terrestrial solar spectral data sets

Solar Energy, Vol. 30, No. 6, pp. 563-573, 1983 0038-092X183/060563~11503.00/0 Printed in Great Britain. © 1983 Pergamon Press Ltd.

TERRESTRIAL SOLAR SPECTRAL DATA SETS

R. E. BIRD and R. L. HULSTROM Solar Energy Research Institute, 1617 Cole Boulevard, Golden, CO 80401, U.S.A.

and

L. J. LEWIS Georgia Institute of Technology, Atlanta, GA 30332, U.S.A.

(Received 12 March 1982; in revised form 13 July 1982)

Abstract--Two data sets are presented that were generated with a rigorous radiative transfer code. One data set is an AM1.5 direct normal spectrum, and the other data set is an AM1.5 global spectrum on a surface tilted 37 ° from the horizontal towards the sun. These data are updates to data that are nearing acceptance as standards of the American Society of Testing and Materials. An improved extraterrestrial spectrum and other refinements were made to imrpove the accuracy of these data sets. A preliminary comparison between modeled and measured data is shown, which supports the accuracy of the data sets.

l. INTRODUCTION

Spectral irradiance data sets that represent average conditions in the U.S. are useful in evaluating the performance of competitive products. Absorptance, reflectance and transmittance of terrestrial solar energy are important factors in solar thermal system performance, photovoltaic system performance, materials studies, biomass studies, and solar simulation activities. The spectral distribution of the solar energy is required for accurate calculations in each of these areas because the interaction of solar energy with matter varies with wavelength.

In the past, terrestrial spectra have been generated by using computer modeling methods. However, computer codes have been developed in the past few years that are more rigorous and accurate than codes used previously by the solar community. The improvement in accuracy is especially evident in the scattered (diffuse) portion of the total radiation arriving at the earth's surface. Since previous modelers, with the exception of Dave[l], had to estimate the diffuse component, they incurred significant errors in the total spectrum.

In 1978, the Solar Energy Research Institute (SERI) began to investigate rigorous radiative transfer codes developed primarily for military and space applications. SERI acquired one of these codes and modified it for solar applications[2]. Radiation Research Associates developed the code, called BRITE, which uses Monte Carlo methods to solve the transfer problem.

Unfortunately, these rigorous codes have not been properly verified between 0.3 and 2.5 tzm wavelength because good spectral data that include simultaneous atmospheric measurements have not existed. We are verifying the codes in this region and will present some preliminary results.

The following sections describe the atmospheric model that was used. to generate these data and present them in graphical and tabulated form.

2. ATMOSPHERIC CONSIDERATIONS

The structure of the Earth's atmosphere is complex, and the methods used to model the transport of radiation through it can be equally complicated. This section des- cribes both the atmospheric parameters that are essential for characterizing the atmosphere and the atmospheric model chosen for generating data.

2.1 Atmospheric parameters The minimum parameters required to characterize the

atmosphere for optical modeling and spectral measurements research are turbidity and total precipitable water vapor. One should also know the surface pressure and the total amount of ozone. For these modeled data presented here, these parameter values are determined by the atmospheric and aerosol models chosen. To compare these modeled data with experimental spectral data, one needs to know these parameters at the time of the spectral measurements. Section 2.1 will describe how some of these parameters are measured.

The total optical depth and the amount of water vapor between the observer and the sun is measured with an optical filter instrument called a sun photometer. It measures the irradiance from the sun within the bandwidth of several filters. The World Meteorological Organization has recommended four wavelengths for turbidity measurements[3] (i.e. 0.368/~m, 0.500t~m, 0.778 ~m and 0.862 gm). Water vapor measurements are often made at 0.942 ~m or 1.13 t~m wavelength. The field-of-view of these instruments is typically 1-3 °, and the bandwidth of the filters is usually <~ 10 nm. The instruments can be calibrated in the laboratory by various methods [4, 5], or can be calibrated with outdoor measurements. More will be said about calibration later.

Once the instrument is calibrated, the total optical depth r(h) is obtained by:

z(h) = - In [V(h)/Vo(h)], (1)

563

564 R. E. BIRD et al.

where V(3`) is the voltage response of the instrument in the channel centered on the wavelength 3, to the terrestrial irradiance and Vo(3`) is the response to the extraterrestrial irradiance in the same wavelength channel. Equation (1) assumes that Beer's law operatres for transmittance calculations over a finite bandwidth; it is, in fact, a statement of Beer's law.

The total optical depth can include attenuation due to aerosols, Rayleigh (molecular) scattering, and molecular absorption. The turbidity that was mentioned previously is the optical depth in a vertical path due to aerosols (suspended particulate matter such as dust). The turbidity r,(A) is given by:

T,,(3`) = ":(A ) I M - . r . (3` ) - ~-,.,,(3` ),

where M is the relative air mass (AM),'rR(A) is the Rayleigh optical depth in a vertical path, and r,,,(3`) is the optical depth in a vertical path caused by molecular absorption. We used Kasten's formula[6] to calculate the air mass, which is given by:

M = [cos Z + 0.15(93.885 - Z)- ' 253] - ' , (3)

where Z is the apparent solar zenith angle. We employed the time, latitude, and longitude of the measurements to calculate the geometric zenith angle for use in eqn (3). By using the Rayleigh scattering equation[7] with a depolarization factor of 0,027918], we calculated the Rayleigh optical depth. Some values for the Rayleigh optical depth will be presented later. The Rayliegb optical depth can be corrected for differences in surface pressure by:

. : .( 3 ̀) = .:,,,,( x ) P/ Po,

where ~'R,,(3`) is the Rayleigh optical depth at 1013 mb pressure, P is the measured surface pressure, and Po = 1013 mb. The molecular absorption optical depth is calculated by using the absorption coefficient for ozone of Inn[9] and an ozone amount calculation[10].

The turbidity channels can be calibrated by using the Langley plot method. A Langley plot is a plot of the logarithm of the voltage reading [In V(3`)] of the sun photometer vs the air mass at the time of the measurement. This calibration must be performed on stable days when the atmosphere is homogeneous in the horizontal dimension. The plot should produce a straight line, and the voltage intercept at M = 0 is In [Vo(3`)]. The value of Vo(3 )̀ is the calibration value for the extraterrestrial irradiance.

The method of obtaining the total water vapor with a sun photometer consists of taking the ratio of a reading next to a water vapor band to that inside the band. For example, we used the 0.862 and 0.942 #m channels. This ratio is then used in a formula to obtain precipitable water. For an extensive discussion of this see Bird[ll].

2.2 Atmospheric model The BRITE Monte Carlo code uses a plane-parallel

atmosphere of several layers through which photons are

traced. The Monte Carlo method, as the name implies, uses a random number generator and statistical methods to solve the radiative transfer equation. Photons can undergo scattering from air molecules (Rayleigh scattering), scattering from suspended particulate matter (aerosol scattering), absorption by molecules or aerosols, and reflections from the ground. Figure 1 illustrates these concepts for a plane-parallel atmosphere.

In our modeling, 33 boundaries are defined between sea-level and 100km in altitude. At each of the boundaries, temperature, pressure, aerosol amount, and molecular absorber amount for CO2, H20, 02, 03, N20, CH4, N2 are presented. This produces a fairly accurate replica of the height profile of atmospheric constituents

(2) in a real atmosphere. Some evidence[12] suggests that the irradiance arriving at the ground is not significantly affected by the height profiles of atmospheric constituents, but is affected by the total amount of each constituent in a vertical column. In any event, realistic height profiles are included in this model.

The atmospheric model we chose is called the U.S. Standard (USS) atmosphere[13] and contains 1.42 cm of precipitable water and 0.34 atm-cm of ozone in a vertical column from sea level to an altitude of 100 kin. The rural aerosol model[N] was used in these calculations. The height profile of this aerosol model resembles a moderate volcanic aerosol profile in the stratosphere and is based on Elterman's height profile measurements[15]. A sea- level meteorological range of 25 km was used, which resulted in total aerosol optical depths in a vertical column from sea level (turbidities) of 0.37 at 0.368 #m wavelength, 0.27 at 0.500/zm wavelength, and 0.14 at 0.862/zm wavelength. We calculated the molecular scattering by using a depolarization factor of 0.0279. This

(4) resulted in Rayleigh optical depths in a vertical path from sea level of 0.501 at 0.368 #m, 0.143 at 0.500/~m, and 0.0157 at 0.862 #m wavelength.

The particle size distribution of the aerosol particles is shown in Fig. 2114]. It is a bimodal, log-normal particle size distribution that is assumed to be composed of 70 per cent soluble substances (ammonium and calcium

Extraterrestrial Light

/ / / !, /

Aerosolvl , ~

Solar Collector

N2

Earth

Fig. 1. A representation of the BRITEradiative transfer model.

10 8

10 8

10 '

c "o 10 2 > ,

'- 10 ° 13

.o 10 E

10

10 6

Terrestrial solar spectral data sets

10 8 10 3

m

1 0 2 10 -~ 10 0 . 1 0 ~ 10 2

~ ~ Horizon

Fig. 3. The geometry used for calculations in this report.

R a d i u s ( p . m )

T h e two d o t t e d l ines r e p r e s e n t the i n d i v i d u a l l o g - n o r m a l d i s t r i b u t i o n s w h i c h c o m b i n e to m a k e up the rura l m o d e t

Fig 2. Aerosol particle size distribution for rural model.

sulfates and organic compounds) and 30 per cent dustlike aerosols. The resulting refractive index, the single scattering albedo, and the asymmetry factor of the mixture

565

are shown in Table 1 as a function of selected wavelengths. This aerosol model is believed to resemble the type of aerosol that exists at rural locations within the U.S.

We chose the ground albedo to be 0.2 for our data This parameter normally varies with wavelength, but was kept constant because a large variety of albedos exist for different soils and ground covers. The 0.2 value is an average value for bare soils.

Table 1. Optical parameters of a rural aerosol model at selected wavelengths

h a nl b n2 c Wod <COS B> e

0.305 1.53 0.008 0.9280 0.6636 0.31 1.53 0.0072 0.9337 0.6612 0.32 1.53 0.0069 0.9356 0.6596 0.33 1.53 0.0059 0.9430 0.6581 0.35 1.53 0.0059 0.9426 0.6555 0.40 1.53 0.0059 0.9423 0.6511 0.45 1.53 0.0059 0.9416 0.6474 0.50 1.53 0.0059 0.9404 0.6436 0.55 1.53 0.0066 0.9333 0.6397 0.65 1.53 0.0068 0.9293 0.6352 0.75 1.527 0.00827 0.9144 0.6333 0.80 1.521 0.00989 0.9020 0.6329 0.84 1.521 0.0104 0.8932 0.6333 0.90 1.520 0.0115 0.8820 0.6323 0.95 1.520 0.0124 0.8728 0.6313 I.I 1.516 0.0147 0.8438 0.6307 1.29 1.496 0.0163 0.8178 0.6382 1.395 1.488 0.0172 0.8022 0.6421 1.52 1.478 0.0184 0.7823 0.6479 1.61 1.474 0.0173 0.7845 0.6503 1.80 1.421 0.0143 0.7835 0.6794 2.198 1.350 0.0108 0.71

awavelength (~m)

brea[ refractive index

Cimagtnary refractive index

detngle scattering albedo

easy-=metry factor

from the horizontal towards the sun with the vector (ri) normal to the collector surface in the same plane as the line from the collector to the sun (see Fig. 3).

The standard spectra presented here are for the sun at a zenith angle of 48.19 ° (AM1.5) There has been some disagreement in the past over which air mass value should be used for an average value The Solar Energy Research Institute (SERI) selected AM1.5 based on work at the Jet Propulsion Laboratory [16, 17]. Figure 4 illustrates some of the results of their work and presents data based on measurements made at several locations in the U.S. It shows that approximately 50 per cent of the annual energy output at selected U.S. locations collected by a surface that

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80 ABQ Albuquerque NM CAH Cape Hatteras NC CAR Caribou ME

~o_ 70 GRF Great Falls, MT PHX Phoemx AZ SAM Santa M a r i a CA

w ~ so

SAM ABQ

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CAR g ac ~. GRF

2O

CAH

1£

[ I I I [ I L I 10 15 20 25 30 35 40 45 50

A," Mass

Fig 4. Annual energy output vs air mass for various cities in the U.S.

2.3 Geometry Figure 1 illustrates the geometry used for generating data

that will be presented later. How one visualizes this geometry makes no difference to the horizontally homogeneous atmospheric model used for the calculations. The critical element in understanding the geometry is the position of the flat collector relative to the sun's position. The flat surface collecting the global radiation is tilted 37 °

566 R. E. BIRD et al.

is tilted towards the south at the latitude angle is at air mass values greater than AM1.5. Therefore, AM1.5 is a good average value for the annual energy available in the U.S.

We chose the 37 ° tilt angle because it is the average latitude for the 48 contiguous states. Also, the USS atmospheric model represents average atmospheric conditions in the U.S.

2,4 Molecular absorption The molecular absorbers that have a significant affect

on the solar spectrum between 0.3 and 2.5#m wavelength are water vapor (H20), ozone (O3), oxygen (09, and carbon dioxide (CO2). Figure 5 illustrates the regions of spectrum that are affected by each absorber. It is apparent from the illustration that 03 is a broadband absorber, which means that it can be accounted for with a Beer's law formalism for relatively large bandwidths. The other absorbers exhibit much narrower absorption bands and for many applications require the use of a band model.

210C

180C Fe Mg (SUN)

150C F 1 % . 0 I H (SUN)

~ ~\ ,o }20C Fe (SUN~ , O

HO ~ ~o~ I , ~ , o , o o

i,I O H O CO, 30C O , O, CH. H~O CO

Wavelength (Micrometers)

Fig. 5. Global spectral irradiance from Bedford, Mass., 18 July 1980 at 12:36 LSP with spectral absorption features designated.

3. EXTRATERRESTRIAL SPECTRUM

Modelers have used several different extraterrestrial spectra in past years[18]. Recently, most modelers have used either Thekaekara's spectrum[19] or Lab's and Neckel's spectrum[20]. Thekaekara's spectrum is the result of measurements taken aboard a high-altitude aircraft flying at an altitude of 11.6 km where 5 different instruments were used. The results were combined with measurements of one instrument aboard three different aircraft. Labs and Neckel took ground measurements from 0.33 to 1.25/Lm at an altitude of 3.6 km and then combined normalized measurements of other workers with their measurements to extend the spectral range.

Recent publications[21,22] indicate that Labs and Neckel revised their spectrum by employing newer limb- darkening data to convert from radiance to irradiance. Comparisons by Fr6hlich with calibrated sun photometer data from Mauna Loa, Hawaii, indicate that this new spectrum is the best currently available.

We used the new Neckel's and Lab's spectrum in the modeling reported in this paper. A comparison between the revised Neckel's and Labs's spectrum and Thek- aekara's spectrum is shown in Figs. 6 and 7. The resolution of the Neckel's and Labs's spectrum is 0.005 ~m, and the resolution of Thekaekara's spectrum is 0.010 to 1/~m wavelength and 0.050tzm at longer wavelengths. This difference in resolution causes some of the abrupt changes in the ratio shown in Fig. 7. The ratio is shown for 104 wavelengths that are used in calculating spectra later on. Use of more wavelengths would result in even more structure.

4. RESULTS OF CALCULATIONS

To create the new spectra we used: (a) Neckel's and Labs's revised spectrum[23] of the extraterrestrial radiation instead of Thekaekara's spectrum; (b) a different Rayleigh scattering calculation with a depolarization

2200

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1800

~" 1600

1400 E ~ 1200

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"~ 800

± 600

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0 0.3

I [~"k~Neckel & Labs

T h e k a e k a r a .

0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5


Fig. 6. Comparison of Neckers and Labs's revised spectrum with Thekaekara's extraterrestrial spectrum.

Terrestrial solar spectral data sets 567

1 . 2 0 ~ _

1.05

.o 1.00 tr"

0.95

0.90

0.85

0.80 0.3

, I , I , t , I I , t , I , t -I, I 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3


Fig, 7. Ratio of Neckd's and Labs's spectrum to Thekaekara spectrum,

1

2.5

factor of 0.0279; (c) a more accurate sampling method for scattering calculations; and (d) different wavelengths within some of the H:O bands. Although we made slight changes in the aerosol height profile, it appears that this made little difference (possible a slightly lower value of the irradiance). The new spectra should resemble 0.005 txm resolution data; whereas the old spectra were of lower resolution everywhere except in the I-I20 bands,

A comparison of the new and old direct normal spectra is shown in Figs. 8 and 9. Figure 8 shows both spectra (irradiance compared with wavelength), and Fig, 9 shows the ratio of the new over the old spectrum, The ratio in some of the HzO bands was not taken because the

wavelengths did not match. In general, the new spectrum reflects the changes in the extraterrestrial spectrum for all wavelengths except for those below 0,5 tzm, In this region of the spectrum, these new data are lower by as much as ~ 4 per cent. This is believed to be caused by the increased attenuation from the new Rayleigh scattering calculation. Compare Figs. 7 and 9 to see these results, but keep in mind that Fig, 7 is for 12 more wavelengths with the differences mostly occurring in the H20 bands.

A comparison of the new and old global spectra are illustrated in Figs. 10 and 11. Again, Fig. l0 is an irradiance plot, and Fig, 11 is the ratio of the new over the old

1400

1200

1000 E

E 800

8 6o0 t-" t~

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400

200

0 0.3

. ~ ,,~.~-New

/ , t , 1 , 1 , I ' , I k . J " I r 1

0.5 0.7 0.9 1.1 t.3 1.5 1.7 1.9 2.1


Fig, 8, Comparison of new and old AMI.5 direct normal spectral data sets.

2.3 2.5

568 R.E. Bl~ et al.

1.20

1.15'

1.10

1.05

.0 1.00 I+ ¢:

0.95

0.90

0.85

0.8OH: , I 0.3 0.5

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1

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0.9 1.1 1.3 1.5 1.7 1.9

Wavelength Micrometers

Fig. 9. Ratio of new over old direct normal data sets.

' \_+/ l \ \ \

, I + I +

2.1 2.3 2.5

spectrum. In contrast to the direct normal spectra, the new global spectrum is significantly lower between 0.4 and 1.1/~m wavelength than the old global spectrum (compare Figs. 9 and 11). The difference is greatest near 0.48/zm. The effects of the changes in the extraterrestrial spectrum follow the same pattern in both the direct normal and the global spectra. The cause of the lower global spectrum near 0.48/zm is not understood. It could possibly be caused by the more accurate sampling methods used in the new data set.

Tabular data for these spectra are presented in Tables 2 and 3. Table 2 contains the direct normal spectrum, and

Table 3 contains the 37°-tilted global spectrum. Included in each of these tables is the wavelength, the terrestrial spectral irradiance, the integrated irradiance to the wavelength specified, and the fraction of the integrated irradiance to the specified wavelength as compared to the total irradiance to 2.45/xm. The broadband irradiance to 4.0/zm is 761.8W]m 2 in the direct normal spectrum and 964.1 W/m 2 in the global spectrum.

The direct normal spectrum presented here includes the circumsolar radiation in a 5.8 ° field-of-view. This circumsolar radiation adds approx. 1.5 per cent near 0.5/zm wavelength and a smaller percentage elsewhere.

1800

A

E

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1600

1400

1200

1000

800

600

400

200

0 0.3

,OId

I i [ I I * I f , I ~ , J . / I , [ I I I ' I I 1 | '

0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1


Fig. 10. Comparison of new and old AMI.5 37 ° tilted global data sets.

2.3 2.5


1.20

1.15

1.10

1.05

0 "~ 1.00

0.95

0.90

0.85

0 . 8 0 " 0.3

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I I ' I ' I ' I ' I ' I ' I ' I 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9


Fig. 11. Ratio of new over old global data sets.

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2;5

5. C O M P A R I S O N S B E T W E E N M O D E L E D A N D

E X P E R I M E N T A L D A T A

We said earlier that solar irradiance models have not been adequately verified because data on turbidity, water vapor, and surface pressure are required, together with an accurate solar spectrum to make a proper comparison. As far as we know, all of these data have not been available in the past. We have carefully designed the equipment to obtain accurate measurements of all of these data.

The spectroradiometer has been described elsewhere[24]. The sun photometer used to gather turbidity values at three wavelengths and to measure the precipitable water was built for SERI by the Instrument Division of Systems and Applied Sciences Corporation, Anaheim, California. The sun photometer was based on a design recommended by the World Meteorological Organization[3] with the addition of a water vapor channel. This instrument is temperature controlled, and is an integral part of an active solar tracker and a microprocessor-based data logging system. A very accurate pressure transducer has been integrated into this system. Considerable effort has gone into calibrating the water vapor channel[11].

One set of spectral data was recorded on 5 August 1981 in Golden, Colorado, together with sun photometer data. A global horizontal spectrum was recorded at 15:09 Mountain Standard Time (MST) under the following conditions:

zenith = 44.80 turbidity at 0.368/~m = 0.39 turbidity at 0.500/zm = 0.28 turbidity at 0.862 tzm = 0.13 water vapor = 2.25 cm surface pressure = 829 mb.

The spectroradiometer was situated on a light-colored cement pad that was surrounded by dark, dry soil with a small amount of vegetation. We assumed the albedo to be 0.2. The amount of ozone was calculated to be 0.33 atmcm[10], which produced an ozone optical depth of 0.009 in a vertical path[9] at 0.500 ~m wavelength. The measured spectrum was approximately of 0.010/~m resolution.

The modeled data were calculated at 108 discrete wavelengths, and the resolution of the molecular absorption coefficients was 20 cm-L The resolution of the extraterrestrial spectra was 0.005 ~tm. Because of the different resolutions mentioned here and the small number of wavelength calculations, it is difficult to make comparisons between experiment and theory in water vapor bands and in deep Fraunhofer lines. The effect of this will be seen in the comparisons.

A comparison of the global horizontal spectra is shown in Fig. 12, and the percentage of difference between the measured and modeled spectra is shown in Fig. 13. In general, the two spectra agree within _+ 5 per cent over most of the wavelength range. The sharp difference in the 0.4-~m region is believed to be due to the higher resolution in the extraterrestrial spectrum. This same feature is present in Figs. 7, 9 and ll. The large dip in Fig. 13 at 0.59/~m is believed to be partially caused by the high resolution ( - 0.69 ~t m) of water vapor absorption coefficients in this wavelength region.

The other water vapor bands were not compared in Fig. 13 because no attempt was made to approximate the correct resolution of the measured data. The wavelengths used in the BRITE code in the H20 bands are the same as those in the old data sets. They were placed at maxima and minima within the bands. We used this comparison, in fact, to select wavelengths for the new data sets.

570 R.E. BIRD et al.

Table 2. Direct normal AM1.5 irradiance data set (1.42 cm HzO, 0.34 cm 03, r = 0,273

A a II~, b ZO_~ ' c EO_ ~ A a Z~, b Zo_~ ' c Eo- ~

(urn) (w/,*Z/u,) (w/m 2) Z o ~ d (urn) (w/mZ/um) (W/m 2) "o J d

0.3050 0.3100 0.3150 0.3200 0.3250 0.3300 0.3350 0.3400 0.3450 0.3500 0.3600 0.3700 0.3800 0.3900 0.4000 0.4100 0.4200 0.4300 0.4400 0.4500 0.4600 0.4700 0.4800 0.4900 0.5000 0.5100 0.5200 0.5300 0.5400 0.5500 0.5700 0.5900 0.6100 0.6300 0.6500 0.6700 0.6900 0.7100 0.7~80 0.7244 0.7400 0.7525 0.7575 0.7625 0.7675 0,7800 0.8000 0.8160 0.8237 0.8315 0.8400 0.8600

3.4 0.02 0.0000 0.8800 778.3 472.55 15.6 0.09 0.0001 0.9050 630.4 483.49 41.t 0.29 0.0004 0.9150 565.2 489.10 71.2 0.64 0.0009 0.9250 586.4 493.47 100.2 1.13 0.0015 0.9300 348.1 495.55 152.4 1.88 0.0025 0.9370 224.2 497.55 155.6 2.64 0.0035 0.9480 271.4 501.32 179.4 3.51 0.0047 0.9650 451.2 508.49 186.7 4.43 0.0059 0.9800 549.7 516.27 212.0 5.98 0.0080 0.9935 630.1 535.04 240.5 8.34 0.0111 1.0400 582.9 557.19 324.0 11.51 0.0154 1.0700 539.7 573.27 362.4 15.07 0.0201 1.1000 366.2 582.38 381.7 18.82 0.0251 1.1200 98.1 583.84 556.0 24.29 0.0324 1.1300 169.5 585.27 656.3 30.75 0.0410 1.1370 118.7 587.10 690.8 37.55 0.0501 1.1610 301.9 593.56 641.9 43.88 0.0585 1,1800 406.8 601.44 798.5 51.76 0.0690 1.2900 375.2 611.70 956.6 61.21 0.0816 1.2350 423.6 630.66 990.8 70.97 0.0947 1.2900 365.7 646.11 998.0 80.81 0.1078 1.3200 223.4 652.78 1046.1 91.13 0.1215 1.3500 30.1 653.90 I005.1 101.05 0.1348 1.3950 1.4 653.q7 1026.7 111.19 0.1483 1.4425 51.6 655.70 1066.7 121.73 0.1624 1.4625 97.0 657.37 1011.5 131.73 0.1757 1.4770 97.3 659.04 1084.9 142.46 0.1900 1.4970 167.1 662.61 1082.4 153.17 0.2043 1.5200 239.3 667.62 ~102.2 169.54 0.2261 1.5390 248.8 672.32 1087.4 191.04 0.2548 1.5580 249.3 677.16 1024.3 211.30 0.2818 1.5780 222.3 680.92 1088.8 232.84 0.3105 1.5920 227.3 684.54 1062.1 253.86 0.3386 1.6100 210.5 688.52 1061.7 274.88 0.3666 1.6300 224.7 692.54 1046.2 295.60 0.3942 1.6460 215.9 697.70 859.2 312.62 0.4169 1.6780 202.8 707.18

!902.4 326.52 0.4355 1.7400 158.2 716.78 816.9 332.35 0.4433 1.8000 28.6 718.49 842.3 341.53 0.4555 1.8600 1.8 718.60 971.0 355.06 0.4735 1.9200 I,I 718.66 956.3 363.35 0.4846 1.9600 19.7 719.29 942.2 368.02 0.4908 1.9850 84.9 721.20 524.8 370.62 0.4943 2.0050 25.0 721.82 830.7 377.83 0.5039 2.0350 92.5 724.59 908.9 392.47 0.5234 2.0650 56.3 726.41 873.4 408.05 0.5442 2.1000 82.7 729.83 712.0 416.42 0.5554 2.1480 76.2 733.56 660.2 421.50 0.5622 2.1980 66.4 737.59 765.5 427.69 0.5704 2.2700 65.0 742.84 799.8 439.00 0.5855 2.3600 57.6 748.01 815.2 455.17 0.6071 2.4500 19.8 749.79

0.6302 0.6448 0.6523 0.6581 0.6609 0.6636 0.6686 0.6782 0.6886 0.7136 0.7431 0.7646 0.7767 0.7787 0.7806 0.7830 0.7916 0.8021 0.8158 0.8411 0.8617 0.8706 0.8721 0.8722 0.8745 0.8767 0.8790 0.8837 0.8904 0.8967 0.9031 0.9081 0.9130 0.9183 0.9236 0.9305 0.9432 0.9560 0.9583 0.9584 0.9585 0.9593 0.9619 0.9627 0.9664 0.9688 0.9734 0.9783 0.9837 0.9907 0.9976 1.0000

a~ = Wavelength.

b ~ = DlrecC n o r ~ l s p e c t r a l i r r a d l a n c e averaged over 20/cm c e n t e r e d at A.

CEo_ A - Ynte~rated d i r e c t normal I r r a d l a n o s to the w a v e l e n s t h r a n p 0 to X.

dYo_ . - Intesrated dlrec~ ~ormal Irradiance over the eotlre spectr~a.


Table 3, Global AM1.5 spectral irradiance data sets for 0.2 ground albedo, and 37°-tilted surface (1.42 cm H-'O, 0.34 cm 03, 1- = 0.27)

h a Ek b EO_X c EO-~ ha El b Eo_h c Eo-X

(~m) (W/m2/~m) (W/m 2 ) Eo~d (~m) (W/m2/~m) (W/m 2 ) Bo~d

0.3050 9.2 0.05 0.0000 0.8800 899.4 647.34 0.6803 0.3100 40.8 0.25 0.0003 0.9050 721.4 659.96 0.6936 0.3150 103.9 1.77 0.0008 0.9150 643.3 666.39 0.7003 0.3200 174.4 1.64 0.0017 0.9250 865.3 671.38 0.7056 0.3250 237.9 2.83 0.0030 0.9300 389.0 673.72 0.7080 0.3300 381.0 4.74 0.0050 0.9370 248.9 675.96 0.7104 0.3350 376.0 6.62 0.0070 0.9480 302.2 680.19 0.7148 0.3400 419.5 8.71 0.0092 0.9650 507.7 688.31 0.7234 0.3450 423.0 10.83 0.0114 0.9800 623.0 697.19 0,7327 0.3500 466.2 14.32 0.0151 0.9935 719.7 718.78 0.7554 0.3600 501.4 19.34 0.0203 1.0400 665.5 744.24 0.7821 0.3700 6~2.1 25.76 0.0271 1.0700 614.4 762.67 0.8015 0.3800 686.7 32.63 0.0343 I.I000 397.6 772.61 0.8120 0.3900 694.6 39.57 0.0416 1.1200 105.0 774.18 0.8136 0.4000 976.4 49.34 0.0518 1.1300 182.2 775.73 0.8152 0.4100 1116.2 60.50 0.0636 1.1370 127.4 777.71 0.8173 0.4200 1141.1 71.91 0.0756 1.1610 326.7 784.73 0.9247 0.4300 1033.0 82.24 0.0864 1.1800 443.3 793.38 0,8338 0.4400 1254.8 94.79 0.0996 1.2000 408.2 804.60 0.8456 0.4500 1470.7 109.49 0.1151 1.2350 463.1 825.44 0.8675 0.4600 1541.6 124.91 0.1313 1.2900 398,1 842.36 0.8853 0.4700 1523.7 140.15 0.1473 1.3200 241.1 849.59 0.8929 O. 4800 1569.3 155.84 0.1638 i. 3500 31.3 850.77 O. 8941 0.4900 1483.4 170,67 0.1794 1.3950 1.5 850.84 0.8942 0.5000 1492.6 185.60 0.1951 1.4425 53.7 852.65 0.8961 0.5100 1529.0 200,89 0.2111 1.4625 101.3 854.40 0.8979 0.5200 1431.1 215,20 0.2262 1.4770 101.7 856.15 0.8998 0.5300 1515.4 230.35 0.2421 1.4970 175.5 859.92 0.9037 0.5400 1494.5 245.30 0.2578 1.5200 253.1 865.24 0.9093 0.5500 1504.9 267.87 0.2815 1.5390 264.3 870.26 0.9146 0.5700 1447.1 296.82 0.3119 1.5580 265.0 875.43 0.9200 0.5900 1344.9 323.71 0.3402 1.5780 235.7 879.44 0.9242 0.6100 1431.5 352.34 0.3703 1.5920 238.4 883.25 0.9282 0.6300 1382.1 379.98 0.3993 1.6100 220.4 887.44 0.9326 0.6500 1369.4 407.35 0.4281 1.6300 235.6 891.68 0.9371 0.6700 1341.8 434.19 0.4563 1.6460 226.3 897.11 0.9429 0.6900 1089.0 455.97 0.4792 !.6780 212.5 907.10 0.9533 0.7100 1269.0 473.74 0.4979 1.7400 165.3 917.19 0.9639 0.7180 973.7 480.75 0.5052 1.8000 29.6 918.96 0.9658 0.7244 1005.4 491.81 0.5169 1.8600 1.9 919.07 0.9659 0.7400 1167.3 508.21 0.5341 1.9200 1.2 919.13 0.9660 0.7525 1150.6 518.27 0.5447 1.9600 20.4 919.80 0.9666 0.7575 1132.9 523.94 0.5506 1.9850 87.8 921.77 0.9687 0 . 7 6 2 5 6 1 9 . 8 527 .04 0 .5539 2 .0050 2 5 . 8 922 .41 0 . 9 6 9 4 0 . 7 6 7 5 993 .3 535.73 0 . 5 6 3 0 2 . 0 3 5 0 95 .9 925 .29 0 . 9 7 2 4 0.7800 1090.1 553.44 0.5816 2.0650 58.2 927.18 0.9744 0 . 8 0 0 0 1042 .4 572 ,21 0 .6014 2 . 1 0 0 0 8 5 . 9 930 .75 0 .9782 0 . 8 1 6 0 8 1 8 . 4 581 .90 0 .6115 2 .1480 7 9 . 2 934 .63 0 . 9 8 2 2 0.8237 756.5 587.77 0.6177 2.1980 68.9 938.83 0.9867 0 .8315 8 8 3 . 2 594 .96 0 . 6 2 5 3 2 .2700 67.7 944 ,31 0 . 9 9 2 4 0.8400 925.1 608.15 0.6391 2.3600 59.8 949,69 0.9981 0.8600 943.4 627.01 0.6590 2.4500 20.4 951.53 1.0000

a~ . Wavelength.

b~ . D£rect normal spectral tcradiance averased over 20 c~ -I centered ac

CEO_ ~ - I n t e g r a t e d g l o b a l L r r a d i a n c e tn the w a v e l e n s t h r a n p 0 to ~.

d~o=~ - I n t e g r a t e d $1oba l l r r a d i a n c e over the e n t i r e s p e c t r u m .

h.

572 R.E. BIRD et al.

1500

1200

E

--" 900

600 i -

a~

3OO

03 2.3

~ Me!ieled sured

I J f I '1 I " I ] 0.5 0.7 0.9 1.1 1.3 1.5 1.7


Fig. 12. Comparison of measured global horizontal spectrum taken at Golden, Colorado, on 5 August 1981, with modeled data.

20

15

10 o ~- 5

0

/5 -5

- I0

-15

-20 0.3

I I i I I i i I I

0.5 0.7 0,9 :1.1 1.3 1.5 1.7 1.9 2.1 Wavelength (Micrometers)

2.3

Fig. 13. Percentage of difference between modeled and measured solar spectra (Golden, Colorado, 5 August 1981).

There is absorption between 1.15 and 1.3/~m in the measured data that is not present in the modeled data. This was partially corrected by adding a new wavelength (1.2/~m) in the new data set, but there is still unexplained absorption in this region. The deviation beyond 2.0 p.m is primarily caused by the very small signal. A small difference can be a large percentage of a small number. It is evident that the wavelength calibration of the spectroradiometer is erroneous at the long wavelength end. This is a result of the slope of the linear wavelength calibration method being held constant in the infrared channel. This will be corrected in the future.

6. CONCLUSIONS

We have created new data sets that are more accurate than previous ones published by us as a result of using: (a) a new extraterrestrial spectrum, (b) a different value for the depolarization factor in the Rayleigh scattering calculation, (c) a more accurate sampling technique for calculating scattered irradiance, and (d) a better choice

of wavelengths to perform the calculations. Also, we have compared measured and modeled data, adding confidence to the accuracy of our modeled data. One data set is for the direct normal irradiance within a 5.80 field-of-view (FOV), and the second data set is for the global irradiance falling on a flat surface (1800 FOV) tilted 37 ° from the horizontal towards the sun. Atmos- pheric conditions for both standards are:

airmass = 1.5 precipitable water = 1.42 cm ozone = 0.34 atm-cm turbidity (500 nm) = 0.27 ground albedo = 0.2 surfacepressure = 1013mb.

These data are useful as a basis for comparing the performance of solar products and can be used for absorptance, reflectance, transmittance, and response evaluations of various devices and materials.


REFERENCES

1. J. V. Dave, Extensive datasets of diffuse radiation in realistic atmospheric models with aerosols and common absorbing gases. Solar Energy 21,361 (1978).

2. R. E. Bird, Terrestrial solar spectral modeling, Solar Cells 7, 107 (1983).

3. W. V. L. Weiman, Report of. 2rid WMO Expert Meeting on Turbidity Measurements. Boulder, Colorado (1978).

4. J. Geist, B. Steiner, R. Schaefer, E. Zalewski and A. Corrons, Electrically based power measurements through use of tun- able CW laser. Appl. Phys. Lett. 26, 309-311 (1975).

5. E. F. Zalewski and J. Geist, Silicon photodiode absolute spectral response self-calibration. Appl. Opt. 19, 1214-1216 (1980).

6. F. Kasten, A new table and approximation formula for the relative optical air mass, Arch. Met. Geophys. Bioklem. B14, PR-206-223 (1966).

7. M. Kerker, The Scattering of Light and Other Electromag- netic Radiation, p. 31. Academic Press, New York (1969).

8. A. T. Young, On Rayleigh-scattering optical depth of the atmosphere. J. Appl. Met. 20, 328--330 (1981).

9. E. C. Y. Inn and Y. Tanaka, Absorption coefficient of ozone in the ultra-violet and visible regions. J, Opt. Soc. Am. 43, 870-873 (1953).

10. T. K. Van Heuklon, Estimating atmospheric ozone for solar radiation models. Solar Energy 22, 63-68 (1979).

11. R. E. Bird and R. L. Hulstrom, Precipitable water measurements with sun photometers, J. Appl. Met. 21, 1196 (1982).

12. M. D. King and B. M, Herman, Determination of ground albedo and the index of absorption of atmospheric parti- culates by remote sensing--l. Theory. 3. Atmos. Sci. 36, 163-173 (1979).

13. R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Voltz and J. S. Garing, Optical Properties of the Atmosphere. 3rd Edn. AFCRL-72-0497. Bedford, MA: Air Force Cambridge Research Laboratories (1972).

14. E. P. Shettle and R. W. Fenn, Models of the atmospheric aerosol and their optical properties. Proc. AGARD Conf. No. 183: Optical Propagation in the Atmosphere, pp. 2.1-2.16. Electromagnetic Wave Propagation Panel Symposium. Lyngby, Denmark (1975).

15. L. Elterman, UV Visible and IR Attenuation for Altitudes to 50 kin, 1968. AFCRL-68-0153. Air Force Cambridge Research Laboratories, Bedford, Massachusetts (1968).

16. R. Ross, Photovoltaic Electrical Performance Specification Considerations. Presented at American Society for Testing and Materials Meeting, Lake Tahoe, Nevada (1979).

17. C. C. Gonzalez and R. G. Ross, Performance Measurement Reference Conditions for Terrestrial Photovoltaics, Presen- ted at the American Section of the International Solar Energy Society Annual Conference, Phoenix, Arizona (1980).

18. M. P. Thekaekara, Extraterrestrial solar spectral irradiance. The Extraterrestrial Solar Spectrum (Edited by A. J. Drum- mond and M. P. Thekaekara). Institute of Environmental Sciences, Mount Prospect, Illinois (1973).

19. M. P. Thekaekara, Extraterrestrial solar spectrum, 3000- 6100 A, at 1-~ intervals. Appl. Opt. 3, 518-522 (1974).

20. D. Labs and H. Neckel, Solar Physics. 15, 79 (1970). 21. C. Frrhlich, Photometry and Solar Radiation. Presented at

the Annual Meeting of the Schweiz. Gesellschaft for Astro- physik und Astronomie (1980).

22. J. Hardrop, The Sun Among the Stars--IIl. Solar Dis- tribution of 16 Northern G-Type Stars and Solar Flux Cali- bration. Astronomy and Astrophysics 91, 221 (1980).

23. Provided by C. Frrhlich, World Radiation Center, Davrs, Switzerland.

24. A. W. Kliman and H. G. Eldering, Design and development of a solar spectroradiometer. Electro-Optical Systems Design 53-61 (1981).

terrestrial solar spectral data sets

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