Arab J Sci Eng (2014) 39:175–179DOI 10.1007/s13369-013-0819-3

RESEARCH ARTICLE - EARTH SCIENCES

Estimating Global, Diffuse Solar Radiation for Chhorand Validation with Satellite-Based Data

Asif Ali Abbasi · M. Shahid Qureshi

Received: 13 November 2012 / Accepted: 15 April 2013 / Published online: 26 October 2013© King Fahd University of Petroleum and Minerals 2013

Abstract The study of solar irradiation has been carriedout for the first time over Chhor (city of Sindh province inPakistan). In the present work, measured data of bright sun-shine hour of the regions have been used to estimate monthlyaverage daily global and diffuse solar radiation. Regressioncoefficients a and b have been calculated from the first-orderAngstrom type correlation for the city using relationshipgiven by Tiware and Sangeeta. The results obtained throughfour empirical models i.e., Angstrom, Liu and Jordon, Page,Hawas and Muneer were compared with values obtainedfrom NASA Satellite-based Global and Diffuse radiationdata. A good agreement was found between satellite-basedvalues with Muneer and Hawaas model. The global irradia-tion is found high from April to July for the period of study.The statistical error tests—mean bias error, root mean squareerrors are used to validate the estimates using satellite-baseddata. MBE has lowest values for diffuse solar radiation thanglobal radiation and shows over estimation. The value ofcoefficient of determination implies that 98.7 % of NASA canbe accounted by estimation of global solar radiation Chhor.Low values of variance suggest that the correlation is bestfitted.

Keywords Global and diffuse radiation · Angstromcoefficient · Mean bias error · Root mean square error

A. A. Abbasi (B)Institute of Space and Planetary Astrophysics,University of Karachi, Karachi, Pakistane-mail: asifhamal@gmail.com

M. S. QureshiDepartment of Mathematical Sciences, IBA, Karachi, Pakistan

1 Introduction

The sun radiant energy is the only source that influencesthe atmospheric motion which can be used as an alterna-tive energy resource, in view of future depletion of fossilfuel reservoirs. Information about global solar radiation isthe most important for wide variety of applications, e.g.solar energy system’s design, building’s design, crop dry-ing, photosynthesis etc. Solar radiation data are collected inthe major parts of the world but is unavailable in develop-ing countries like Pakistan which cannot afford expensiveinstruments Viorel Badescu [1]. Due to the fact, it is impor-tant to develop methods of estimating the solar radiation onthe basis of available meteorological data. Several formulashave also been developed by various authors to estimate theamount of global solar radiation on horizontal surfaces usingvarious parameters, such as sunshine duration, cloud cover,

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humidity, maximum and minimum temperatures, wind speedetc. Recently, Wu et al. [2], used the meteorological data ofNanchang Station (China) to predict daily global solar radia-tion from sunshine hours and dew points. An effective resultwas achieved by model which uses sunshine duration. Araset al. [3], developed empirical models to predict the monthlyaverage daily global solar radiation over twelve provinces inthe Central Anatolia Region (CAR) of Turkey and to com-pare calculated values obtained from developed models withdata measured by the Turkish State Meteorological Service(DMI) in the period from January 1990 to December 1996based on the various statistical methods. The measured dataof global and diffuse solar radiation on a horizontal surface,the number of bright sunshine hours, mean daily ambienttemperature, maximum and minimum ambient temperatures,relative humidity, and amount of cloud cover for Jeddah (lati-tude 21◦42′37′′N, longitude 39◦11′12′′E), Saudi Arabia, dur-ing the period (1996–2007) were analyzed by El-Sebaii et al.[4], Recently Viorel Badescu et al. [5,6], computed globaland diffuse solar hourly irradiation on clear sky as well asdiscussed the accuracy and sensitivity analysis for 54 mod-els of computing hourly diffuse solar irradiation on clearsky. Mehmet Kaya [7] studied the models of global solarradiation on the horizontal surface in the literature that areinvestigated, and new empirical models based on the sun-shine hour data for Erzincan, Turkey are developed. Severalresearchers have used one or more meteorological data forthe estimation of global solar radiation on horizontal surfacein Pakistan. Firoz Ahmed et al. [8], studied the prospects ofsolar energy utilization in Karachi’s. Ilyas et al. [9], stud-ied global solar radiation over Pakistan. Akhlaque Ahmedet al. [10,11], estimated global and diffuse solar radiation ofHyderabad and Lahore in recent years. Chhor is located atlatitude 25.52◦ and longitude of 69.46◦ near to Thar Desertof Sindh, Pakistan. In this study, an attempt was made by cal-culating regression coefficient from the first-order Angstromtype correlation as well as to estimate monthly average dailyglobal and diffuse radiation for Chhor. The significance ofestimating the averaged daily diffuse radiation on a horizon-tal surface is that, when the sun is obscured by thick cloud, orthe sun is below the horizon, gives a direct measurement ofthe energy received on a horizontal solar panel. Dependingon the altitude and azimuth of the sun at any moment if thesolar panel can be adjusted according to the solar angle, thereis increase in the energy received. Such estimates then leadto the obtained estimates of the energy output from any solarinstallation, depending on the efficiency of the system. In theend, mean bias error (MBE) and root mean bias error (RMSE)were also used to evaluate the accuracy of data Karakoti andDatta [12]. The objective of this study is to develop a sin-gle correlation between global radiation and bright sunshinehours, which can be used to estimate monthly average globalsolar radiation with the input of only sunshine records. This

procedure will be implemented by using the measured datafor both of these parameters for Chhor station. It also com-pares statistically the performance of our correlation.

2 Methodology

The Angstrom [13], equation relates monthly averaged dailyirradiation Ho to clear day irradiation H and the number n ofhours of bright sunshine.

H = Ho[a + b(n/N )] (1)

Ho is the monthly-mean daily radiation on a horizontal sur-face in the absence of atmosphere. To compute coefficientsa and b, the relationship given by Tiware and Sangeeta[14], can be used. The values of Ho, the radiation receivedunder the absence of any atmosphere may be calculated byMuneer [15]:

Ho = (0.024)/Isc[1 + 0.033 cos(360 DN/365)]× [cos LAT cos DEC sin Ws + (2πWs/360)

× sin LAT sin DEC (2)

where Isc is the solar constant, LAT is the latitude, DEC isthe solar declination, and Ws is the sunset hour angles.

Yallop’s algorithm [16], enables a high precision com-putation of DEC. The routine in this algorithm is valid forthe period 1980–2050 and has an accuracy of 1 min of arcfor DEC. For longer period high precession calculation, thecomplete version of VSOP theory, Bretagnon and Francou[17], may be used.

3 Prediction of Diffuse Solar Radiation

A regression between monthly averaged values of diffuse andglobal irradiation was first developed by Liu and Jordon [18],which correlate diffuse fraction (ratio of diffuse radiation Hd

and global radiation H) with clearness index which is theratio of the global radiation to extraterrestrial radiation Ho

i.e., KT = H/Ho, where Hd is the monthly average dailydiffuse radiation incident on horizontal surface.

Hd/H = 1.390 − 4.027KT + 5.53(KT)2 − 3.108(KT)3

(3)

Hawas and Muneer [19], worked on the data which was basedon long-term measurement undertaken at 13 stations in Indiafor the period 1957–1975 and the model proposed for Indiansubcontinent is

Hd/H = 1.35 − 1.61KT (4)

For temperate climates and for location close to the tropics,the correlation developed by Page [20], is widely used and isgiven as follows

Hd/H = 1.00 − 1.13KT (5)

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4 The Validation Method

The ground measurement and satellite-derived solar radia-tion data complement each other and are required to builda complete solar radiation database. The model accuracy isdetermined by comparison of modeled data series againstground-estimated parameters as shown in the studies of Boyoand Adeyemi [21], Davies et al. [22], Djemaa and Delorme[23], Perez et al. [24], Pereira et al. [25], Argirion et al. [26],Schillings et al. [27], and Lefevre and Wald [28]. The sta-tistical indicator allows models to be compared and at thesame time indicate whether or not a model’s estimates arestatistically significant at a particular confidence level Stone[29]. Mean bias error and RMSE have been found out, andthe values of correlation coefficient of determination (R2),variance (S), were also determined for regression equationdeveloped for Chhor.

MBE =[∑

(Hic − Hio)]/

n (6)

RMSE ={ [∑

(Hic − Hio)2] /

n

}1/2

(7)

In general, a low RMSE is desirable. The positive MBEshows overestimation, while a negative MBE indicatesunderestimation.

5 Results and Discussion

Table 1 gives the input parameters declination of the sun, sun-shine hour’s n, and day length N, for each month. The daylength N and Angstrom coefficients a and b were calculatedusing equation given by Tiware and Sangeet. Monthly meandaily extraterrestrial radiation Ho is estimated from Eq. (2)and values are listed in Table 2. The values of Angstrom coef-

Table 1 Input parameters forestimation of monthly averagedaily global solar Chhor

Months Declination(in deg)

Monthly meansunshine hour (n)

Monthly averageday length (N)

Coefficient“a”

Coefficient“b”

Jan −19.95 9.55 10.672 0.3911 0.329

Feb −10.63 9.88 11.316 0.384 0.344

Mar 0.15 10.15 12 0.375 0.362

Apr 11.78 10.91 12.75 0.378 0.356

May 20.13 10.91 13.33 0.366 0.382

June 23.43 9.61 13.58 0.33 0.455

July 20.13 7.31 13.34 0.266 0.565

Aug 12.18 7.62 12.76 0.294 0.536

Sep 0.78 9.87 12.04 0.366 0.382

Oct −10.61 10.53 11.31 0.402 0.304

Nov −19.86 10.2 10.67 0.410 0.287

Dec −23.43 9.40 10.41 0.393 0.324

Table 2 Monthly average dailyglobal solar radiation data Chhor Months Ho

(kWh/m2)

Hest(kWh/m2)

HNASA(kWh/m2)

KT(H/H0)

Hd/H(LJ)

Hd/H(MH)

Hd/H(Page)

Jan 6.57 4.52 4.12 0.687 0.218 0.244 0.224

Feb 7.748 5.34 4.89 0.689 0.22 0.241 0.222

Mar 9.115 6.25 5.61 0.686 0.228 0.246 0.225

Apr 10.295 7.06 6.30 0.686 0.228 0.246 0.225

May 10.948 7.45 6.51 0.681 0.229 0.254 0.231

June 11.145 7.27 6.56 0.652 0.281 0.301 0.264

July 11.012 6.36 5.85 0.577 0.306 0.422 0.348

Aug 10.511 6.42 5.57 0.611 0.282 0.367 0.31

Sep 9.508 6.43 5.55 0.677 0.231 0.261 0.235

Oct 8.129 5.55 4.95 0.683 0.228 0.251 0.229

Nov 6.835 4.66 4.20 0.683 0.228 0.251 0.229

Dec 6.222 4.26 3.90 0.685 0.228 0.248 0.226

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ficient are then used to estimate monthly average daily globalsolar radiation Hest using Eq. (1) and are given in Table 2.Measured data are taken from NASA satellite for the globalsolar radiation HNASA as shown in Table 2. The transparencyof the atmosphere is indicated by KT fraction of extraterres-trial radiation that reaches the earth surface as global solarradiation. It is a measure of the degree of clearness of thesky. KT is calculated in Table 2 and values show that sky isvery clear almost throughout the year (i.e., 60 %). The ratioof the monthly average daily diffuse radiation to the monthlyaverage daily global radiation (Hd/H ) is calculated usingEqs. (3), (4) and (5) from different diffuse solar radiationmodels. The diffuse fraction is calculated for Liu and Jor-don, Page, Hawas and Muneer models and given in Table 2.

Table 3 Monthly averaged daily diffuse solar radiation data Chhor

Months Hd, LJ(kWh/m2)

Hd, MH(kWh/m2)

Hd, Page(kWh/m2)

Hd, NASA datasatellite-based(kWh/m2)

Jan 0.98 1.102 1.012 1.04

Feb 1.17 1.286 1.185 1.26

Mar 1.425 1.537 1.406 1.62

Apr 1.609 1.736 1.588 1.93

May 1.706 1.892 1.72 2.19

Jun 2.04 2.188 1.919 2.27

Jul 1.946 2.683 2.21 2.37

Aug 1.81 2.356 1.99 2.21

Sep 1.48 1.678 1.51 1.81

Oct 1.265 1.393 1.27 1.43

Nov 1.06 1.169 1.067 1.13

Dec 0.97 1.056 0.962 0.96

Table 4 MBE and RMSE for global and diffuse radiation of Chhor

Radiation MBE (KWh/m2) RMSE (KWh/m2)

Global −0.63 0.65

Diffuse −0.12 0.15

There is remarkable agreement between the estimated andmeasured values for global solar radiation. The maximumof global radiation for the month of June and July is quiteappreciable. Table 3 gives the values of diffuse solar radi-ation. Diffuse solar radiation is not commonly measured inany meteorological station of Pakistan; therefore, the dif-fuse solar is estimated by Liu and Jordon, Page, Hawas andMuneer method using Eqs. (3), (4) and (5). The estimated val-ues of diffuse solar radiation by Liu and Jordon, Page, Hawasand Muneer models are listed in columns (1–3), respectively,of Table 3.

NASA measured values of diffuse solar radiation are alsotaken into account. There is a good agreement between theestimated and measured values and the NASA satellite datafor diffuse solar radiation and was best fitted with the valuesestimated from Muneer and Hawaas model. The statisticalerrors (MBE and RMSE) for global and diffuse solar radi-ation are given in Table 4. The RMSE and MBE values arevery low, indicating fairly good agreements. MBE has low-est values for diffuse solar radiation than global radiationand shows overestimation (the negative values indicate thatthe present correlations slightly overestimate H). RMSE alsohas smaller values for diffuse radiation than global radiationdata.

The value of coefficient of determination implies that98.7 % of NASA can be accounted by estimation of globalsolar radiation Chhor as shown in Fig. 1. Low values of vari-ance suggest that the correlation is best fitted.

6 Conclusion

The estimated values of global and diffuse solar radiationsuggest that solar radiation can be used as an alternate energyresource for this region. The difference in ground-based andsatellite-derived data was small on clear sky. NASA satellitedata of diffuse radiation show good agreement with the valuesfrom Muneer and Hawaas model. The result obtained showsthat the solar energy utilization has bright prospects in Chhor.The analysis of the estimated and measured values of H

Fig. 1 Fitted regression line forthe estimated and NASAsatellite data of Chhor

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shows that the maximum values of global solar radiation areobserved in June while the minimum appeared in December.It is further suggested that Hawaas and Muneer model maybe best for an estimation of monthly daily diffuse radiationover this region.

Acknowledgments The data of global and diffuse solar radiationwere obtained from the NASA (Langley Research Center AtmosphericSciences Data Center POWER Project) [30]. The Pakistan Meteorolog-ical Department, Karachi, Sindh has also kindly provided the data setsof sunshine duration utilized in this study.

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