andoverestimation, respectively. The smaller values of MPE, MBE and

RMSE show more accuracy of a particular model compared withothers in the same category. For each city, this criterion is used forchoosing the best model in each category as well as the best modelamong all.

5. Results and discussion

Regression analysis for 11 models in 3 different categories for thesix major cities of Iran was conducted using establishing data series.The regression coefficients obtained have been presented in Table 4.Then, for the six nominated cities and for all of the models thestatistical indicators were calculated using the evaluation data series.The calculated statistical indicators have been presented in Table 5.

For each city the best model in each category was recognized by

comparing the statistical parameters related to all of the models in the

same category. In Table 6, the best model of each category and its

related coefficient of determination (R

2

) have been presented for the


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nominated cities. As seen from Table 6 the values ofR2 are closeto unity.

For all of the cities considered, the measured values andpredictions of the best model of each category are shown in Fig. 2. Itis evident from Fig. 2 that for the cities of Isfahan, Mashhad andShiraz the predictions of the best models of three different cate-gories agree better with each other as well as with the measuredvalues. However, for other cities similar agreement does not exist.Also, as presented in Fig. 3, the values of statistical parameters from

one city to another city differ vastly. The largest and worst statis-tical parameters obtained are those of Tabriz. This is due to notabledifferences existing between the measured values by IMO in dataseries for model establishing and data series for evaluating.

In order to choose the best model among all of the models foreach city, the values of MPE, MBE and RMSE for the best modelsof different categories were compared. It was found that it is notpossible to introduce a unique model for all of the cities considered.In the following subsections after a brief description about climaticconditions of each city the best model is introduced.

5.1. Isfahan

Isfahan, center of the Isfahan province, is located in semi-dessert

region in central part of Iran. Its weather condition is totally mildand dry and amount of rainfall and snowfall is low. According toIMO long-term measured data, its annual average temperature is16.2

C, its annual average relative humidity is 40% and its average

annual precipitation is 123 mm. Based on the Klippen classificationits climate is categorized as BWk, which relates to arid desert cold[44]. For Isfahan the best result in category (1) was acquired for


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Table 4

Regression coefficients of different models applied for the six cities considered.

Station Category Model a b c d

Isfahan 1 1 0.3046 0.42922 0.3785 0.2304 0.13233 5.4433 -20.2655 27.6542 -12.26284 0.7267 0.51265 0.3738 0.6867

2 6 0.3950 0.2737 0.00157 0.5285 0.2077 -0.00168 0.6235 0.2404 -0.0030 -0.0036

3 9 0.169110 0.1589 0.037811 0.8025 -0.0019 -0.0040

Karaj 1 1 0.3640 0.27142 0.3922 0.1841 0.06533 -0.0323 2.1476 -2.9149 1.48544 0.6241 0.32705 0.3901 0.4987

2 6 0.3700 0.2579 0.00027 0.4085 0.2331 -0.00048 0.4938 0.2640 -0.0024 -0.0018

3 9 0.150810 0.0752 0.273311 0.5921 0.0014 -0.0014

Mashhad 1 1 0.3278 0.32142 0.2564 0.5617 -0.18923 0.5929 -1.1391 2.5821 -1.45944 0.6353 0.37525 0.3593 0.6093

2 6 0.2768 0.4734 -0.00327 -0.1101 0.6661 0.00398 0.2148 0.5057 -0.0027 0.0006

3 9 0.143810 0.1575 -0.050911 1.1474 -0.0092 -0.0086

Shiraz 1 1 0.3746 0.34002 0.5442 -0.1211 0.30993 -2.0639 10.6699 -14.4747 6.70744 0.7069 0.39875 0.4191 0.5413

2 6 0.3893 0.3131 0.00037 0.3960 0.3184 -0.0001

8 0.3367 0.3347 0.0011 0.00063 9 0.1630

10 0.0863 0.296311 0.7500 -0.0015 -0.0024

Tabriz 1 1 0.2281 0.48372 0.2639 0.3685 0.08903 1.3244 -4.9422 8.7139 -4.54854 0.6946 0.56415 0.2996 0.9020

2 6 0.2188 0.5043 -0.00037 0.0783 0.6108 0.00138 -0.0896 0.6254 0.0031 0.0036

3 9 0.164310 0.1786 -0.047711 0.6694 0.0019 -0.0030

Tehran 1 1 0.2843 0.48682 -0.1286 1.8056 -1.0125

3-

0.9894

5.9364-

7.4931

3.32624 0.7595 0.53385 0.3489 0.8266

2 6 0.2223 0.6353 -0.00227 0.2613 0.5076 0.00028 0.3569 0.6327 -0.0049 -0.0020

3 9 0.191110 0.2424 -0.1614

11 0.6418 0.0033 -0.0022

model (1) with MPE = -0.0781%, MBE = 0.0017 MJ/m2 and RMSE= 0.4795 MJ/m2. Moreover, the best result in category (2) wasobtained for model (7) with MPE = -0.3994%, MBE = 0.0289 MJ/m2and RMSE = 0.5097 MJ/m2 and the best result in category (3) was

obtained for model (11) with MPE = -0.3521%, MBE = 0.0870

Table 5

MPE, MBE and RMSE of different models for the six cities considered.

Station Category Model # MPE (%) MBE (MJ/m2) RMSE (MJ/m

2)

Isfahan 1 1 -0.0781 0.0017 0.47952 -0.0122 0.0161 0.49233 -0.4816 -0.0969 0.47434 -0.1683 -0.0175 0.46855 -0.0222 0.0148 0.4952

2 6 -0.7184 -0.0825 0.51417 -0.3994 0.0289 0.50978 0.4447 0.2231 0.6026

3 9 2.0057 0.4846 0.823310 1.7983 0.4274 0.757111 -0.3521 0.0870 0.6953

Karaj 1 1 -5.2821 -0.5918 2.23582 -5.2794 -0.5914 2.23983 -5.1752 -0.5760 2.21644 -5.3048 -0.5962 2.22425 -5.2922 -0.5936 2.2403

2 6 -5.3473 -0.5978 2.25017 -5.2880 -0.5828 2.25598 -4.4835 -0.4751 2.1603

3 9 -9.2317 -1.0600 3.157110 -7.9576 -0.9803 2.511611 -6.0356 -0.6565 2.3937

Mashhad 1 1 -0.0103 -0.0773 0.78022 0.0452 -0.0869 0.84913 -0.2131 -0.1375 0.96764 0.0172 -0.0880 0.82985 -0.0734 -0.0751 0.7448

2 6 0.3787 -0.0984 0.72167 0.1055 -0.1735 0.73808 0.3396 -0.1106 0.7146

3 9 -3.9809 -0.8138 1.561410 -4.3426 -0.8388 1.514111 0.8545 0.0646 1.1532

Shiraz 1 1 0.1356 0.1081 2.07942 0.1394 0.1144 2.26393 0.2295 0.1386 1.94594 0.1157 0.1010 2.06375 0.1271 0.1079 2.0575

2 6 0.0396 0.0978 1.09937 0.0672 0.0989 1.0273

8 0.0802 0.1103 1.11843 9 -3.2953 -0.4684 2.4772

10 -2.3429 -0.3803 2.098411 -1.0276 -0.1105 1.7928

Tabriz 1 1 16.1608 2.2352 2.54102 16.2056 2.2426 2.55893 15.5036 2.1453 2.44024 16.0151 2.2060 2.48345 16.1860 2.2451 2.5829

2 6 16.1482 2.2267 2.53307 15.9295 2.1841 2.55038 15.6524 2.1803 2.6645

3 9 16.3819 2.2057 2.381910 16.1742 2.2227 2.422811 16.9675 2.3527 2.5849

Tehran 1 1 5.0525 0.4045 1.38952 2.1075 0.1323 1.4145

3 0.1097 -0.0673 1.62234 4.2381 0.3365 1.38765 5.4550 0.4455 1.4168

2 6 3.8483 0.2265 1.52017 5.0036 0.3936 1.41068 2.7570 0.0993 1.5012

3 9 10.4660 1.1486 1.552410 10.3069 1.3158 1.6129

11 7.9379 0.7859 1.3814

MJ/m2 and RMSE = 0.6953 MJ/m2. After comparing the statisticalindicators for the three aforementioned models for Isfahan, the model

(1) from category (1) in which:

( / )

H/Ho = 0.3046 + 0.4292 n N


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a b

c ____________________________

e _____________________________ f

Fig. 2. Predictions of the best models compared with the measured values.


Table 6

The best model of each category and its related coefficient of determination for thesix cities considered.

City Category Model # R2 City Category Model # R2

Isfahan 1 1 0.9966 Karaj 1 3 0.93422 7 0.9978 2 8 0.93253 11 0.9862 3 11 0.9289

Mashhad 1 5 0.9802 Shiraz 1 4 0.9881

2 8 0.9961 2 6 0.98793 11 0.9724 3 11 0.9783Tabriz 1 3 0.9853 Tehran 1 3 0.9761

2 8 0.9819 2 8 0.9802

3 9 0.9721 3 11 0.9706

is assessed as the best model among all. As a result and irrespectiveof climatic parameters, the simple Angstrm model, in which onlymonthly average relative sunshine duration is considered, performswell for Isfahan. A similar model proposed for Isfahan using PSOtechnique by Behrang et al. [22] is:

( / )H/Ho = 0.4276 + 0.2746 n N

By using the data series for evaluation the statistical indicatorsfor this model were calculated as MPE = 0.4804%, MBE =0.0388 MJ/m

2and RMSE = 0.4641 MJ/m2. Comparing these

statistical indicators with those of model (1) reveals betterperformance of the newly proposed model (1) of this study.

5.2. Karaj

Karaj, center of the Alborz province, is located toward north ofIran close to capital Tehran. Due to height differences in the lowlandsand highlands, Karaj enjoys vegetation diversity. Its annual averagetemperature is 14.9

C, its annual average relative humidity is 47%

and its average annual precipitation is 244 mm. Based on the Kppenclassification its climate is categorized as BSk, which relates to aridsteppe cold [44]. For Karaj the best result in


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H. Khorasanizadeh, IC Mohammadi / Energy 51 (2013) 257-266 263

0.03

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Fig. 3. MPE, MBE and RMSE of the best models of each category.

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category (1) was obtained for model (3) with MPE = -5.1752%, MBE= -0.5760 MJ/m

2and RMSE = 2.2164 MJ/m

2. Moreover, the best

result in category (2) was obtained for model (8) with MPE = -4.4835%, MBE = -0.4751 MJ/m2 and RMSE = 2.1603 MJ/m2andthe best result in category (3) was obtained for model (11) with MPE= -6.0356%, MBE = -0.6565 MJ/m2 and RMSE = 2.3937 MJ/ m2.According to comparison of statistical indicators for the threeaforementioned models, the model (8) from category (2) in which:

~ . ~H/Ho = 0.4938 + 0.2640 n N- 0.0024Tavg - 0.0018Rh

is assessed as the best model among all for Karaj. It pretends thatfor Karaj in addition to monthly average relative sunshineduration the climatic parameters of monthly average temperatureand relative humidity play role. This is the first time a model isbeing proposed for Karaj, therefore there is no chance of makingany comparison.

5.3. Mashhad

Mashhad, center of the Khorasan Razavi province, is located in the

north-east part of Iran. The weather condition in Mashhad is mild andvariable. Its annual average temperature is 14.1 C, its annual averagerelative humidity is 55% and its average annual precipitation is 255mm. Based on the Klippen classification its climate is cate-gorized asBSk, which relates to arid steppe cold [44]. For Mashhad the bestresult in category (1) was obtained for model (5) with MPE = -0.0734%, MBE = -0.0751 MJ/m2 and RMSE = 0.7448 MJ/m2.Likewise, the best result in category (2) was obtained for model (8)with MPE = 0.3396%, MBE = -0.1106 MJ/m

2and RMSE = 0.7146

MJ/ m2 and the best result in category (3) was obtained for model (11)with MPE = 0.8545%, MBE = 0.0646 MJ/m2 and RMSE = 1.1532MJ/ m

2. After comparing the statistical indicators for the three afore-

mentioned models, the model (5) from category (1) in which:

~ ~ . ~~H/Ho = 0.3593exp 0.6093 n N

is assessed as the best model among all. It means the monthlyaverage relative sunshine duration is definitive for Mashhad.Another model proposed for Mashhad is the one obtained byBehrang et al. [22] using PSO technique as:

~ ~ . ~~H/Ho = 0.862 + 0.3575cos 0.0775 n N

~ ~ . ~~+ 0.1213sin 0.0775 n N

~ ~ . ~~+ 0.8962cos 0.155 n N

~ ~ . ~~0.6353sin 0.15 5 n N

~ ~ . ~~0.0707cos 0.2325 n N

~ ~ . ~~0.0037sin 0.2325 n N

By using the data series for evaluation the statistical indicatorsfor this model were calculated as MPE = 3.823%, MBE = 0.2835MJ/ m2 and RMSE = 0.7268 MJ/m2. Comparing these statisticalindi-cators with those of model (5) reveals better performance ofthe proposed model (5) of this study.

5.4. Shiraz

Shiraz, center of the Fars province, is located in the region

between the south and west-south of Iran. Weather condition in

Shiraz is similar to Mediterranean. Its annual average temperature is17.7 C, its annual average relative humidity is equal to 41% and itsaverage annual precipitation is 346 mm. Based on the Klippenclassification the Shiraz climate condition is categorized as BSk,which relates to arid steppe cold [44]. For Shiraz the best result incategory (1) was obtained for model (4) with MPE = 0.1157%, MBE= 0.1010 MJ/m2 and RMSE = 2.0637 MJ/m2. Also, the best result incategory (2) was obtained for model (6) with MPE = 0.0396%, MBE= 0.0978 MJ/m2 and RMSE = 1.0993 MJ/m2and the best result incategory (3) was obtained for model (11) with MPE = -1.0276%,MBE = -0.1105 MJ/m2 and RMSE = 1.7928 MJ/m2. Aftercomparing the statistical indicators for three aforementioned models,the model (6) from category (2) in which:

~ . ~H/Ho = 0.3893 + 0.3131 n N+ 0.0003Tavg

is assessed as the best model among all. It pretends that for Shirazin addition to monthly average relative sunshine duration themonthly average temperature is important. Behrang et al. [22] byusing PSO technique suggested the following model for Shiraz:

~ . ~H/Ho = 0.3661 + 0.1133exp n N

By using the data series for evaluation the statistical indicatorsfor this model for Shiraz were calculated as MPE = -12.0844%,MBE = -2.0925 MJ/m2 and RMSE = 2.4979 MJ/m2. Comparingthese statistical indicators with those of model (6) reveals betterperformance of the proposed model (6) of this study.

5.5. Tabriz

Tabriz, center of west Azarbaijan, is located in the north-westpart of Iran. The city enjoys mild and fine climate in spring, dry andsemi-hot in summer, humid and rainy in autumn and snowy cold inwinter. Its annual average temperature is 12.5 C, its annual average

relative humidity is 54% and its average annual precipita-tion is341 mm. However, based on the Klippen classification the Tabrizclimate condition is categorized as BSk, which relates to arid steppecold [44]. For Tabriz the best result in category (1) was ob-tainedfor model (3) with MPE = 15.5036%, MBE = 2.1453 MJ/m2andRMSE = 2.4402 MJ/m2. Moreover, the best result in category (2)was obtained for model (8) with MPE = 15.6524%, MBE = 2.1803MJ/m

2and RMSE = 2.6645 MJ/m2 and the best result in category

(3) was obtained for model (9) with MPE = 16.3819%, MBE =2.2057 MJ/m

2and RMSE = 2.3819 MJ/m2. After comparing the

statistical indicators for three aforementioned models, the model (3)in category (1), in which:

~ . ~H/Ho = 1.3244 - 4.9422 n N

2 3

+ 8.7139 (n .N) -4.5485 (n. N)

is assessed as the best model among all. It means that for Tabriz themonthly average relative sunshine duration is authoritative. By usingPSO technique, Behrang et al. [22] for Tabriz suggested:

~ . ~H/Ho = 0.5672 + 0.2197log n N

By using the data series for evaluation, the statistical indicatorsfor this model were calculated as MPE = 12.9720%, MBE =1.4152 MJ/m

2and RMSE = 1.5385 MJ/m2 indicating better

performance of this model compared with model (3) of this study.

This may be due to different time periods for data series of this


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study compared to that of Behrang et al. as well as the fact that in cities of Tabriz and Tehran, due to considerable differences in

the present study forfinding which reported solar radiation values monthly averaged measured meteorological parameters of thesewere not correct a different method was used compared with that two cities, the corresponding regression constants for the proposedof Behrang et al. [22]. The method of this study was explained in model differed vastly. This emphasizes that a particular verifiedSection 3 but Behrang et al. [22] did not report clearly the criterion model for a region can be used for another region only if the detailthey used. of variations of relative sunshine duration and other meteorological

parameters throughout the year are very similar.

5.6. Tehran Acknowledgments

Tehran is the capital and the largest city of Iran. Tehran s climateis mainly defined by its geographic location, with the toweringAlborz Mountains to its north and the central desert to the south. Itcan be generally described as mild in the spring and autumn, hot anddry in the summer and cold in the winter. Due to population densityand huge number of cars, Tehran is a polluted city. Tehran has 2meteorological stations, one located in the south-west (Mehrabadairport station) and the other is located in the north part of the city(North station). In the present study, the data collected at Tehrannorth station were used. For north station, the annual averagetemperature is 15.5 C, annual average relative humidity is 46% andaverage annual precipitation is 429 mm. Based on the Kppenclassification the Tehran climate condition is cate-gorized as BSk,which relates to arid steppe cold [44]. For Tehran the best result incategory (1) was acquired for model (3) with MPE = 0.1097%, MBE= -0.0673 MJ/m


2. Also, the best result in

category (2) was obtained for model (8) with MPE = 2.7570%, MBE= 0.0993 MJ/m


2and the best result in

category (3) was obtained for model (11) with MPE = 7.9379%,MBE = 0.7859 MJ/m


2. After comparing

the statistical indicators for the three aforemen-tioned models, themodel (3) in category (1) in which:

( / )H/Ho = -0.9894 + 5.9364 n N

( /)2 ( /)3- 7 .4931 n N +3 .3262 n N

is assessed as the best model among all. It means for Tehran themonthly average relative sunshine duration is definitive. This isthe first time a model is being proposed for Tehran based on thenorth station data, consequently there is no chance of making acomparison.

6. Conclusion

In this study, 11 different models classified into 3 categories werenominated from the literature. After performing regression analysisand evaluating these models, according to the measured dataprovided by IMO, the best model has been introduced for each of sixmajor cities of Iran, named Isfahan, Karaj, Mashhad, Shiraz, Tabriz

and Tehran. Based on Kppen classification, except Isfahan withBWk climate type the other cities belong to BSk climate type.However, the results show that there is no chance of introducing asingle and similar model even for the cities in a similar climatic type.Kppen BWk and BSk classifications are based on average annualprecipitation as well as the absolute annual mean temper-ature. Theresults of this study show that as for solar predictions the detailedvariation of meteorological parameters throughout the year is moreimportant than annually averaged values. It was found that themodels from category 3, in which relative sunshine dura-tion is notconsidered, are not suitable to present the solar data for differentcities of this study. However, the best models preferred for the sixconsidered cities are all from categories 1 and 2, in which relativesunshine duration is a variable. Although a similar cubic sunshine

duration based model was recognized suitable for the

The authors wish to thank the energy research institute of theUniversity of Kashan for supporting this research (Grant No.158576/3). Also thanks are extended to Iranian meteorologicalorganization for providing raw data.

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http://dx.doi.org/10.1155/2007/94786http://dx.doi.org/10.1155/2007/94786http://dx.doi.org/10.1155/2007/94786http://dx.doi.org/10.1155/2007/94786

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