measurements of spectral-band solar irradiance in bangi, malaysia

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Solar Energy 89 (2013) 62–80

Measurements of spectral-band solar irradiance in Bangi, Malaysia

Yousef A. Eltbaakh a,⇑, M.H. Ruslan b,⇑, M.A. Alghoul b,⇑, M.Y. Othman b, K. Sopian b

a Department of Physics, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysiab Solar Energy Research Institute, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia

Received 6 December 2011; received in revised form 10 November 2012; accepted 24 November 2012Available online 19 January 2013

Communicated by: Associate Editor Christian Gueymard

Abstract

In the present study, a series of global spectral-band solar irradiance measurements over a wide range of optical air masses and atmo-spheric conditions in the interval of 400–1100 nm is presented. The measurements were obtained continuously using 12 Li-200SA pyr-anometers equipped with different Schott glass, flat, circular, and long-pass filters on a horizontal surface at Universiti KebangsaanMalaysia (2�550N, 101�460E) between September 1 and November 30, 2011. By combining the measurements obtained using differentfilters, obtaining global solar irradiance in various wavebands is possible. To support the experimental data, the results were comparedwith the simulated results of the Simple Model for the Atmospheric Radiative Transfer of Sunshine (SMARTS2) model. Forecastingperformance parameters such as the normalized root mean square error (NRMSE), the normalized mean bias error (NMBE), and R2

have been used to test the accuracy of observed data. NRMSE for the whole spectrum varies from 0.7% to 5.3%, whereas NMBE variesfrom �2.1% to 2.3%. The determination coefficient R2 results for all air masses are near 1.0. Simulated and measured data show goodagreement over the whole measured spectrum. The measurement of solar radiation using pyranometers equipped with filters is much lesscomplicated, more compact, and is less costly than using spectroradiometers.� 2012 Elsevier Ltd. All rights reserved.

Keywords: Li-200SA pyranometers; Filters; Experimental measurement; SMARTS2 model; Statistical tests

1. Introduction

Solar radiation energy received at the earth’s surface isthe basic data in a variety of fields. Knowing the amount(the integral of all electromagnetic radiation, also called“broadband”) of solar radiation is very important formany applications, such as atmospheric energy-balancestudies; analysis of the thermal load on buildings; design-ing, operation, and economic assessment of energy andrenewable energy systems; and for some environmentalimpact analysis (Jacovides et al., 2004; Iqbal, 1983; Muneeret al., 2007). In recent years, due to an increase in terrestrial

0038-092X/$ - see front matter � 2012 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.solener.2012.11.016

⇑ Corresponding authors.E-mail addresses: [email protected] (Y.A. Eltbaakh), hafidz-

[email protected] (M.H. Ruslan), [email protected] (M.A. Al-ghoul).

applications of solar energy, the scientific interest hasexpanded from the total amount of solar energy to its spec-tral distribution (Kaskaoutis and Kambezidis, 2009).Many physical and chemical processes are activated morepowerfully at some wavelengths than at others. This condi-tion is especially true and important in the field of solarenergy engineering for the design of certain solar energyapplications such as photovoltaic cells for electric genera-tion and selective absorbers for thermal collectors, andfor practical applications in environmental and agrometeo-rological research (Iqbal, 1983; Jacovides and Kallos, 1993;Gueymard, 2008).

While global solar irradiance (GSI) measurements arenow routinely made at many locations throughout theworld, global spectral solar irradiance (GSSI) measure-ments are uncommon in many areas throughout the world.This is principally due to the spectral irradiance measuring


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Nomenclature

Roman letters

kt clearness indexk the diffuse ratioV visibilityVr the meteorological rangeVm maximum meteorological range (340.85 km)CA cloud cover amountS sunshine fractionRh relative humidityTLI-200 Li-200SA temperatureTair air temperatureTo reference temperatureE Li-200SA measured irradianceCcorr the factor for correcting the temperature influ-

ence on Li-200SAf(hz) spectral correction of the global irradiance asso-

ciated with the solar angle of incidence for Li-200SA

W(k) smoothing function for broadening the mod-elled spectra to match the bandpass shape andwidth resulting from the combination of differ-ent long-pass filters

Greek letters

b Angstrom turbidity coefficienta Angstrom wavelength exponent for the whole

spectruma1 Angstrom wavelength exponent for k < 500 nma2 Angstrom wavelength exponent for k > 500 nmdA aerosol optical depth

C1–C3 coefficients of Eq. (11)D1–D4 coefficients of Eq. (12)hz solar zenith anglek wavelengthac temperature coefficient correction for Li-200SA

combination with each filterg a constant resulting from the relative definitions

of V and Vr (g = 1.306)km the wavelength corresponding to 50% of the fil-

ter transmittance from the main band transmis-sion (also defined as the center of the cutoff)

kc1 the starting position of the uniform transmit-tance (90%) resulting from the combination ofany two long-pass filters

kc2 the end position of the uniform transmittance(90%) resulting from the combination of anytwo long-pass filters

Acronyms

GSI global solar irradianceGSSI global spectral solar irradianceSPPs silicon-photodiode pyranometersUKM Universiti Kebangsaan MalaysiaCC calibration constantAM air massSMARTS Simple Model for the Atmospheric Radiative

Transfer of SunshinePMs parameterized modelsPRTMs rigorous radiative transfer modelsFWHM full width half maximum

Y.A. Eltbaakh et al. / Solar Energy 89 (2013) 62–80 63

systems are more sophisticated and more elaborate calibra-tion process. Furthermore, depending on sensor type, theoperation of spectral radiometers can be labor intensive,often leading to increased costs. Unfortunately, this eco-nomic barrier has contributed to the lack of spectral dat-abases (Morley, 2003). Measurement of GSSI is similarto the measurement of GSI with the important additionalcomplexity that incoming solar radiation must first be sep-arated by wavelength (scanning-type instruments) ordivided based on the interference phenomenon (FourierTransform Instruments) before the detector records the sig-nal (Calisesi et al., 2007; Dyer, 2001).

Due to the absence of high-resolution spectral measure-ments, which are possible only with very sophisticatedinstruments, a simple and comparatively inexpensiveinstrument, pyrheliometer or pyranometer, in combinationwith glass filters may be used (Jacovides and Kallos, 1993;Iqbal, 1983). Several authors (Kvifte et al., 1983; Iqbal,1983; Jacovides and Kallos, 1993; Utrillas et al., 2000) haveused pyrheliometer equipped with different filters to obtaindirect solar radiation in various wavebands. In this study,an attempt has been made to expand this method to

investigate global solar radiation, taking into account thediffuse portion of radiation. The present study aims todescribe a simple way of measuring the global spectral-band solar radiation with an inexpensive set-up in the inter-val of 400–1100 nm. Experimental and simulation (SimpleModel for the Atmospheric Radiative Transfer of Sunshine[SMARTS2] model) results under cloud-free conditions arecompared in this study.

2. Experimental site

The climate of Malaysia is equatorial, being hot andhumid throughout the year. The year can be subdividedinto two distinct seasons. The dry season commences fromthe month of May and continues until September, which isalso the time of the southwest monsoon. The rainy seasonis from the middle of November to March, marked by thearrival of the northeast monsoon (Azhari et al., 2007). Theexperimental work was conducted continuously betweenthe last month of the dry season (September 1) and the firstmonth of the rainy season (November 30, 2011). The atmo-spheric conditions in this period are characterized by heavy

64 Y.A. Eltbaakh et al. / Solar Energy 89 (2013) 62–80

rainfall. The measurements were taken on the roof of abuilding, at the Physics Department of Universiti Kebang-saan Malaysia (UKM), with geographical coordinates of2�550N latitude and 101�460E longitude, and with theinstrument altitude of approximately 45 m above sea level.The available area on the roof was about 10 m2 and is sur-rounded by other buildings of the university. The horizonwas unobstructed in all directions from sunrise to sunset,except at the very high solar zenith angles (hz > 85�). Themeasurement site was located on the main campus of theuniversity, which spans an area of about 1096.29 hectares,situated in a valley surrounded by hills and green areas inthe district of Bangi, Malaysia. Topographically, the areais moderately flat with several small streams and patchesof swamps and is located at an altitude of 40–110 m abovesea level (Bhaskar and Mehta, 2010).

3. Experimental set-up and methodology

The system used in the present study has three majorparts:

3.1. Li-COR pyranometer (Li-200SA)

“Silicon-photodiode pyranometers (SPPs) are nowwidely used for solar irradiance measurements associatedwith solar thermal and photovoltaic power systems, as wellas for agricultural applications” (King and Myers, 1997).“They are small, light weight, provide the opportunity forlow-cost redundancy, can be calibrated quickly with a solarsimulator and can easily be modified to measure direct nor-mal irradiance” (King et al., 1998). SPPs may be handheldor mounted at any required angle, provided that reflectedradiation is not a significant portion of the total. In its mostfrequent application, the pyranometer sensor is set on alevel surface that is free from any obstruction to eitherdirect or diffuse radiation. Among the Silicon-photodiodepyranometers, Li-200SA has been chosen for the presentstudy. Li-200SA is an instrument used to measure globalsolar radiation received from a whole hemisphere in thewavelength range of 400–1100 nm. The instrument has arapid response time of about 10 ls, making the sensorappropriate for measuring rapid solar radiation changes

Fig. 1. Li-200SA spectral response curve.

associated with intervals when clouds move in front ofthe sun (Alados-Arboledas et al., 1995). The responseregion of Li-200 SA pyranometer includes about 70–75%of the total energy in the terrestrial solar spectral distribu-tion from 300 nm to 4000 nm (Myers, 2011). A typicalresponse curve of Li-200SA pyranometer is presented inFig. 1 (LI-COR, 2005).

3.2. Filters

To determine the irradiance corresponding to differentspectral bands, 12 different Schott glass, flat, circular, andlong-pass filters were used: FGL400, FGL430, FGL495,FGL515, FGL550, FGL590, FGL610, FGL665,FGL715, FGL780, FGL850, and FGL1000. These filtersare specified by their center wavelengths. Angstrom andDrummond (1959) showed that the wavelength corre-sponding to 50% of the filter transmittance from the mainband transmission is defined as the center of the cutoff (km).For longer wavelengths (about 1800 nm), the filter is char-acterized by almost perfected transmission. Shorter wave-lengths (less than cutoff wavelength) are characterized byalmost total opaqueness (Angstrom and Drummond,1961). Long-pass filters are constructed from hard, durablesurface materials covered with dielectric coatings. Thewavelength limits of each filter are nominal values, whichmay vary with temperature. The spectral transmissioncurve of each filter is approximately 90%. Fig. 2 showsthe actual transmissivity curves of two of these filters asobtained from http://www.thorlabs.com. The high cutoffwavelength for all filters is considered as 1100 nm becauseLi-200SA pyranometers are sensitive only up to 1100 nm.Hence, the global solar radiation can be determined inthe following regions: 400–1100 nm, 435–1100 nm,495–1100 nm, 515–1100 nm, 550–1100 nm, 590–1100 nm,610–1100 nm, 665–1100 nm, 715–1100 nm, 780–1100 nm,850–1100 nm, and 1000–1100 nm.

Adding a filter on top of the Li-200SA pyranometer willresult in a complex spectral response because the relativespectral response of Li-200SA does not extend uniformlyover the full solar radiation range of 400–1100 nm asshown in Fig. 1. Hence, the only way to correctly calibratethe Li-200SA/filter arrangement would be against a stan-dard lamp in the laboratory or against the sun with theLangley plot method as with sunphotometers or spectrora-diometers. The calibration method used in the presentstudy is as follows: the calibration process is handled foreach Li-200SA-filter independently at the UKM solar sim-ulator laboratory by exposing the Li-200SA-filter to a sta-bilized halogen lamp installed at the end of an opticalbench. The Brillanta halogen lamp is made in Malaysia,with its emission limited to the solar spectrum by a quartzwindow and with output power of 500 W. By reading theoutput current of Li-200SA fixed sensor from the workinglamp, the calibration constant may be found using the fol-lowing equation:

http://www.thorlabs.com

Fig. 2. Transmissivity curves of FGL400 and FGL665 long-pass filters. Source: WWW.thorlabs.com.


Calibration constant ðCCÞ

¼ sensor current

lamp output� specified unit

specified unitð1Þ

The “specified unit” is an arbitrary amount of measur-able radiation with which a sensor is specified. Each sensortype has a specific value, either 1000 lmol, 100,000 lux, or1000 W m�2. For example, if the calibration lamp produces40 W m�2 and an Li-200SA sensor puts out 3.6 lA, then

CC ¼ 3:6

40� 1000 W m�2

1000 W m�2¼ 90 lA=1000 W m�2

If the sample sensor produces 12.1 lA, then it is measur-ing radiation of (12.1/90) � 1000 = 134.4 W m�2.

Through a series of subtracted reading made with differ-ent filter pyranometers, obtaining incident energy intensi-ties in more wavelength bands is possible. For example,by coupling the filters (FGL400, FGL430, and FGL495),it is possible to evaluate experimentally the GSI in therange of 400–1100 nm, 430–1100 nm, and 495–1100 nm.Z 1100

400

E dk;Z 1100

430

E dk; and

Z 1100

495

E dk ð2Þ

where E is the Li-200SA measured irradianceBy combining the three functions, the following bands

can also be evaluated:Z 430

400

E dk ¼Z 1100

400

E dk�Z 1100

430

E dk ð3ÞZ 495

400

E dk ¼Z 1100

400

E dk�Z 1100

495

E dk ð4ÞZ 495

430

E dk ¼Z 1100

430

E dk�Z 1100

495

E dk ð5Þ

By combining the 12 filters, it is possible to create a 48-spectral band.

As previously mentioned, the wavelength limits of eachfilter may vary with temperature and this might introduceuncertainty when evaluating narrow bands, such as withEq. (3). Long-pass filters will shift to longer wavelengthwith increasing temperatures or to shorter wavelength withdecreasing temperature. This wavelength shift is caused by

thermal expansion/contraction of the coating materials.The shift is often expressed in nanometers per degree Cel-sius and is normally extremely small (0.01–0.2 nm �C�1).The temperature effect can be approximately calculatedusing the following formula:

k ð�CÞ ¼ ðkmÞ þ DT ðDk0=1 �CÞ ð6Þ

The uncertainty introduced at the center of the cutoff ofthe band 400–430 nm is approximately equal to 0.25%,whereas that in the case of the band 400–495 nm is approx-imately equal to 0.08%. In general, the uncertainty at thecenter of the cutoff for all bands is in the range of 0.012–0.38%.

3.3. Data acquisition system

The data acquisition system used in the present study isa specially built data acquisition system for accurate out-door measurement conditions. It consists of a computer(PC), data acquisition module, and computer software.This system does not need a big memory capacity. There-fore, a Pentium III computer has been used in this dataacquisition system. Advantech data acquisition modulewith ADAM model 4000 series was chosen for this systembased on its suitability operated in scale and types of thesignal received from the sensors to be analyzed. Modulesused are ADAM 4018 and ADAM 4561.

Outdoor data acquisition consists of two ADAM 4018modules. Each ADAM 4018 module has its own address.Address determiner is needed because each channel on eachmodule brings different signals depending on the band ofthe solar irradiance measured. ADAM 4018 model is aninput thermocouple module with eight channels, six ofwhich are differentiated and two are single-channel ends.Analog input module contains input scales ±15 mV,±50 mV, ±100 mV, ±500 mV, ±1 V, ±2.5 V, and± 20 mA. ADAM 4018 modules use an external powersupply. Inside the laboratory, the data acquisition systemconsists of one module (ADAM-4561), with one-port iso-lated USB to RS-232/422/485 converter. ADAM-4561can convert USB to RS-232/422/485 with plug-in terminal.

http://WWW.thorlabs.com


No external power supply is needed as power is derivedfrom the USB port.

4. Sources of errors associated with Li-200SA-filters

measurements

The main influencing factors on the sensor accuracy arethe sensor temperature dependence, the non-uniform spec-tral response of the Li-200SA, and the incident angle ofirradiation.

4.1. The non-uniform spectral response of Li-200SA (NSR)

This error is due to the spectral response of the sensornot conforming to the ideal spectral response. Fig. 1 showsthat Li-200SA is not spectrally ideal (same spectralresponse from 400 nm to 1100 nm). In such case, the spec-tral response error of the system (Li-200SA combinationwith filters) is calculated as the product of the detectorspectral response, the filter transmission curve, and an“ideal” transmission curve. The spectral response correc-tions for Li-200SA combined with each filter along withthe temperature coefficient correction (ac) are illustratedin Table 1.

4.2. Sensor temperature

The influence of temperature on the response of a sili-con-based irradiance sensor is typically small, resulting inless than 0.1%/�C. The compensation for the influence oftemperature can be accomplished by determining thedevice temperature and applying a temperature coefficient,which translates the measured response to a reference tem-perature, To. The temperature coefficient can be deter-mined in the same manner routinely used for thecalibration of photovoltaic reference cells. Several methodscan be used to determine the device temperature duringoperation, most of which add complexity and cost. Ther-mocouples can be attached to the device to directly mea-sure the temperature (King et al., 1998). For the mostgeneral case, in which we only have at our disposal envi-ronmental temperature registers, an empirical expressionhas been adjusted relating the sensor temperature (TLI-

200) to air temperature (Tair) and E (Raıch et al., 2007):

T LI-200 ¼ 0:99327T air � 0:00001E2 þ 0:02041E

þ 1:45113 ð7Þ

Table 1The spectral response corrections with the temperature coefficient corrections

Filter FGL400 FGL430 FGL49NSR% 7.8 7.5 6.9ac 0.000162 0.000163 0.00017

Filter FGL610 FGL665 FGL71NSR% 5.6 4.9 4.4ac 0.000240 0.000283 0.00035

As a common reference temperature, the value of 25 �Cwas chosen. Finally, the factor for correcting the tempera-ture influence is calculated as follows:

Ccorr ¼ ð1� 0:0007 � ðT LI-200 � 25 �CÞÞ ð8Þ

According to Raıch et al. (2007), the temperature coeffi-cient strongly depends on the chosen temperature interval.Thus, for temperatures less than 20 �C, the ratio presentsstrong increases of up to 3 � 10�3 C�1; for 20–30 �C, theincreases are more moderate, while for temperatures higherthan 35 �C, saturation is reached. Table 2 illustrates thetemperature corrections for Li-200SA pyranometer combi-nation with each filter for September 13, 2011. For theother days, see Appendix A.

4.3. The incident angle of irradiation

The cosine response is a (lab-measured) description ofhow the sensor_actually_ responds to changes in zenithangle. The _ideal_ cosine response is Lambertian, i.e., apure cos ðhzÞ function. In practice, there is a deviationbetween the actual and ideal response. This difference isso-called the cosine error. A cosine correction is an empir-ical function used to correct the reading a posteriori tomake the resulting (effective) cosine error as small as possi-ble. King and Myers (1997) and King et al. (1997) reportedthe spectral distribution of direct solar irradiance changessignificantly over the day, whereas the spectral distributionof diffuse solar irradiance remains nominally the same.Thus, the response of the pyranometer to diffuse irradianceis assumed to have no dependence on the angle of inci-dence. King and Myers (1997) offered a generic spectralcorrection of the global irradiance associated with the solarangle of incidence ðhzÞ for Li-200SA pyranometers asfollows:

fðhzÞ ¼ �4:504E� 7ðhzÞ3 þ 1:357E� 5ðhzÞ2 þ 6:074E

� 4ðhzÞ þ 1 ð9Þ

Table 3 shows the cosine correction of Li-200SA pyra-nometer for different angles of incidence.

5. The SMARTS2 model

Measurement of spectral global solar irradiance is notavailable in many instances, which is mainly due to techni-cal difficulties and prohibitive costs. Hence the only way tofill this gap mainly over extended areas where in situ

for Li-200SA combination with each filter.

5 FGL515 FGL550 FGL5906.7 6.3 5.8

6 0.000188 0.000203 0.000223

5 FGL780 FGL850 FGL10003.7 3.3 2.0

0 0.00050 0.000797 0.00245

Table 2Temperature corrections for Li-200SA combination with each filter for September 13, 2011.

Filter band AM 2 AM 1.5 AM 1.3 AM 1.15

Tair TLI-200 Ccorr Tair TLI-200 Ccorr Tair TLI-200 Ccorr Tair TLI-200 Ccorr

FGL400 24.60 30.00 0.996 27.60 36.89 0.991 28.22 39.90 0.989 28.05 43.09 0.987FGL430 24.60 29.88 0.996 27.60 36.61 0.991 28.22 39.55 0.989 28.05 42.67 0.987FGL495 24.60 29.53 0.996 27.60 35.98 0.992 28.22 38.69 0.990 28.05 41.62 0.988FGL515 24.60 29.42 0.996 27.60 35.79 0.992 28.22 38.41 0.990 28.05 41.24 0.988FGL550 24.60 29.19 0.997 27.60 35.35 0.992 28.22 37.88 0.990 28.05 40.63 0.989FGL590 24.60 28.91 0.997 27.60 34.88 0.993 28.22 37.28 0.991 28.05 39.89 0.989FGL610 24.60 28.77 0.997 27.60 34.64 0.993 28.22 36.98 0.991 28.05 39.53 0.989FGL665 24.60 28.38 0.997 27.60 33.98 0.993 28.22 36.17 0.992 28.05 38.55 0.990FGL715 24.60 28.06 0.997 27.60 33.47 0.994 28.22 35.47 0.992 28.05 37.73 0.991FGL780 24.60 27.61 0.998 27.60 32.77 0.994 28.22 34.67 0.993 28.05 36.76 0.991FGL850 24.60 27.35 0.998 27.60 32.32 0.994 28.22 34.07 0.993 28.05 36.05 0.992FGL1000 24.60 26.45 0.998 27.60 31.00 0.995 28.22 32.51 0.994 28.05 34.22 0.993

Table 3Relative response of Li-200SA pyranometer versus solarangle-of-incidence.

Incidence angle hz

(degree)Spectral correction of theincidence angle f(hz)

30 1.01940 1.01848.18 1.01160 0.989


observations are rare is to use models (Jacovides et al.,2004; Muneer et al., 2004). Two general types of spectralirradiance models may be used to predict or analyze solarradiation on the earth’s surface (Gueymard, 2001). First,simple atmospheric transmittance models (parameterizedmodels [PMs]) take into account that the atmosphere isapproximated as a one-layer medium attenuating the extra-terrestrial solar irradiance by means of several identifiedscattering and absorption processes. Second, rigorous radi-ative transfer models (RRTMs) consider the vertical atmo-sphere as an inhomogeneous through a series ofsuperimposed scattering and absorbing layers (Kaskaoutisand Kambezidis, 2008). PMs can usually meet the needs ofusers (Gueymard et al., 2002).

All RRTMs are developed around a specific spectral res-olution at essentially very monochromatic narrow band(Muneer et al., 2004). RRTMs can address complex scenar-ios, including clouds, fog, smoke, many choices of stan-dards and user-defined aerosol properties, atmosphericstructure for up to 33 different layers, and extraterrestrialspectra (Myers, 2005). RRTMs are inappropriate for manyapplications, such as solar energy system engineering, andany researchers other than those in the physical sciencesfield may find it difficult to use because of their mathemat-ical and computational complexity. RRTMs are generallythe most complex; they solve equations of radiative trans-fer not only wavelength by wavelength, but also layer bylayer in the atmosphere (Gueymard et al., 2002; Kaskaou-tis and Kambezidis, 2008). In addition to their simplicity,

PMs compute separately the direct and diffuse portionsof the global irradiance (Gregg and Carder, 1990). Themost updated and accurate model among the differentPMs is SMARTS. SMARTS has gained acceptance in boththe atmospheric and engineering fields due to its versatility,ease of use, execution speed, and various refinements (Gue-ymard, 2008). In the present study, the model SMARTSversion 2.9.5 is used to simulate the GSSI under cloud-freeconditions.

Gueymard (1995) introduced the SMARTS2 model in1995. It is an extensive revision of SMARTS1, a spectralmodel used to calculate direct beam and diffuse radiation.SMARTS2 can be used to predict cloudless direct, diffuse,global, and circumsolar irradiance on any horizontal ortilted surface using separate parameterization of the vari-ous extinction processes (gaseous absorption, aerosol,and molecule scattering) affecting the transfer of short-wave radiation in a cloudless atmosphere. SMARTS2 isthe first parameterized model adding nitrogen dioxide(NO2) to the list of absorbers (Gueymard, 1995).

The solar extraterrestrial spectrum used in the modelcovers the wavelength range from k = 280 nm tok = 4020 nm (1882 wavelengths) (Gueymard, 1995). Thespectral step size of the extraterrestrial spectra is 0.5 nmfrom 280 nm to 400 nm, 1 nm from 400 nm to a transi-tional wavelength at 1702 nm, and 5 nm from 1705 nmand thereafter. The effective spectral resolution forSMARTS2 at each computed point is equivalent to thewavelength intervals of 0.5 nm, 1 nm, or 5 nm. The modelaccounts for Rayleigh scattering and ozone, nitrogen diox-ide, mixed gases, 10 pollutant gases, water vapor, and aer-osol extinction properties (Myers et al., 2004). Theaccuracy of this model is normally within 1% for directirradiance or 2% for diffuse irradiance when compared tomore sophisticated atmospheric models, and within theinstrumental uncertainty (�5%) when compared to high-quality measured irradiance spectra. SMARTS2 has gainedacceptance in both the atmospheric and engineering fieldsdue to its versatility, ease of use, execution speed, and var-ious refinements (Gueymard, 2008).


The model allows the introduction of ground meteoro-logical data, or alternatively the choice of 10 different ref-erence atmospheres if ground data are not available. Italso allows the choice of nine predefined aerosol modelsor the introduction of a different model proposed by theuser. The aerosol models available are as follows: the fourproposed by Shettle and Fenn, namely, rural (SFR), urban(SFU), maritime (SFM), and tropospheric (SFT); the twoproposed by Braslau and Dave, namely, aerosol type C(BDC) and aerosol type L (BDL); and the three corre-sponding to the standard radiation atmosphere (SRA),namely, continental (SC), urban (SU), and maritime(SM) (Utrillas et al., 1998; Kaskaoutis and Kambezidis,2008). The aerosol models included in SMARTS2 havetwo average values of Angstrom’s wavelength exponent,a1 and a2, for wavebands separated by 500 nm, respec-tively. Thus, the Angstrom’s exponent a is the averagevalue (Alados et al., 2002). The classic formula of Ang-strom has been used to estimate an aerosol depth becauseof the lack of onsite aerosol optical thickness measure-ments in UKM.

dA ¼ bk�a ð10Þ

where b is called Angstrom turbidity coefficient and a is theAngstrom wavelength exponent for the whole spectrumthat defines the spectral dependence of the aerosol opticaldepth, dA.

Gueymard et al. (2002) stated if turbidity data are notavailable, it is possible to estimate the aerosol optical thick-ness from ground observations of visibility (V). V indicatesthe distance in a horizontal direction at which one can dis-cern and identify an object through the atmosphere. V is

Table 4The atmospheric conditions for September 3 and 13, October 17, and Novem

Day Air mass(AM)

Temperature(�C)

Relative humidity Rh

(%)Visi(km

September 3,2011

2.00 25.7 80.8 121.50 27.2 83.5 131.30 28.5 81.1 131.15 28.1 79.7 15

September 13,2011

2.00 24.6 81.7 101.50 27.6 84.4 121.30 28.2 86.9 121.15 28.1 85.2 14

October 17,2011

2.00 25.3 83.4 131.50 26.7 81.3 141.30 26.4 79.9 151.15 28.6 80.7 15

November 10,2011

2.00 24.1 85.3 121.50 26.3 83.5 131.30 28.5 79.6 131.15 27.7 76.2 14

November 21,2011

2.00 25.8 80.1 111.50 27.7 83.8 121.30 28.6 84.3 121.15 29.6 83.5 13

a1: Angstrom wavelength exponent for k < 500 nm, a2: Angstrom wavelength

known to be inversely related to the aerosol optical depthand to b in particular (El-Wakil et al., 2001). It is smallerfor high turbidity and larger for low turbidity conditions(Gueymard et al., 2002). In practice, V is reported at air-ports by human observers who use a few non-ideal markersirregularly spaced. Various difficulties complicate theobservation conditions. In many cases, the environmentaround the observer’s site cannot provide the necessaryfixed markers beyond a certain distance, so that visibilitythus obtained is only a crude estimate of the desired mete-orological range (Gueymard, 1995, 2001). Consequently,the turbidity estimates from V is then incorrectly skewedtoward large values and an anomalously feeble inverse cor-relation is observed between V and b (El-Wakil et al., 2001;Gueymard, 2001). Gueymard (2001) emphasized that V

can provide an acceptable estimate of b only at those siteswhere visibility data are of consistent quality. The Visibilitydata used in this work has been measured at city’s airport(as obtained from Malaysian Meteorological Department).

As mentioned above, SMARTS2 model permits thechoice among nine aerosol models. In the present study,SMARTS2 was evaluated using the urban (SFU) modelto give a good indication of the atmosphere over UKMas a polluted (urban) area. a1 and a2 have been calculatedaccording to Gueymard (1995), given by the followingequations:

a1 ¼ ðC1 þ C2X rhÞ=ð1þ C3X rhÞ ð11Þa2 ¼ D1 þ D2X rh þ D3X 2

rh

� �=ð1þ D4X rhÞ ð12Þ

where Ci and Di are constants and Xrh is given by thefollowing:

ber 10 and 21, 2011.

bility)

Precipitable water vapor(cm)

Cloud cover(%)

a1 a2 b

5.13 8 0.809 1.233 0.2155.14 10 0.802 1.237 0.2015.13 9 0.808 1.234 0.2015.13 12 0.811 1.232 0.179

5.74 11 0.807 1.235 0.2315.82 13 0.800 1.238 0.2155.86 15 0.790 1.240 0.2145.86 18 0.797 1.239 0.189

5.52 10 0.803 1.237 0.2015.52 12 0.808 1.234 0.1895.53 17 0.811 1.232 0.1795.54 15 0.809 1.233 0.179

4.96 12 0.797 1.239 0.2145.01 15 0.802 1.237 0.2015.01 17 0.811 1.232 0.2015.07 18 0.817 1.226 0.190

6.04 11 0.810 1.232 0.2156.08 15 0.801 1.237 0.2316.08 14 0.800 1.238 0.2316.11 16 0.802 1.237 0.215

exponent for k > 500 nm, and b: Angstrom turbidity coefficient.

Table 5Global spectral-band in designated spectral intervals for September 3 and 13, October 17, and November 10 and 21, 2011 at air masses 2, 1.5, 1.3 and 1.15.

Day AM Spectral bands solar irradiance intensity (W m�2)

400–1100

435–1100

495–1100

515–1100

550–1100

590–1100

610–1100

665–1100

715–1100

780–1100

850–1100

1000–1100

September 3,2011

2.00 224.0 218.7 201.0 194.5 183.3 169.3 162.3 142.0 125.9 104.5 94.00 47.001.50 445.4 434.0 400.9 389.7 369.0 344.9 333.1 299.9 272.8 239.3 220.3 149.71.30 540.2 524.5 480.4 465.2 441.1 410.5 395.8 354.9 320.8 280.3 258.3 175.71.15 668.8 648.6 592.9 575.7 542.5 504.8 486.2 435.9 394.8 347.1 315.7 220.7

September 13,2011

2.00 201.5 196.0 179.0 173.5 162.0 148.3 141.6 122.7 106.7 85.00 72.00 28.001.50 391.9 381.0 349.0 338.1 318.0 295.0 283.5 251.0 226.0 191.5 169.5 105.01.30 509.8 495.0 451.4 437.7 412.0 382.5 367.9 327.9 293.8 254.4 225.4 148.71.15 674.8 656.0 603.4 584.7 555.0 518.6 500.9 452.9 412.8 365.3 330.3 240.7

October 17,2011

2.00 211.0 182.7 166.5 159.5 148.5 134.3 127.5 108.0 91.90 71.50 60.00 10.001.50 428.8 418.0 385.9 375.2 356.0 332.5 321.1 288.9 262.8 230.3 213.3 143.71.30 527.2 512.0 469.4 455.2 430.0 400.5 386.1 345.9 312.8 272.3 250.3 167.71.15 628.8 610.6 557.9 540.7 510.5 474.2 456.7 407.9 368.8 321.1 288.7 195.7

November 10,2011

2.00 194.8 189.9 174.0 167.5 158.0 145.0 138.5 120.0 103.9 84.50 71.00 29.001.50 380.0 370.0 339.5 328.0 311.0 288.5 277.0 246.5 220.0 189.0 168.0 104.01.30 495.3 480.9 439.9 426.1 402.2 373.3 359.3 319.9 287.8 250.1 220.7 144.71.15 630.2 612.2 561.9 545.7 515.5 480.0 463.0 416.9 376.8 330.0 298.7 229.7

November 21,2011

2.00 191.0 186.7 172.0 167.5 157.0 144.5 138.5 121.0 105.9 86.50 74.00 33.001.50 376.0 366.0 338.5 327.0 311.0 289.0 278.5 248.5 224.0 193.0 172.0 109.01.30 492.0 478.0 439.0 426.0 403.0 375.4 361.7 324.0 293.0 255.0 227.0 153.01.15 630.8 613.6 565.4 548.7 521.0 487.0 470.0 423.9 387.8 341.9 307.7 223.7

Table 6Global spectral-band solar irradiance for September 13, 2011 at different optical air masses.

AM Solar irradiance intensity (W m�2 lm�1)Wavelength (lm)

0.445 0.447 0.457 0.462 0.472 0.475 0.490 0.495 0.505 0.510 0.520 0.522

2.00 183.3 236.8 243.4 261.5 264.7 263.3 283.3 280.0 285.2 298.1 302.2 309.01.50 360.0 450.5 466.9 492.3 504.7 492.0 525.0 509.4 515.7 537.5 541.6 563.61.30 494.0 614.5 626.6 670.1 673.4 652.1 691.6 670.1 675.8 703.1 706.1 717.01.15 627.3 751.3 783.1 808.6 838.1 798.8 841.6 822.2 828.1 858.7 861.6 880.7

0.532 0.547 0.553 0.559 0.564 0.567 0.573 0.576 0.583 0.590 0.600 0.607

2.00 297.3 323.1 311.9 325.2 300.9 335.7 342.5 313.3 331.1 306.5 335.0 341.71.50 531.3 568.4 553.1 569.5 526.3 574.7 575.0 543.8 576.4 527.1 575.0 582.61.30 686.3 725.6 710.8 726.4 685.5 735.3 737.5 705.7 726.4 672.2 730.0 730.91.15 837.2 893.0 864.0 891.6 831.6 882.7 910 853.1 885.2 814.3 885.0 887.4

0.615 0.627 0.632 0.637 0.647 0.652 0.665 0.685 0.690 0.695 0.700 0.715

2.00 334.0 341.3 335.1 329.8 333.9 332.8 334.7 333.1 320.0 332.9 289.1 294.71.50 560.5 586.6 557.5 552.6 553.2 552.0 550.0 544.7 500.0 541.1 478.0 484.21.30 719.5 727.4 716 691.5 692.0 709.1 685.3 674.4 681.6 667.8 601.8 607.41.15 859.5 875.4 861.4 835.3 827.9 845.9 824.5 806.5 801.6 797.2 723.4 728.5

0.720 0.722 0.730 0.747 0.757 0.775 0.795 0.805 0.815 0.832 0.857 0.890

2.00 293.4 327.8 290.0 299.0 300.0 297.7 293.4 291.2 185.7 282.6 276.1 259.01.50 482.6 517.3 475.0 483.1 480.6 473.3 463.4 457.6 314.2 435.8 424.5 393.11.30 604.3 639.8 593.9 599.4 595.9 585.0 570.1 561.9 414.2 534.9 509.1 480.01.15 724.0 761.5 710.5 718.2 709.3 698.3 677.7 667.0 500.0 633.4 603.9 566.4


X rh ¼ cosð0:9RhÞ ð13Þ

where Rh is the relative humidity and b is given by thefollowing:

b¼ 0:55a2 1:3307 V �1r �V �1

m

� �0:614þ3:4875 V �1r �V �1

m

� �h ið14Þ

where Vm = 340.85 km and Vr is the meteorological range,which is given by the following:

V r ¼ gV ð15Þwhere g is a constant resulting from the relative definitionsof V and Vr, g = 1.306.

Fig. 3. Measured spectral-band irradiances as a function of the air mass. (A) September 13, 2011 and (B) November 21, 2011 for solar zenith angles of 60�,48.18�, 40� and 30�.


The ozone column measurements taken by MalaysianMeteorological Departments using a Brewer Ozone Spectro-photometer have been used. “The precipitable water datawere obtained from predictions of the MERRA reanalysismodel, which are available at hourly intervals on a 2/3� � 1/2� horizontal grid (http://gdata1.sci.gsfc.nasa.gov/daac-bin/G3/gui.cgi?instance_id=MERRA_HOUR_2D).”because no in situ measurements were available. NO2 occursnaturally in the stratosphere and artificially in the tropo-sphere in urban environments. Stratospheric NO2 has littleeffect on the spectrum, while tropospheric NO2 can have amajor effect in polluted environments. NO2 absorbs in theblue region, from 300 nm to 650 nm, making the spectrumredder. SMARTS2 is the first parameterized model toinclude the effect of NO2. At the site, the stratosphericNO2 (ns) concentration is assumed to have a limited sea-sonal variation of between 2 � 10�4 atm-cm in summerand 1 � 10�4 atm-cm in winter. In contrast, the troposphericNO2 (nt) abundance varies considerably with weather andpollution conditions (Gueymard, 1995). Since direct mea-surements of the total NO2 column are not available inUKM, the present study conservatively assumed that thetropospheric NO2 column is 2.11 � 10�4 atm-cm aroundthe measurement site. In the present study, the SMARTS2is used to simulate the spectral global solar irradiance undercloud-free conditions on a horizontal surface at UKMbetween September 1 and November 30, 2011. The model’spredictions are used to support the experimental results.

Fig. 4. Example of smoothing function for broadening the modelledspectra to match the bandpass shape and width resulting from thecombination of FGL400 and FGL665 filters.

6. Method of statistical test

The accuracy of the measured values of global spectral-band solar irradiance is assessed by means of two widelyused statistical indicators tests, the root mean square error(RMSE) and the mean bias error (MBE), in addition todetermination coefficients R2 (Falayi et al., 2011). A low

MBE is desired. The RMSE is always positive, but a zerois ideal (Iqbal, 1983). To ease the comparison, all parame-ters are normalized and expressed as percentage of the meanmeasured global spectral-band solar irradiance (Krishnaiahet al., 2007). A relative percentage error between �10% and+10% is considered acceptable (Jiang, 2009) for represent-ing the estimation data to experimental data. The resultingdimensionless parameters are defined as follows:

NRMSE ð%Þ ¼ 100 � NPNi¼1xi

" #�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPNi¼1ðyi � xiÞ2

N

sð16Þ

NMBE ð%Þ ¼ 100 �PN

i¼1ðyi � xiÞPNi¼1xi

ð17Þ

R2 ¼ 1�PN

i¼1ðyi � xiÞ2PNi¼1ðxiÞ2

ð18Þ

http://gdata1.sci.gsfc.nasa.gov/daac-bin/G3/gui.cgi?instance_id=MERRA_HOUR_2D

http://gdata1.sci.gsfc.nasa.gov/daac-bin/G3/gui.cgi?instance_id=MERRA_HOUR_2D


where N is the number of data pair, yi is the predicted valueand xi is the measured values.

7. Results and discussion

During the three-month measurement campaign, 364data sets of instantaneous measurements of global spec-tral-band solar irradiance have been collected. These corre-spond to 91 days starting from September 1 to November30, 2011. They were all taken on a horizontal surface withair masses (AMs) varying from 2 to 1.15 at a local time indifferent atmospheric conditions. For the experimentalanalysis, only those days with cloudless skies conditionshave been considered. Different methods have been usedin the literature to identify the clear days from the availablesynoptic parameters. These methods are cloud coveramount, CA, sunshine fraction, S, clearness index kt (the

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400

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Glo

bal I

rradi

ance

(W m

-2μm

-1)

Wavelength (μm)

3 September 2011θz = 60o (AM2)

SMARTS v. 2.9.5Measured

A B

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Glo

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Wavelength (μm)

3 September 2011θz = 40o (AM1.3)


C D

O2

H2O

O3

O3

O2

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Fig. 5. SMARTS GSSI predictions (line) smoothed to spectral interval measurefor (A) air mass 2, (B) 1.5, (C) 1.3 and (D) 1.15. Day: 3 September 2011.

ratio of global horizontal terrestrial irradiance to extrater-restrial-irradiance) and the diffuse ratio k (the ratio of dif-fuse horizontal irradiance to global horizontal terrestrialirradiance) (Younes and Muneer, 2007).

Since the information on CA was only available at themeasuring site, the clear days were defined on the basisof CA. The condition imposed on the measured data wasCA < 2 oktas (20%) based on similar studies conducted inother parts of the world (Barbaro et al., 1981; Hussainand Siddique, 1990; Mateos et al., 2010; Kryza et al.,2010). Using this criterion, 13 “clear” days have beenobserved and analyzed. Each day includes four individuallymeasured values at different optical AMs. Among the over-all set of 13 days, a set of 5 days was selected and presentedin the present study. The main reasons for this decisionwere as follows: (1) all 13 days have CA of less than 20%as shown in Tables 4 and B.1, (2) to satisfy a fair

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Glo

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3 September 2011θz = 48.18o (AM1.5)


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Glo

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0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

ments resulting from the combination of any two long-pass filters (symbol)


distribution over the three months of measurement, and (3)to avoid unnecessary repetition.

Table 5 represents the spectral-band solar irradiancecorresponding to five distinct days: September 3 and 13,October 17, and November 10 and 21, 2011 for opticalAMs 2 (a solar zenith angle of 60�), 1.5 (48.18�), 1.3(40�), and 1.15 (30�) under cloud-free conditions. Theentries in Table 5 show that the various spectral intervalsvary approximately in the same manner. As shown in thetable, the values of global spectral broad-band on Septem-ber 3 and 13 are slightly higher than other days. This wasobserved for most of the optical AMs.

Using the methodology described in Section 3.2, anattempt has been made to estimate the incident energyintensities in various wavebands. Through a series of sub-tracted readings made with 12 filters mentioned above,about 48 spectral-bands have been created. Sample global

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0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Glo

bal I

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(W m

-2μm

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13 September 2011θz = 60o (AM2)


A

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bal I

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C

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Fig. 6. SMARTS GSSI predictions (line) smoothed to spectral interval measurefor (A) air mass 2, (B) 1.5, (C) 1.3 and (D) 1.15. Day: 13 September 2011.

spectral-bands for September 13, 2011 at AMs 2, 1.5, 1.3,and 1.15 are illustrated in Table 6.

The spectral distribution of solar radiation under cloud-less sky condition depends on a number of atmospheric andsurface parameters (Jacovides et al., 2000). AM, atmo-spheric turbidity (as determined from the refractive index,size distribution, and the number of aerosols in the atmo-spheric column), and the total amount of atmospheric waterhave great effects on spectral irradiance variations; mean-while, surface pressure, ground reflectance, and the amountof ozone have less effects. Generally, these are the parame-ters that are varied at different levels of detail and complex-ity in models to predict spectral irradiance (Faine et al.,1991; Jacovides et al., 1997). In this section, the dependenceof global spectral solar radiation on AM is considered.

AM describes the relative path length that the sun’s raystraverse through the atmosphere before reaching the

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Wavelength (μm)

13 September 2011θz = 48.18o (AM1.5)


B

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D

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0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Glo

bal I

rradi

ance

(W m

-2μm

-1)



ground. When AM = 1 condition, the sun is directly over-head at sea level; when AM P 10, it is near sunrise or sun-set. AM is calculated based on the zenith angle of the sun(King et al., 1997). Fig. 3A and B describe the dependenceof global solar radiation on optical AMs taken at fourAMs (2, 1.5, 1.3, and 1.15) on two separate days (September13 and November 21, 2011) under almost similar turbidityconditions. In Fig. 3A and B, the spectral distribution ofglobal solar radiation changes by the day. At short wave-lengths (visible spectrum), high hz yields significantly lowvalues of global solar radiation, compared with low hz. Aswavelength increases (infrared portion), the effect of hz

becomes small because solar radiation is more depleted byRayleigh scattering in the short wave than in the infraredportion. The reason is that Rayleigh scattering is inverselyproportional to the fourth power of wavelength.

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Glo

bal I

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-2μm

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SMARTS v. 2.9.5

Measured

A

Glo

bal I

rradi

ance

(W m

-2μm

-1)

Wavelength (μm)

17 October 2011θz = 40o (AM1.3)

SMARTS v. 2.9.5

Measured

C

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Fig. 7. SMARTS GSSI predictions (line) smoothed to spectral interval measurefor (A) air mass 2, (B) 1.5, (C) 1.3 and (D) 1.15. Day: 17 October 2011.

8. Comparison of the experimental results with the

SMARTS2 model

Several authors compared the experimental data onspectral solar radiation with the simulation results of thespectral models (Utrillas et al., 1998; Alados et al., 2002;Jacovides et al., 2004; Kaskaoutis and Kambezidis, 2008).These authors used either SPCTRAL2 or SMARTS2 mod-els, or both, for the comparison. In the present study, theexperimental results of global spectral-band solar radiationwere compared with the simulated results of theSMARTS2 model. About 13 data sets of spectral-bandsolar irradiance under clear sky conditions at four AMs(2, 1.5, 1.3, and 1.15) registered at UKM from Septemberto November 2011 were compared with those of theSMARTS2 model.

Glo

bal I

rradi

ance

(W m

-2μm

-1)

Wavelength (μm)

17 October 2011θz = 48.18o (AM1.5)


B

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Glo

bal I

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Wavelength (μm)

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SMARTS v. 2.9.5

Measured

D

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1



Because the methodology involved here implies a com-parison between modelled spectra and measured spectrathat do not have the same resolution, the modelled spectraneed to be broadened to match the bandpass shape andwidth of the monitoring instrument (pyranometer). It is rel-atively easy to ‘degrade’ a high resolution spectral data filewith a given filter or smoothing function shape, with a well-defined full width half maximum (FWHM) passband byperforming the convolution integral of spectrum and thepassband function (Gueymard, 2005, 2002). The smooth-ing function W(k) is obtained from the combination of dif-ferent actual passband filters. There would be one specificfunction per spectral interval resulting from the combina-tion of any two filters. For instance, combining the trans-mittance curves of FGL400 and FGL665 as shown inFig. 4 roughly results in a trapezoidal filter function (or

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0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Glo

bal I

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(W m

-2μm

-1)

Wavelength (μm)

10 November 2011θz = 60o (AM2)


A

Glo

bal I

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ance

(W m

-2μ m

-1)

Wavelength (μm)

10 November 2011θz = 40o (AM1.3)


C

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Fig. 8. SMARTS GSSI predictions (line) smoothed to spectral interval measurefor (A) air mass 2, (B) 1.5, (C) 1.3 and (D) 1.15. Day: 10 November 2011.

more exactly a truncated Gaussian) which can be definedas:

W ðkÞ ¼0:9 exp � ðk�k1Þ2

2r2

h ik 6 k1

0:9 k1 6 k 6 k2

0:9 exp � ðk�k2Þ22r2

h ik P k2

8>>><>>>:

ð19Þ

The variables k1 and k2 respectively represent the start andend position of almost uniform transmittance (representedby AB in Fig. 4) and r is the standard deviation which canbe obtained as:

r ¼ ðFWHM-ABÞ � ð8 ln 2Þ�0:5 ð20Þ

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650G

loba

l Irra

dian

ce (W

m-2

μm-1

)

Wavelength (μm)

10 November 2011θz = 48.18o (AM1.5)


B

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Glo

bal I

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Wavelength (μm)

10 November 2011θz = 30o (AM1.15)


D

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1


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21 November 2011θz = 60o (AM2)


A

Glo

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(W m

-2μm

-1)

Wavelength (μm)

21 November 2011θz = 48.18o (AM1.5)


B

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21 November 2011θz = 40o (AM1.3)


C

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m-1

)

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21 November 2011θz = 30o (AM1.15)


D

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Fig. 9. SMARTS GSSI predictions (line) smoothed to spectral interval measurements resulting from the combination of any two long-pass filters (symbol)for (A) air mass 2, (B) 1.5, (C) 1.3 and (D) 1.15. Day: 21 November 2011.

0

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6

7

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

NR

MSE

%

Wavelength (μm)

AM1.15AM1.3AM1.5AM2

A

0

1

2

3

4

5

6

NR

MSE

%

Wavelength (μm)

AM1.15AM1.3AM1.5AM2

B

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Fig. 10. Variation of NRMSE against wavelength at different values of air masses for (A) September 13 and (B) November 21, 2011 for Bangi, Malaysia.


-6-4-202468

10

Wavelength (μm)

NM

BE%

AM1.15 AM1.3 AM1.5 AM2A

-6

-4

-2

0

2

4

6

Wavelength (μm)

NM

BE%

AM1.15 AM1.3 AM1.5 AM2B

0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Fig. 11. Variation of NMBE against wavelength at different values of air masses for (A) September 13 and (B) November 21, 2011 for Bangi, Malaysia.

Table 7Statistical characteristics of the deviations (NRMSE and NMBE) between modeled SMARTS2 and experimental values of the spectral irradiance forSeptember 3, 6, 7, 13 and 29, October 12, 17, 24 and 31, and November 10, 11, 21 and 28, 2011 at air masses 2, 1.5, 1.3 and 1.15.

Day AM NRMES % NMBE % R2 Day AM NRMES % NMBE % R2

September 3, 2011 2.00 1.4 �0.8 0.998 September 6, 2011 2.00 1.7 0.9 0.9981.50 1.8 �1.0 0.998 1.50 2.5 1.4 0.9981.30 2.3 �1.2 0.998 1.30 3.1 1.6 0.9981.15 4.0 �2.0 0.998 1.15 5.3 2.3 0.997

September 7, 2011 2.00 1.5 �1.1 0.998 September 13, 2011 2.00 1.2 0.5 0.9981.50 2.3 �1.4 0.998 1.50 1.5 0.6 0.9981.30 2.9 �1.7 0.997 1.30 2.1 0.8 0.9981.15 4.7 �2.1 0.997 1.15 2.8 1.2 0.998

September 29, 2011 2.00 1.3 �1.0 0.998 October 12, 2011 2.00 1.1 �0.7 0.9971.50 1.5 �1.2 0.998 1.50 1.4 �1.1 0.9971.30 2.2 1.1 0.998 1.30 2.1 �1.3 0.9971.15 3.1 1.7 0.998 1.15 2.7 �1.5 0.997

October 17, 2011 2.00 1.2 �0.3 0.998 October 24, 2011 2.00 1.0 �0.2 0.9981.50 1.5 �0.4 0.998 1.50 1.1 �0.7 0.9981.30 2.0 �0.5 0.998 1.30 1.3 �1.1 0.9981.15 3.4 �1.1 0.998 1.15 1.7 �1.4 0.998

October 31, 2011 2.00 0.7 0.2 0.998 November 10, 2011 2.00 1.4 �0.8 0.9971.50 0.9 0.2 0.998 1.50 1.8 �1.1 0.9971.30 1.2 �0.2 0.998 1.30 2.3 �1.3 0.9971.15 1.3 �0.3 0.998 1.15 3.7 �1.6 0.997

November 11, 2011 2.00 1.0 0.2 0.998 November 21, 2011 2.00 1.1 �0.2 0.9981.50 1.3 0.3 0.998 1.50 1.5 �0.4 0.9981.30 1.7 �0.3 0.998 1.30 1.9 �0.5 0.9981.15 2.1 �0.4 0.998 1.15 2.4 �0.6 0.998

November 28, 2011 2.00 1.2 0.6 0.9971.50 1.6 0.9 0.9971.30 2.0 1.1 0.9971.15 3.3 1.3 0.997


The broadened, or smoothed, value of a spectral vari-able X(k) irradiance or transmittance, is finally obtainednumerically as (Gueymard, 1995):

X ¼Xkx

kn

W ðkÞX ðkÞ,Xkx

kn

W ðkÞ ð21Þ

where kn and kx are the beginning and end of the spectralinterval that results from the combination of different ac-tual passband filters.

The results of the comparison between the measuredglobal spectral-band and the simulated results of the

SMARTS2 model for September 3 and 13, October 17,and November 10 and 21, 2011 are presented in Figs. 5–9, respectively.

The comparisons, as shown in Figs. 5–9, indicated thatmost of the measured points were close to the SMARTS2curve and that the degree of deviation from the SMARTS2curve was small.

Aside from the absorption within the solar atmosphere,the variability and magnitude of spectral irradiance on theearth’s surface is governed by atmospheric absorption. Themost important air molecule absorption in the range ofapproximately 400–1100 nm is indicated in Fig. 5A for


September 13, 2011. Specifically, the distinct irradiancetroughs at 0.72 and 0.82 lm are attributable to water vaporabsorption, and those at 0.63 and 0.69 lm are attributableto diatomic oxygen absorption. Ozone exhibits a numberof absorption bands in the visible and near infrared(NIR) regions. Ozone has strong bands in the visible regionfrom 0.45 lm to 0.77 lm (Chappuis bands) (Iqbal, 1983).The depressions caused by the Chappuis bands, whichare centered around 0.645 lm, are illustrated in the spectraldistribution in Fig. 5A. The effect of NO2 on the globalradiative partitioning is small. However, enhanced NO2

in polluted areas can change the partitioning of absorbedsolar radiation between the atmosphere and the surface.It produces atmospheric heating in the troposphere andcontributes to the dimming (reduction of solar radiation)on the surface (Vasilkov et al., 2009). NO2 contributes tothe depletion of solar irradiance throughout the spectralrange of 0.3–0.65 lm, with a maximum of near 0.4 lm.Noticeably, the depressions on September 13 were alwayshigher than those on November 21 for the different AMs.This phenomenon is attributed to, as mentioned earlier,the increase in relative humidity, as derived from meteoro-logical data, either at a particular wavelength or under con-sideration of the growth of aerosol particle size.

Table A.1Temperature corrections for Li-200SA combination with each filter for 3 Sept

Filter band AM 2 AM 1.5

Tair TLI-200 Ccorr Tair TLI-200 Ccorr

FGL400 25.70 31.54 0.995 27.20 37.55 0.991FGL430 25.70 31.44 0.995 27.20 37.32 0.991FGL495 25.70 31.07 0.996 27.20 36.64 0.991FGL515 25.70 30.94 0.996 27.20 36.41 0.992FGL550 25.70 30.71 0.996 27.20 35.99 0.992FGL590 25.70 30.43 0.996 27.20 35.50 0.992FGL610 25.70 30.28 0.996 27.20 35.26 0.992FGL665 25.70 29.87 0.997 27.20 34.58 0.993FGL715 25.70 29.54 0.997 27.20 34.03 0.993FGL780 25.70 29.11 0.997 27.20 33.34 0.994FGL850 25.70 28.89 0.997 27.20 32.96 0.994FGL1000 25.70 27.93 0.998 27.20 31.52 0.995

Table A.2Temperature corrections for Li-200SA combination with each filter for 17 Oc

Filter band AM 2 AM 1.5


FGL400 25.30 30.42 0.996 26.70 36.72 0.992FGL430 25.30 30.31 0.996 26.70 36.50 0.992FGL495 25.30 29.98 0.997 26.70 35.84 0.992FGL515 25.30 29.83 0.997 26.70 35.63 0.993FGL550 25.30 29.61 0.997 26.70 35.23 0.993FGL590 25.30 29.32 0.997 26.70 34.75 0.993FGL610 25.30 29.18 0.997 26.70 34.52 0.993FGL665 25.30 28.78 0.997 26.70 33.86 0.994FGL715 25.30 28.46 0.998 26.70 33.33 0.994FGL780 25.30 28.04 0.998 26.70 32.67 0.995FGL850 25.30 27.80 0.998 26.70 32.32 0.995FGL1000 25.30 26.91 0.999 26.70 30.90 0.996

The degree of accuracy of the measurement data waspredicted on the basis of statistical error tests: the normal-ized root mean square error (NRMSE) and the normalizedmean bias error (NMBE). In our case, since existing mea-sured data will be validated with the simulated results ofthe SMARTS2 model, because the latter is already well val-idated. Thus, the symbols in Eqs. (16)–(18) will exchangeplaces with each other. Statistical deviations were calcu-lated for the 48 discrete spectral bands and for the entirespectrum (400–1100 nm) on all clear sky days. Fig. 10Aand B present the variation in NRMSE of the 48 discretespectral bands on two representative days (September 13and November 21, 2011) with AMs of 2, 1.5, 1.3, and1.15, respectively. As can be seen, the variation in NRMSEon each day had nearly similar behavior. The differencesassociated with the observed global spectral-band solarirradiance were lower in the visible spectrum comparedto the NIR spectral bands. The minimum NRMSE valueon September 13, 2011 was obtained at an angle of 30�,which is about 0.2%, and slightly increased as the incidentangle increased. The same behavior was observed inFig. 9B on November 21, 2011, in which the minimumvalue of NRMSR was 0.4% at the incident angle of 30�,and the maximum was about 4.4% at the incident angle

ember, 2011.

AM 1.3 AM 1.15


28.50 40.78 0.989 28.10 43.00 0.98728.50 40.46 0.989 28.10 42.59 0.98728.50 39.56 0.989 28.10 41.45 0.98828.50 39.25 0.990 28.10 41.10 0.98828.50 38.76 0.990 28.10 40.42 0.98928.50 38.13 0.990 28.10 39.65 0.98928.50 37.83 0.991 28.10 39.28 0.99028.50 37.00 0.991 28.10 38.25 0.99028.50 36.30 0.992 28.10 37.41 0.99128.50 35.48 0.992 28.10 36.44 0.99128.50 35.03 0.993 28.10 35.80 0.99228.50 33.34 0.994 28.10 33.86 0.993

tober, 2011.

AM 1.3 AM 1.15


26.40 38.43 0.990 28.60 42.69 0.98826.40 38.12 0.990 28.60 42.31 0.98826.40 37.25 0.991 28.60 41.24 0.98926.40 36.96 0.991 28.60 40.89 0.98926.40 36.45 0.992 28.60 40.27 0.98926.40 35.84 0.992 28.60 39.53 0.99026.40 35.55 0.992 28.60 39.18 0.99026.40 34.73 0.993 28.60 38.18 0.99126.40 34.05 0.993 28.60 37.38 0.99126.40 33.23 0.994 28.60 36.41 0.99226.40 32.78 0.994 28.60 35.75 0.99226.40 31.09 0.995 28.60 33.85 0.994

Table A.3Temperature corrections for Li-200SA combination with each filter for 10 November,2011.




Table A.4Temperature corrections for Li-200SA combination with each filter for 21 November, 2011.





of 60�. These results may be due to the instrument’s read-ing was not correctly compensated for its cosine error and/or its spectral error.

Fig. 11A and B show a similar analysis performed toevaluate the possible relationship between statisticalNMBE and AM. Higher NMBE values appeared in theNIR band, ranging from �3.8% to 6.5% on September13 and from �4.5% to 3.5% on November 21. The visiblespectrum showed the lowest NMBE value, ranging from�1.5% to 4.8% and from �3.3% to 3% for September 13and November 21 respectively.

Table 7 summarizes the statistical deviations betweenthe estimated and measured spectral irradiances for thewhole spectrum on all measured clear sky days. For the13 days considered, the NRMSE values ranged from0.7% to 5.3%. In addition, the low NMBE values are par-ticularly remarkable. The NMBE values showed thatAM = 1.15 yielded the best results. The negative NMBEvalues presented in Table 7 show that the values on Sep-tember 3 and 7, October 12, 17, and 24, and November10 and 21 were underestimated, whereas those on Novem-ber 28 and September 6 and 13 were overestimated. For theother three days, the NMBE values were highly skewed inboth positive and negative values, reflecting over/underestimations of the modeled irradiance. The slight increase

in NRMSE exhibited by the AMs can be attributed tothe small differences in w values. The coefficient of determi-nation (R2 value) obtained for the data set at different AMsvaried from 0.996 to 998. In this respect, as the coefficientof determination gets closer to unity, the accuracy ofprediction gets better. As the R2 value approaches 1, thesolution to the problem becomes more accurate. In general,good agreement was found between the measured valuesand the simulated results of the SMARTS2 model; thiscan be confirmed from the NRMSE and NMBE values,which did not significantly vary for the entire data set.

9. Conclusion

The measurement of solar radiation using pyranometersequipped with filters is much less complicated, more com-pact, and less costly than spectroradiometers. Despite theirsimplicity, filter radiometers are able to provide results thatare reasonably close to those of the SMARTS2 model. Acomparison between the observed and the estimated valuesshowed that both results were relatively in close agreementover the entire measured spectrum. The distribution ofspectral global solar irradiance at different AMs had nearlysimilar trends because atmospheric content is approxi-mately constant during the course of the measurements.

Table B.1The atmospheric conditions for September 6, 7 and 29, October 12, 24 and 31, and November 11 and 28, 2011.

Day Air mass(AM)

Temperature(�C)

Relative humidity Rh

(%)Visibility(km)

Precipitable water vapor(cm)

Cloud cover(%)

a1 a2 b

September 6,2011

2.00 20.8 80.5 11 4.82 10 0.810 1.233 0.2311.50 23.3 83.2 12 4.84 9 0.803 1.236 0.2151.30 23.7 81.9 13 4.88 13 0.806 1.235 0.2011.15 25.2 79.7 13 4.88 12 0.811 1.232 0.201

September 7,2011

2.00 23.7 84.8 10 4.96 10 0.798 1.238 0.2501.50 25.2 82.3 11 4.98 12 0.806 1.235 0.2311.30 27.8 81.5 12 5.02 14 0.807 1.234 0.2151.15 28.0 78.7 14 5.02 17 0.813 1.230 0.189

September 29,2011

2.00 22.3 80.0 11 5.20 14 0.811 1.232 0.2321.50 24.0 82.4 13 5.08 16 0.805 1.235 0.2011.30 27.6 82.7 12 5.20 15 0.804 1.236 0.2151.15 29.2 83.0 14 5.20 18 0.804 1.236 0.189

October 12,2011

2.00 24.2 82.7 11 4.81 13 0.804 1.236 0.2311.50 25.7 80.3 12 4.81 17 0.810 1.233 0.2151.30 28.3 78.1 13 4.76 19 0.814 1.229 0.2021.15 29.0 73.6 13 4.72 16 0.815 1.229 0.202

October 24,2011

2.00 21.4 85.1 12 5.75 12 0.797 1.239 0.2141.50 24.7 83.5 13 5.75 15 0.802 1.237 0.2011.30 26.9 81.3 13 5.83 13 0.808 1.234 0.2011.15 28.0 73.6 14 5.87 15 0.811 1.232 0.189

October 31,2011

2.00 21.0 83.7 10 5.78 13 0.802 1.237 0.2501.50 24.3 85.2 12 5.78 15 0.797 1.239 0.2141.30 27.8 82.5 13 5.88 17 0.805 1.236 0.2011.15 30.0 80.0 13 6.00 18 0.811 1.232 0.201

November 11,2011

2.00 21.7 84.2 13 5.59 10 0.800 1.238 0.2011.50 25.3 80.5 14 5.61 12 0.810 1.233 0.1891.30 28.0 78.7 14 5.61 15 0.813 1.230 0.1891.15 31.0 80.0 15 5.64 13 0.811 1.232 0.179

November 28,2011

2.00 23.4 82.0 13 5.59 12 0.806 1.235 0.2151.50 25.7 80.0 14 5.61 15 0.811 1.232 0.1791.30 26.0 78.0 13 5.61 14 0.814 1.229 0.1901.15 28.0 79.0 14 6.00 17 0.813 1.231 0.161

a1: Angstrom wavelength exponent for k < 500 nm, a2: Angstrom wavelength exponent for k > 500 nm, and b: Angstrom turbidity coefficient.


Since some key input data to the model had to be defaultedor grossly estimated in this preliminary study, the authorssuggest that more validation is necessary under better con-trolled conditions.

Appendix A. See Tables A.1–A.4.

Appendix B. See Table B.1.

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measurements of spectral-band solar irradiance in bangi, malaysia

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