Solar Cells, 15 (1985) 365 - 391 365

SPECTRAL SOLAR IRRADIANCE DATA SETS FOR SELECTED TERRESTRIAL CONDITIONS

R. HULSTROM, R. BIRD and C. RIORDAN

Solar Energy Research Institute, 161 7 Cole Boulevard, Golden, CO 80401 (U.S.A.)

(Received August 2, 1985; accepted August 2, 1985)

Summary

Direct normal and global spectral solar irradiance data sets are pre- sented for selected terrestrial conditions, along with a brief review of pre- vious data sets. The new data sets presented cover the 0.305/~m to 4.045 #m region and were generated with the rigorous BRITE Monte Carlo radiative transfer code, the revised Neckel and Labs extraterrestrial solar spectrum, the U.S. standard atmosphere model, and a rural aerosol model. The data for the 2.45 ~m to 4.045 #m region were taken from existing ASTM standards (E891-82 and E892-82). Tabular and graphical data presentations include irradiance v e r s u s wavelength, photon flux density v e r s u s wavelength, and photon flux density v e r s u s photon energy.

1. Introduct ion

Terrestrial solar spectral data are useful for the development and design of photovoltaic devices (cells, submodules, modules) and systems for terres- trial applications. For example, the short-circuit current of a particular cell is predicted by integrating the product of the spectral irradiance data and the spectral response of the cell. Since outdoor solar spectral distributions vary with atmospheric conditions and sun angle, the photovoltaic communi ty often selects a representative spectral solar irradiance distribution so that solar cells can be compared on a common basis.

In the past, the National Aeronautics and Space Administration (NASA), the American Society for Testing and Materials (ASTM) and others have adopted particular spectral irradiance data sets as standard reference spectra. Two such data sets adopted as ASTM standards [1, 2] were gener- ated by the Solar Energy Research Institute (SERI). One data set is a direct normal spectrum at air mass (AM) 1.5 and the other is an AM 1.5 global spectrum on a sun-facing surface tilted 37 ° f rom the horizontal. These two data sets were updated and improved by SERI and the results were published

0379-6787/85/$3.30 © Elsevier Sequoia/Printed in The Netherlands

366

by SERI in 1983 [3]. We have expanded these data sets by extending the spectra to 4.045 pm, calculating cumulative integrals from 0.305 to 4.045 pm, normalizing the global spectrum to 1000 W m -2 and providing conver~ sions of spectral irradiance to photon flux density in intervals of both wavelength and energy (eV).

2. Background

Spectral irradiance data commonly referenced for terrestrial solar cell application include the NASA, ASTM and SERI tabulated data for AM 1.5 [1 - 4]. These data were generated by models that calculate the wavelength- dependent transmittance of extraterrestrial (AM 0) solar irradiance by the earth's atmosphere. The accuracy of these modeled spectral irradiance data has improved over the years due to better models and an improved AM 0 spectrum [3, 5]. These data and some of the recent improvements are briefly reviewed here.

Interest in developing standards for solar cell testing was demonstrated in an Energy Research and Development Administration (ERDA)/NASA workshop held in 1975 [6]. As a result of this workshop, NASA published "Interim Cell Testing Procedures for Terrestrial Applications" [7] which included a tabulated direct normal AM 2 reference spectrum. This spectrum was derived using a model by Thekaekara [8] and the Thekaekara/NASA/ ASTM AM 0 spectrum [9 - 11]. In a follow-up workshop held in 1976 [12], Curtis [13] reported the results of using the Thekaekara model to examine the impact of spectral irradiance variations on silicon solar cell performance. Before using the Thekaekara model, Curtis corrected an erroneous water vapor absorption band, described in ref. 14, by adjusting the absorption coefficients in the spectral region from 0.835 to 0.925 tLm.

The NASA Interim Procedures were replaced following the second workshop in 1976. The new procedures [4] give a direct normal AM 1.5 reference spectrum that was generated using the Thekaekara model with the revised absorption coefficients and AM 0 data reported by Labs and Neckel [15]. In addition, the forward-scattered radiation around the sun (circum- solar radiation) was modeled and added to the direct beam values. The circumsolar component was approximated by assuming that it is equal to 50% of the radiation scattered out of the direct beam by aerosols. A com- parison of the resulting direct beam (plus circumsolar) spectrum with one generated by SERI using the same atmospheric parameters and the rigorous radiative transfer model BRITE [16] shows that the approximation over- estimates the circumsolar radiation (Fig. 1). This comparison also indicates a spurious absorption band in the NASA spectrum at 0.85 pm.

SERI used the rigorous BRITE model and the Thekaekara AM 0 spectrum [9 - 11] to produce AM 1.5 direct normal (plus circumsolar) and global spectral irradiance data sets for the ASTM. Since adoption by ASTM, these data have been updated by making refinements to the BRITE model

367

1400

1200

~ 1000

800.

600.

400

200.

0 "~ - - - r - - - -f ] T - - ] ~ ~ - - - - 7 - - ~ 0.2 0.6 1.0 1.4 1.8 2.2 2.6

Wavelength (,um)

Fig. 1. Comparison of the NASA direct normal spectrum [4] and a SERI-generated spectrum using the same atmospheric parameters: o, NASA 1977 model; o, SERI BRITE model.

calculations and by using an improved AM 0 spectrum. These data were published in 1983 [3] and are further described in the following sections.

3. Atmospheric transmittance model

Details of the BRITE Monte Carlo radiative transfer model and param- eters used to generate the AM 1.5 spectral irradiance data sets are given in ref. 3. Briefly, this model traces the path of photons through 33 atmospheric layers characterized by temperature, pressure, aerosol amount and molecular absorber amount. The Monte Carlo method uses a random number generator and statistical methods to predict the absorption, scattering, transmittance or ground reflection of the photons.

The U.S. Standard Atmosphere [17], which contains 1.42 cm of precip- itable water and 0.34 atm cm of ozone in a vertical column from sea level to 100 km, and a rural aerosol model [18] were used for the BRITE calcula- tions. The height profile of the aerosol model resembles a moderate volcanic aerosol profile in the stratosphere and is based on Elterman's height profile measurements [ 19]. Aerosol optical depths (turbidities} in a vertical column from sea level are calculated using these profiles and a sea level visibility (meteorological range) of 25 km. They are 0.37 at 0368/am, 0.27 at 0.500 /~m and 0.14 at 0.862 #m.

A ground albedo of 0.2 was used in the BRITE model. This value normally varies with wavelength but was held constant because a large range of albedos exists for different surfaces. The value of 0.2 is representative of bare soils.

For the updated spectral irradiance data sets given here and in ref. 3, a revised Neckel and Labs AM 0 spectrum obtained from the World Radiation Centre [20] was used rather than the Thekaekara AM 0 spectrum. In addi- tion, refinements were made to absorption and scattering calculations using the BRITE model. These refinements consist of (a) a different value for the

368

depolarization factor in the Rayleigh scattering calculation, (b) a more accurate sampling technique for calculating the scattered irradiance and {c) a better choice of wavelengths in some of the water absorption bands. Com- parisons of the revised Labs and Neckel spectrum and the Thekaekara AM 0 spectrum, as well as the old and new spectral irradiance data sets, are given in ref. 3.

4. Geometry

The spectral irradiance data were calculated for the sun at a solar zenith angle of 48.19 °. This zenith angle corresponds to an air mass of 1.5 (the ratio of the direct beam solar irradiance path length through the atmosphere at a solar zenith angle of 48.19 ° to the path length when the sun is in a vertical position). SERI selected AM 1.5 based on work at the Jet Propulsion Labo- ratory [21, 22], which shows that approximately 50% of the annual energy output at selected U.S. locations is at air mass values greater than AM 1.5 for collector surfaces facing south and tilted at the latitude angle.

The AM 1.5 global irradiance was calculated for a fiat collector surface tilted 37 ° from the horizontal and facing the sun. The 37 ° tilt angle was chosen because it is a representative latitude for the 48 contiguous United States. This global spectrum is very close to, but is not a global normal spectrum. To calculate spectral irradiance on a flat collector surface with the direct beam normal to the surface (global normal spectral irradiance), the tilt angle must equal the solar zenith angle. The resultant global normal spectral irradiance would be approximately 1.8% greater than the global irradiance on the 37 ° ti l ted surface. For the AM 1.5 direct normal spectrum, a 5.8 ° field-of-view was used which includes the circumsolar radiation. This circumsolar radiation adds approximately 1.5% to the direct beam irradiance near 0.5 pm and a smaller percentage elsewhere in the spectrum.

5. Selected spectral irradiance and pho ton flux density data sets

The most recent and improved SERI-generated AM 1.5 direct normal and global spectral irradiance data sets [ 3 ] were simply extended from the previous wavelength cu tof f of 2.45 pm to 4.045 pm. This was done to account for the solar irradiance in this region which accounts for approximately 1.5% of the total irradiance between 0.305 and 4.045 pm. The total solar irradiance be- tween 0.305 and 4.045 pm accounts for approximately 99.7% of the total between 0.305 and 14.3 pm. The extension of the spectral data sets was accomplished by utilizing the values given in the ASTM standards [1, 2] for the 2.45 to 4.045 #m region. This approach is justified because the two sets of spectra [1 - 3] are very similar in the infrared. A difference of only 0.4 W m 2 and 0.6 W m -2 for the direct normal and global irradiance between 2.005 and 2.45 pm exists between the two spectra. This small difference does not

369

j u s t i f y u t i l i z i n g t h e c o m p u t e r - i n t e n s i v e a n d e x p e n s i v e B R I T E m o d e l t o gen-

e r a t e n e w va lues f o r t h e r e l a t i v e l y i n s i g n i f i c a n t 2 . 4 5 t o 4 . 0 4 5 # m r e g i o n . T h e n e w A M 1 .5 d i r e c t n o r m a l a n d g l o b a l s p e c t r a l i r r a d i a n c e d a t a se ts

a re p r e s e n t e d in T a b l e s I (a, b , c) a n d 2 (a, b , c) , a n d a re s h o w n in Fig . 2. T h e n e w i n t e g r a l s w e r e c a l c u l a t e d us ing t h r e e d i f f e r e n t i n t e g r a t i o n t e c h - n i q u e s t h a t h a v e b e e n p r o p o s e d in t h e p a s t ( A p p e n d i x A) . F i g u r e 3 s h o w s

2100. ~l~ ~ A i r Mass 0

1800 I ' V

-~'E 1500 I ~ " ~ G l ° b a l ' 37° Tilt' Air Mass 1 5

1200 ; " , Air Mass 15

900

600-

300-

0- 02 1.0 1.8 2.6 3.4 4.2

Wavelength (pm)

10

08-I_ ~ ~ ~ ~

.~_ 0.6- ~ -

"~ 0.4-

0.2-

0- 0.2 1.0 1.8 2.6 3.4 42

Wavelength (pm)

Fig. 2. Plots of three categories of spectral irradiance vs. wavelength.

Fig. 3. Fractional cumulative integrated irradiance vs. wavelength using three integration techniques: c] rectangular rule; ©, t rapezoidal ;~ , modified trapezoidal.

TABLE l a

Direct normal irradiance vs. wavelength spectrum (rectangular rule integration)

~ki a E~,ib Eo .2ki c F;kid ~i a Ehib Eo .ki c Fk id (pm) (W m -2 (W m -2) (pro) (W m -2 (W m -2 )

pm -1 ) pm -1)

0.3050 3.4 0.02 0.0000 0.9800 549.7 521.79 0.6793 0.3100 15.6 0.10 0.0001 0.9935 630.1 540.69 0.7039 0.3150 41.1 0.30 0.0004 1.0400 582.9 562.99 0.7329 0.3200 71.2 0.66 0.0009 1.0700 539.7 579.18 0.7540 0.3250 100.2 1.16 0.0015 1.1000 366.2 588.34 0.7659 0.3300 152.4 1.92 0.0025 1.1200 98.1 589.81 0.7678 0.3350 155.6 2.70 0.0035 1.1300 169.5 591.25 0.7697 0.3400 179.4 3.59 0.0047 1.1370 118.7 593.09 0.7721 0.3450 186.7 4.53 0.0059 1.1610 301.9 599.58 0.7806 0.3500 212.0 6.12 0.0080 1.1800 406.8 607.51 0.7909 0.3600 240.5 8.52 0.0111 1.2000 375.2 617.83 0.8043 0.3700 324.0 11.76 0.0153 1.2350 423.6 636.89 0.8291 0.3800 362.4 15.39 0.0200 1.2900 365.7 652.43 0.8494 0.3900 381.7 19.20 0.0250 1.3200 223.4 659.14 0.8581 0.4000 556.0 24.76 0.0322 1.3500 30.1 660.26 0.8596 0.4100 656.3 31.33 0.0408 1.3950 1.4 660.33 0.8596 0.4200 690.8 38.24 0.0498 1.4425 51.6 662.07 0.8619

( c o n t i n u e d )

370

TABLE l a (continued)

hi E;~i E° "~.i F)'i hi E hi E° "~.i F~.i (pm) ( W m -2 ( W m 2) ( / lm) ( W i n -2 ( W m --2)

pm--l) p m - 1 )

0 .4300 641.9 44 .65 0 .0581 1 .4625 97.0 663 .74 0 .8641 0 .4400 798 .5 52.64 0 .0685 1 .4770 97.3 665 .42 0 .8663 0 .4500 956.6 62.21 0 .0810 1 .4970 167.1 669.01 0 .8709 0 .4600 990 .8 72.11 0 .0939 1 .5200 239.3 674 .04 0 .8775 0 .4700 998.0 82 .09 0 .1069 1 .5390 248.8 678 .77 0 .8836 0 .4800 1046.1 92 .55 0 .1205 1 .5580 249.3 683 .63 0 .8900 0 .4900 1005.1 102.61 0 .1336 1 .5780 222.3 687.41 0 .8949 0 .5000 1026.7 112.87 0 .1469 1 .5920 227.3 691 .04 0 .8996 0 .5100 1066.7 123 .54 0 .1608 1 .6100 210.5 695 .04 0 .9048 0 .5200 1011 .5 133 .65 0 .1740 1 .6300 224.7 699 .09 0 .9101 0 .5300 1084.9 144 .50 0 .1881 1 .6460 215 .9 704 .27 0 .9168 0 .5400 1082.4 155 .33 0 .2022 1 .6780 202.8 713 .80 0 .9292 0 .5500 1102 .2 171 .86 0 .2237 1 .7400 158.2 723 .45 0 .9418 0 .5700 1087.4 193.61 0 .2520 1 .8000 28.6 725 .17 0 .9440 0 .5900 1024 .3 214 .09 0 .2787 1 .8600 1.8 725 .28 0 .9442 0 .6100 1088 .8 235 .87 0 .3071 1 .9200 1.1 725 .33 0 .9443 0 .6300 1062.1 257.11 0 .3347 1 .9600 19.7 725.97 0 .9451 0 .6500 1061.7 278 .35 0 .3624 1 .9850 84.9 727 .88 0 .9476 0 .6700 1046 .2 299.27 0 .3896 2 .0050 25.0 728.51 0 .9484 0 .6900 859 .2 316 .45 0 .4120 2 .0350 92.5 731 .28 0 .9520 0 .7100 1002 .4 330 .49 0 .4302 2 .0650 56.3 733.11 0 .9544 0 .7180 816 .9 336.37 0 .4379 2 .1000 82.7 736 .54 0 .9589 0 .7244 842 .8 345 .64 0 .4500 2 .1480 76.2 740 .28 0 .9637 0 .7400 971 .0 359 .28 0 .4677 2 .1980 66.4 744 .33 0 .9690 0 .7525 956 .3 367 .65 0 .4786 2 .2700 65.0 749 .59 0 .9758 0 .7575 942 .2 372 .36 0 .4848 2 .3600 57.6 754 .78 0 .9826 0 .7625 524.8 374 .99 0 .4882 2 .4500 19.8 756 .10 0 .9843 0 .7675 830.7 382 .25 0 .4976 2 .4940 17.0 756 .84 0 .9853 0 .7800 908 .9 397 .02 0 .5169 2 .5370 3.0 757.51 0 .9862 0 .8000 873 .4 412 .74 0 .5373 2 .9410 4.0 758 .39 0 .9873 0 .8160 712 .0 421 .18 0 .5483 2 .9730 7.0 758.61 0 .9876 0 .8237 660.2 426 .30 0 .5550 3 .0050 6.0 758 .86 0 .9879 0 .8315 765.5 432 .54 0 .5631 3 .0560 3.0 759 .05 0 .9882 0 .8400 799.8 443 .93 0 .5779 3 .1320 5.0 759 .30 0 .9885 0 .8600 815.2 460 .24 0 .5992 3 .1560 18.0 759 .95 0 .9893 0 .8800 778 .3 477 .75 0 .6220 3 .2040 1.2 760 .00 0 .9894 0 .9050 630.4 488 .78 0 .6363 3 .2450 3.0 760 .17 0 .9896 0 .9150 565.2 494 .43 0 .6437 3 .3170 12.0 760 .76 0 .9904 0 .9250 586.4 498 .83 0 .6494 3 .3440 3.0 760 .96 0 .9906 0 .9300 348.1 500.92 0 .6521 3 .4500 12.2 762 .36 0 .9925 0 .9370 224.2 502 .94 0 .6547 3 .5730 11.0 764 .09 0 .9947 0 .9480 271 .4 506.74 0 .6597 3 .7650 9.0 766 .22 0 .9975 0 .9650 451 .2 513 .96 0 .6691 4 .0450 6.9 768 .15 1 .0000

a)~i, wavelength. bEK. , spectral irradiance at wavelength )k i (centered at )~i and calculated using absorption

1 .

data wlth a resolutlon of 20 cm-1). CE° "~-i' integrated irradiance in the wavelength range o - ~,i.

dFKi , fraction of the total irradiance (integrated over the entire spectrum) that is in the wavelength range o - ~,i.

T A B L E l b

Direct n o r m a l i r rad iance vs. wavelength spec t rum (modi f i ed t r apezo ida l i n t eg ra t i on ) a

371

~'i E~i E° - hi Fki hi Eki E° "~'i Fki (pm) (W m - 2 (W m -2) (pm) (W m -2 (W m -2)

p m -1) # m -1)

0 .3050 3.4 0 .02 0 .0000 0 .9935 630.1 526 .06 0 .6847 0 .3100 15.6 0.07 0 .0001 1 .0400 582 .9 554.26 0 .7214 0 .3150 41.1 0.21 0 .0003 1 .0700 539.7 571 .10 0 .7433 0 .3200 71.2 0 .49 0 .0006 1 .1000 366.2 584.69 0 .7610 0 .3250 100.2 0.92 0 .0012 1 .1200 98.1 589 .33 0 .7670 0 .3300 152.4 1.55 0 .0020 1 .1300 169.5 590.67 0 .7688 0 .3350 155 .6 2.32 0 .0030 1 .1370 118.7 591 .68 0 .7701 0 .3400 179.4 3.16 0 .0041 1 .1610 301.9 596 .73 0 .7767 0 .3450 186.7 4 .08 0 .0053 1 .1800 406.8 603 .46 0 .7854 0 .3500 212.0 5.07 0 .0066 1 .2000 375.2 611 .28 0 .7956 0 .3600 240 .5 7 .34 0 .0095 1 .2350 423 .6 625 .26 0 .8138 0 .3700 324.0 10 .16 0 .0132 1 .2900 365.7 646 .96 0 .8421 0 .3800 362 .4 13 .59 0 .0177 1 .3200 223.4 655 .80 0 .8536 0 .3900 381.7 17.31 0 .0225 1 .3500 30.1 659 .60 0 .8585 0 .4000 556.0 22 .00 0 .0286 1 .3950 1.4 660 .31 0 .8594 0 .4100 656 .3 28 .06 0 .0365 1 .4425 51.6 661 .57 0 .8611 0 .4200 690.8 34 .80 0 .0453 1 .4625 97.0 663 .06 0 .8630 0 .4300 641 .9 41 .46 0 .0540 1 .4770 97.3 664 .46 0 .8648 0 . 4 4 0 0 798 .5 48 .66 0 .0633 1 .4970 167.1 667.11 0 .8683 0 .4500 956 .6 57.44 0 .0748 1 .5200 239.3 671 .78 0 .8744 0 .4600 990 .8 67 .17 0 .0874 1 .5390 248 .8 676 .42 0 .8804 0 .4700 998.0 77 .12 0 .1004 1 .5580 249,3 681 .15 0 .8866 0 .4800 1046 .1 87 .34 0 .1137 1 .5780 222.3 685 .87 0 .8927 0 . 4 9 0 0 1005.1 97 .59 0 .1270 1 ,5920 227.3 689 .01 0 . 8 9 6 8 0 .5000 1026.7 107 .75 0 .1402 1 ,6100 210.5 692 .95 0 .9019 0 .5100 1066.7 118 .22 0 .1539 1 .6300 224.7 697.31 0 .9076 0 .5200 1011 .5 128.61 0 .1674 1 ,6460 215.9 700 .83 0 .9122 0 .5300 1084 .9 139 .09 0 .1810 1 ,6780 202.8 707 .53 0 .9209 0 .5400 1082 .4 149 .93 0 .1951 1 ,7400 158.2 718 .72 0 .9355 0 .5500 1102 .2 160 .85 0 .2094 1 .8000 28.6 724 .33 0 .9428 0 .5700 1087 .4 182 .75 0 .2379 1 .8600 1.8 725 .24 0 .9439 0 .5900 1024 .3 203.87 0 .2653 1 .9200 1.1 725 .32 0 .9441 0 .6100 1088 .8 225 .00 0 .2928 1 ,9600 19.7 725 .74 0 .9446 0 .6300 1062.1 246.51 0 .3208 1 ,9850 84.9 727 ,05 0 .9463 0 .6500 1061.7 267 .74 0 .3485 2 ,0050 25.0 728 .15 0 .9477 0 .6700 1046 .2 288 .82 0 .3759 2 .0350 92.5 729 .91 0 .9500 0 .6900 859 .2 307 .88 0 .4007 2 .0650 56.3 732 .14 0 .9529 0 .7100 1002 .4 326 .49 0 .4249 2 ,1000 82.7 734 .57 0 .9561 0 .7180 816 .9 333.77 0 .4344 2 .1480 76.2 738 .39 0 .9611 0 .7244 842.8 339 .08 0 .4413 2 .1980 66.4 741 .95 0 .9657 0 . 7 4 0 0 971 .0 353 .23 0 .4597 2 .2700 65.0 746 .68 0 .9719 0 .7525 956 .3 365.27 0 .4754 2 .3600 57.6 752 .20 0 .9790 0 .7575 942 .2 370 .02 0 .4816 2 .4500 19.8 755 .68 0 .9836 0 .7625 524.8 373 .69 0 .4864 2 ,4940 17.0 756 .49 0 .9846 0 . 7 6 7 5 830.7 377 .08 0 .4908 2 ,5370 3.0 756 .92 0 .9852 0 .7800 908 .9 387 .95 0 .5049 2 .9410 4.0 758 .34 0 .9870

(continued)

372

T A B L E l b (continued)

~i Eh i E° "~-i F~ i }~i E~ i Eo -- h i F~ i (pm) ( W m 2 ( W i n 2) (pm} ( W m ~ ( W i n :)

p m 1) p m 1)

0 .8000 873.4 405.77 0 .5281 2 .9730 7.0 758.51 0 .9872 0 .8160 712.0 418 .46 0 .5446 3 .0050 6.0 758 .72 0 .9875 0 .8237 660.2 423 .74 0 .5515 3 .0560 3.0 758 .95 0 .9878 0 .8315 765.5 429 .30 0 .5588 3 .1320 5.0 759 .25 0 .9882 0 .8400 799.8 435 .95 0 .5674 3 .1560 18.0 759.53 0 .9886 0 .8600 815.2 452 .10 0 .5884 3 .2040 1.2 759 .99 0 .9892 0 .8800 778.3 468 .04 0 .6092 3 .2450 3.0 760 .08 0 .9893 0 .9050 630.4 485 .65 0 .6321 3 .3170 12.0 760 .62 0 .9900 0 .9150 565.2 491 .62 0 .6399 3 .3440 3.0 760 .82 0 .9902 0 .9250 586.4 497 .38 0 .6474 3 .4500 12.2 761 .62 0 .9913 0 .9300 348.1 499 .72 0 .6504 3 .5730 11.0 763 .05 0 .9932 0 .9370 224.2 501.72 0 .6530 3 .7650 9.0 764.97 0 .9957 0 .9480 271.4 504 .45 0 .6566 4 .0450 6.9 767 .20 0 .9986 0 .9650 451.2 510 .59 0 .6646 4 .0450 768.31 1 .0000 0 .9800 549.7 518.10 0 .6743

aFor def in i t ions see Table la .

TABLE l c

Direct no rma l i r radiance vs. wavelength s p e c t r u m ( t rapezo ida l i n t eg ra t ion ) a

~-i Eh i Eo - h i Fh i ~,i Eh i Eo- h i ( pm) ( W m -2 ( W m -2) (pm) (W m -2 (W m -2)

p m -1) p m -1)

Fh i

0 .3050 3.4 -- - - 0 .9800 549.7 518.07 0 .3100 15.6 0 .05 0 .0001 0 .9935 630.1 526.04 0 .3150 41.1 0 .19 0 .0002 1 .0400 582.9 554.24 0 .3200 71.2 0.47 0 .0006 1 .0700 539.7 571 .08 0 .3250 100.2 0.90 0 . 0 0 1 2 1 .1000 366.2 584.67 0 .3300 152.4 1.53 0 .0020 1 .1200 98.1 589.31 0 .3350 155.6 2.30 0 .0030 1 .1300 169.5 590 .65 0 .3400 179.4 3.14 0 .0041 1 .1370 118.7 591 .65 0 .3450 186.7 4 .05 0 .0053 1 .1610 301.9 596 .70 0 .3500 212.0 5.05 0 .0066 1 .1800 406 .8 603 .43 0 .3600 240.5 7.31 0 .0095 1 .2000 375.2 611 .25 0 .3700 324.0 10 .13 0 .0132 1 .2350 423 .6 625 .23 0 .3800 362.4 13.57 0 .0177 1 .2900 365.7 646 .94 0 .3900 381.7 17 .29 0 .0225 1 .3200 223.4 655 .78 0 .4000 556.0 21 .98 0 .0286 1 .3500 30.1 659 .58 0 .4100 656.3 28 .04 0 .0365 1 .3950 1.4 660 .29 0 .4200 690 .8 34 .77 0 .0453 1 .4425 51.6 661 .55 0 .4300 641 .9 41 .44 0 .0540 1 .4625 97.0 663 .03 0 .4400 798 .5 48 .64 0 .0634 1 .4770 97.3 664 .44 0 .4500 956 .6 57.41 0 .0748 1 .4970 167.1 667 .08 0 .4600 990.8 67 .15 0 .0875 1 .5200 239.3 671 .76

0 .6753 0 .6857 0 .7224 0 .7444 0 .7621 0 .7682 0 .7699 0 .7712 0 . 7 7 7 8 0 .7866 0 . 7 9 6 8 0 .8150 0 .8433 0 .8548 O.8598 0 .8607 0 .8623 0 .8643 0 .8661 0 .8695 0 .8756

TABLE l c (continued)

373

hi Ek i Eo -k i Fk i hi Ek i Eo -k i F~, i (pm) (W m -2 (W m -2) (pm) (W m -2 (W m -2)

p ro- l ) pm -1)

0.4700 998.0 77.09 0.1005 1.5390 248.8 676.40 0.8817 0.4800 1046.1 87.31 0.1138 1.5580 249.3 681.13 0.8878 0.4900 1005.1 97.57 0.1272 1.5780 222.3 685.84 0.8940 0.5000 1026.7 107.73 0.1404 1.5920 227.3 688.99 0.8981 0.5100 1066.7 118.20 0.1541 1.6100 210.5 692.93 0.9032 0.5200 1011.5 128.59 0.1676 1.6300 224.7 697.28 0.9089 0.5300 1084.9 139.07 0.1813 1.6460 215.9 700.81 0.9135 0.5400 1082.4 149.91 0.1954 1.6780 202.8 707.51 0.9222 0.5500 1102.2 160.83 0.2096 1.7400 158.2 718.70 0.9368 0.5700 1087.4 182.73 0.2382 1.8000 28.6 724.30 0.9441 0.5900 1024.3 203.84 0.2657 1.8600 1.8 725.21 0.9453 0.6100 1088.8 224.97 0.2932 1.9200 1.1 725.30 0.9454 0.6300 1062.1 246.48 0.3213 1.9600 19.7 725.72 0.9460 0.6500 1061.7 267.72 0.3490 1.9850 84.9 727.02 0.9477 0.6700 1046.2 288.80 0.3764 2.0050 25.0 728.12 0.9491 0.6900 859.2 307.85 0.4013 2.0350 92.5 729.89 0.9514 0.7100 1002.4 326.47 0.4255 2.0650 56.3 732.12 0.9543 0.7180 816.9 333.75 0.4350 2.1000 82.7 734.55 0.9575 0.7244 842.8 339.06 0.4420 2.1480 76.2 738.36 0.9624 0.7400 971.0 353.21 0.4604 2.1980 66.4 741.93 0.9671 0.7525 956.3 365.25 0.4761 2,2700 65.0 746.66 0.9733 0.7575 942.2 370.00 0.4823 2.3600 57.6 752.18 0.9805 0.7625 524.8 373.66 0.4871 2.4500 19.8 755.66 0.9850 0.7675 830.7 377.05 0.4915 2.4940 17.0 756.47 0.9860 0.7800 908.9 387.93 0.5057 2.5370 3.0 756.90 0.9866 0.8000 873.4 405.75 0.5289 2.9410 4.0 758.31 0.9884 0.8160 712.0 418.43 0.5454 2.9730 7.0 758.49 0.9887 0.8237 660.2 423.72 0.5523 3.0050 6.0 758.70 0.9889 0.8315 765.5 429.28 0.5596 3.0560 3.0 758.93 0.9892 0.8400 799.8 435.93 0.5682 3.1320- 5.0 759.23 0.9896 0.8600 815.2 452.08 0.5893 3.1560 18.0 759.51 0.9900 0.8800 778.3 468.01 0.6100 3.2040 1.2 759.97 0.9906 0.9050 630.4 485.62 0.6330 3.2450 3.0 760.05 0.9907 0.9150 565.2 491.60 0.6408 3.3170 12.0 760.59 0.9914 0.9250 586.4 497.36 0.6483 3.3440 3.0 760.80 0.9917 0.9300 348.1 499.69 0.6513 3.4500 12.2 761.60 0.9927 0.9370 224.2 501.70 0.6540 3.5730 11.0 763.03 0.9946 0,9480 271.4 504.42 0.6575 3.7650 9.0 764.95 0.9971 0,9650 451.2 510,56 0.6655 4.0450 6.9 767.17 1.0000

aFor definitions see Table la.

various techniques. We would also like to note that a small error in the direct normal spectral irradiance cumulative integrals contained in ref. 3 has been corrected. If one is integrating the product of a photovoltaic device spectral response with spectral irradiance to obtain short-circuit, we have found that it may be necessary to use smaller wavelength intervals than those given in

374

TABLE 2a

Global i r radiance v s . wavelength spec t rum for a sun-facing, 37 ° t i l ted surface ( rec tangular rule in tegra t ion)

~i a E~.ib Eo .hi c F h i d E~,ie E ' o . h i e F~ie (~um) (W m -2 (W m -2) (W m 2 (W m- 2)

p m - 1 ) p m - l )

0 .3050 9.2 0 .05 0 .0000 9.5 0 .05 0 .0000 0 .3100 40.8 0 .25 0 .0003 42.3 0 .26 0 .0003 0 .3150 103.9 0.77 0 .0008 107.8 0.80 0 .0008 0 .3200 174 .4 1.64 0 .0017 181.0 1.70 0 .0017 0 .3250 237.9 2.83 0 .0029 246.9 2.94 0 .0029 0 .3300 381.0 4.74 0 .0049 395.4 4.92 0 0 0 4 9 0 .3350 376.0 6.62 0 .0069 390.2 6.87 0 .0069 0 .3400 419 .5 8.71 0 .0090 435 .4 9.04 0 .0090 0 .3450 423 .0 10.83 0 .0112 439 .0 11 .24 0 .0112 0 .3500 466 .2 14.33 0 .0149 483 .8 14.87 0 .0149 0 .3600 501.4 19 .34 0 .0201 520.4 20.07 0 .0201 0 .3700 642.1 25.76 0 .0267 666.4 26 .73 0 .0267 0 .3800 686.7 32.63 0 .0339 712.7 33 .86 0 .0339 0 .3900 694.6 39.57 0 .0411 720.9 41 .07 0 .0411 0 .4000 976.4 49 .34 0 .0512 1013 .3 51.20 0 .0512 0 .4100 1116 .2 60 .50 0 .0628 1158 .4 62 .79 0 .0628 0 .4200 1141.1 71.91 0 .0746 1184 .3 74.63 0 .0746 0 .4300 1033 .0 82 .24 0 .0854 1072.1 85.35 0 .0854 0 .4400 1254 .8 94 .79 0 .0984 1302 .3 98.37 0 .0984 0 .4500 1470.7 109 .50 0 .1136 1526 .3 113 .64 0 .1136 0 .4600 1541 .6 124 .91 0 .1296 1599 .9 129 .63 0 .1296 0 .4700 1523 .7 140 .15 0 .1454 1581 .3 145 .45 0 .1454 0 .4800 1569 .3 155 .84 0 .1617 1628 .6 161 .73 0 .1617 0 .4900 1483 .4 170 .68 0 .1771 1539 .5 177 .13 0 .1771 0 .5000 1492 .6 185.60 0 .1926 1549.0 192 .62 0 .1926 0 .5100 1529 .0 200 .89 0 .2085 1586 .8 208 .49 0 .2085 0 .5200 1431.1 215.20 0 .2233 1485 .2 223.34 0 .2233 0 .5300 1515 .4 230 .36 0 .2391 1572.7 239 .07 0 .2391 0 .5400 1494 .5 245 .30 0 .2546 1551 .0 254 .58 0 .2546 0 .5500 1504 .9 267.87 0 .2780 1561 .8 278.00 0 .2780 0 .5700 1447.1 296 .82 0 .3080 1501 .8 308 .04 0 .3080 0 .5900 1344 .9 323.71 0 .3360 1395 .8 335 .96 0 .3360 0 .6100 1431 .5 352 .34 0 .3657 1485 .6 365.67 0 .3657 0 .6300 1382.1 379 .99 0 .3944 1434.4 394 .36 0 .3944 0 .6500 1368 .4 407 .35 0 .422S 1420.1 422 .76 0 .4228 0 .6700 1341 .8 434 .19 0 .4506 1392 .5 450 .61 0 .4506 0 .6900 1089 .0 455 .97 0 .4732 1130.2 473 .21 0 .4732 0 .7100 1269 .0 473 .74 0 .4917 1317.0 491 .65 0 .4917 0 .7180 973.7 480 .75 0 .4989 1010 .5 498 .93 0 .4989 0 .7244 1005.4 491 .81 0 .5104 1043 .4 510.41 0 .5104 0 .7400 1167 .3 508.21 0 .5274 1211 .4 527 .43 0 . 5 2 7 4 0 .7525 1150 .6 518.27 0 .5379 1194.1 537.87 0 .5379 0 .7575 1132 .9 523.94 0 .5438 1175.7 543.75 0 .5438 0 .7625 619 .8 527.04 0 .5470 643.2 546.97 0 .5470 0 .7675 993 .3 535.73 0 .5560 1030 .9 555.99 0 .5560

TABLE 2a (continued)

;ki Ek i (pro) (W m -2

~m -1)

E~ .ki (Wm -~)

Fk i f

Ek i (Win-2 pm -1)

E o . k i (Wm -2)

0.7800 1090.1 553.44 0.5744 1131.3 574.37 0.8000 1042.4 572.21 0.5938 1081.8 593.85 0.8160 818.4 581.91 0.6039 849.4 603.91 0.8237 756.5 587.77 0.6100 785.1 610.00 0.8315 883.2 594.97 0.6175 916.6 617.47 0.8400 925.1 608.15 0.6311 960.1 631.15 0.8600 943.4 627.02 0.6507 979.1 650.73 0.8800 899.4 647.25 0.6717 933.4 671.73 0.9050 721.4 659.88 0.6848 748,7 684.83 0.9150 643.3 666.31 0.6915 667.6 691.51 0.9250 665.3 671.30 0.6967 690.5 696.69 0.9300 389.0 673.63 0.6991 403.7 699.11 0.9370 248.9 675.87 0.7014 258.3 701.43 0.9480 302.2 680.11 0.7058 313.6 705.83 0.9650 507.7 688.23 0.7143 526.9 714.26 0.9800 623.0 697.11 0.7235 646.6 723.47 0.9935 719.7 718.70 0.7459 746.9 745.88 1.0400 665.5 744.15 0.7723 690.7 772.29 1.0700 614.4 762,58 0.7914 637.6 791.42 1.1000 397.6 772.52 0,8017 412.6 801.74 1.1200 105.0 774.10 0.8034 109.0 803.37 1.1300 182.2 775.65 0.8050 189.1 804.98 1.1370 127,4 777.62 0.8070 132.2 807.03 1.1610 326.7 784.65 0.8143 339.1 814.32 1.1800 443.3 793.29 0.8233 460.1 823.29 1.2000 408.2 804.52 0.8349 423.6 834.94 1.2350 463.1 825.36 0.8566 480.6 856.57 1.2900 398.1 842.28 0.8741 413.2 874.13 1.3200 241.1 849.51 0.8816 250.2 881.64 1.3500 31.3 850.68 0.8829 32.5 882.85 1.3950 1.5 850.75 0.8829 1.6 882.93 1.4425 53.7 852.56 0.8848 55.7 884.81 1.4625 101.3 854.31 0.8866 105.1 886.62 1.4770 101.7 856.07 0.8884 105.5 888.44 1.4970 175.5 859.84 0.8924 182.1 892.36 1.5200 253.1 865.15 0.8979 262.7 897.87 1.5390 264.3 870.18 0.9031 274.3 903.08 1.5580 265.0 875.34 0.9084 275.0 908.45 1.5780 235.7 879.35 0.9126 244.6 912.61 1.5920 238.4 883.16 0.9166 247.4 916.56 1.6100 220.4 887.35 0.9209 228.7 920.91 1.6300 235.6 891.59 0.9253 244.5 925.31 1.6460 226.3 897.02 0.9309 234.9 930.95 1.6780 212.5 907.01 0.9413 220.5 941.31 1.740.0 165.3 917.10 0.9518 171.6 951.78 1.8000 29.6 918.87 0.9536 30.7 953.62 1.8600 1.9 918.99 0.9537 2.0 953.74

375

i

0.5744 O.5938 0.6039 0.6100 0.6175 0.6311 0.6507 0.6717 0.6848 0.6915 0.6967 0.6991 0.7014 0.7058 0.7143 0.7235 0.7459 0.7723 0,7914 0.8017 0.8034 0.8050 0.8070 0.8143 0.8233 0.8349 0.8566 0.8741 0.8816 0.8829 0.8829 0.8848 0,8866 0.8884 0.8924 0.8979 0.9031 0.9084 0.9126 0.9166 0.9209 0.9253 0.9309 0.9413 0.9518 0.9536 0.9537

(continued)

376

TABLE 2a (continued)

)~i Eki E°" ~ki Fki Eki E°" '~-i /~'~J (tim) ( W m 2 ( W m - 2 ) (Win 2 (Win 21

~m- 1) p m - 1)

1.9200 1.2 919.05 0.9538 1.2 953.80 0.9538 1.9600 20.4 919.71 0.9545 21.2 954.49 0.9545 1.9850 87.8 921.68 0.9565 91.1 956.54 0.9565 2.0050 25.8 922.33 0.9572 26.8 957.21 0.9572 2.0350 95.9 925.21 0.9602 99.5 960.20 0.9602 2.0650 58.2 927.10 0.9622 60.4 962.16 0.9622 2.1000 85.9 930.66 0.9659 89.1 965.86 0.9659 2.1480 79.2 934.54 0.9699 82.2 969.89 0.9699 2.1980 68.9 938.75 0.9742 71.5 974.25 0.9742 2.2700 67.7 944.23 0.9799 70.3 979.94 0.9799 2.3600 59.8 949.61 0.9855 62.1 985.52 0.9855 2.4500 20.4 950.98 0.9869 21.2 986.94 0.9869 2.4940 17.8 951.75 0.9877 18.5 987.75 0.9877 2.5370 3.1 952.45 0.9885 3.2 988.46 0.9885 2.9410 4.2 953.36 0.9894 4.4 989.42 0.9894 2.9730 7.3 953.59 0.9897 7.6 989.66 0.9897 3.0050 6.3 953.86 0.9899 6.5 989.93 0.9899 3.0560 3.1 954.05 0.9901 3.2 990.13 0.9901 3.1320 5.2 954.31 0.9904 5.4 990.40 0.9904 3.1560 18.7 954.99 0.9911 19.4 991.10 0.9911 3.2040 1.3 955.04 0.9912 1.3 991.16 0.9912 3.2450 3.1 955.22 0.9913 3.2 991.34 0.9913 3.3170 12.6 955.84 0.9920 13.1 991.99 0.9920 3.3440 3.1 956.05 0.9922 3.2 992.20 0.9922 3.4500 12.8 957.51 0.9937 13.3 993.73 0.9937 3.5730 11.5 959.33 0.9956 11.9 995.61 0.9956 3.7650 9.4 961.54 0.9979 9.8 997.91 0.9979 4.0450 7.2 963.56 1.0000 7.5 1000.00 1.0000

ahi, wavelength. bEk. spectral irradiance at wavelength hi (centered at hl and calculated using absorption

1' data wi th a resolution of 20 cm-1) . CEo-k-, integrated irradiance in the wavelength range o - hi. dF~.i, ~raction of the total irradiance.(integrated over the entire spectrum) that is in the wavelength range o - h i. e ~ ~ r Eki, E o. hi, Fki , as def ined above but for the spectrum normal ized to 1000 W m -2 .

the tables; we recommend linear interpolation to obtain spectral irradiance at intermediate wavelengths.

The photovoltaic community often finds it convenient to use a spec- trum with a total irradiance value of 1000 W m -2. To accommodate these applications, we have normalized the global spectrum to 1000 W m -2 by multiplying the lrradiance at each wavelength by a constant equal to 1000} total irradiance. The exact spectral irradiance values in the normalized spectrum depend on the integration technique used to calculate total irra- diance. Normalized spectral irradiance values are given on the right-hand side of Table 2 (a, b, c).

377

T A B L E 2b

Global i r radiance vs. wavelength s p e c t r u m for a sun-facing, 37 ° t i l ted surface (mod i f i ed t rapezo ida l in t eg ra t ion) a

~'i E ~, i Eo " ki Fk i E~i E'° " ki F~i (pro) (W m -2 ( W m -2) (W m -2 (W m -2)

p m -1 ) /~m -1)

0 . 3 0 5 0 9.2 0 .06 0 .0001 9.5 0 .06 0 .0001 0 .3100 40.8 0 .19 0 .0002 42.3 0 .19 0 .0002 0 .3150 103.9 0 .55 0 .0006 107.8 0.57 0 .0006 0 .3200 174.4 1.25 0 .0013 181.0 1.29 0 .0013 0 .3250 237.9 2.28 0 .0024 246.8 2.36 0 .0024 0 .3300 381.0 3.82 0 .0040 395.3 3.97 0 .0040 0 .3350 376.0 5.72 0 .0059 390.1 5.93 0 .0059 0 .3400 419 .5 7.70 0 .0080 435 .3 7.99 0 .0080 0 .3450 423.0 9.81 0 .0102 438.9 10 .18 0 .0102 0 .3500 466 .2 12.03 0 .0125 483.7 12 .49 0 .0125 0 .3600 501.4 16.87 0 .0175 520.3 17.51 0 .0175 0 .3700 642.1 22 .59 0 .0234 666.2 23 .44 0 .0234 0 .3800 686.7 29 .23 0 .0303 712 .5 30 .33 0 .0303 0 .3900 694 .6 36 .14 0 .0375 720.7 37 .50 0 .0375 0 .4000 976 .4 44 .49 0 .0462 1013.1 46 .17 0 .0462 0 .4100 1116 .2 54 .96 0 .0570 1158 .2 57.02 0 .0570 0 .4200 1141.1 66 .24 0 .0687 1184 .0 68 .74 0 .0687 0 .4300 1033 .0 77 .11 0 .0800 1071 .9 80.01 0 .0800 0 .4400 1254 .8 88 .55 0 .0919 1302 .0 91 .88 0 .0919 0 .4500 1470 .7 102 .18 0 .1060 1526 .0 106 .02 0 .1060 0 .4600 1541 .6 117 .24 0 .1217 1599 .6 121 .65 0 .1217 0 .4700 1523.7 132 .57 0 .1376 1581 .0 137 .55 0 .1376 0 .4800 1569 .3 148 .03 0 .1536 1628 .3 153 .60 0 .1536 0 .4900 1483 .4 163 .30 0 .1694 1539 .2 169 .44 0 .1694 0 .5000 1492 .6 178 .18 0 .1849 1548.7 184 .88 0 .1849 0 .5100 1529 .0 193 .29 0 .2006 1586 .5 200 .55 0 .2006 0 .5200 1431.1 208 .09 0 .2159 1484 .9 215 .91 0 .2159 0 .5300 1515 .4 222 .82 0 .2312 1572 .4 231 .20 0 .2312 0 .5400 1494 .5 237.87 0 .2468 1550.7 246.81 0 .2468 0 .5500 1504.9 252 .87 0 .2624 1561 .5 262 .38 0 .2624 0 .5700 1447.1 282 .39 0 .2930 1501 .5 293 .01 0 .2930 0 .5900 1344 .9 310 .30 0 .3220 1395 .5 321 .98 0 .3220 0 .6100 1431 .5 338 .07 0 .3508 1485 .3 350 .78 0 .3508 0 .6300 1382~1 366 .20 0 .3800 1434.1 379 .98 0 .3800 0 .6500 1368 .4 393.71 0 .4085 1419 .9 408 .52 0 .4085 0 .6700 1341 .8 420 .81 0 .4366 1392 .3 436 .64 0 .4366 0 . 6 9 0 0 1089 .0 445 .12 0 .4619 1130 .0 461 .86 0 .4619 0 . 7 1 0 0 1269 .0 468 .70 0 .4863 1316.7 486 .33 0 .4863 0 .7180 973.7 477.67 0 . 4 9 5 6 1010 .3 495 .64 0 .4956 0 .7244 1005 .4 484 .00 0 .5022 1043 .2 502.21 0 .5022 0 .7400 1167 .3 500 .95 0 .5198 1211 .2 519 .79 0 .5198 0 .7525 1150 .6 515 .44 0 .5348 1193 .9 534 .82 0 .5348 0 .7575 1132 .9 521.15 0 .5407 1175 .5 540 .75 0 .5407 0 .7625 619 .8 525.53 0 .5453 643.1 545 .29 0 .5453 0 .7675 993 .3 529 .56 0 .5495 1030.7 549 .48 0 .5495

(con t inued)

378

TABLE 2b (continued)

hi E;~ i ( p m ) (W m -2

# m - l )

E0 -~-i (W m -2)

Fk i Eki ( W m - 2 p m -1)

E o - h i (W m -2)

FK i

0 .7800 1090.1 542 .58 0 .5630 1131.1 562 .99 0 .5630 0 .8000 1042 .4 563.91 0 .5851 1081 .6 585 .12 0 .5851 0 .8160 818 .4 578.79 0 .6006 849 .2 600 .56 0 .6006 0 .8237 756.5 584.86 0 .6069 785 .0 606 .85 0 .6069 0 .8315 883 .2 591.25 0 .6135 916 .4 613 .49 0 .6135 0 .8400 925.1 598.94 0 .6215 959 .9 621 .46 0 .6215 0 .8600 943 .4 617 .62 0 .6409 978 .9 640 .85 0 .6409 0 .8800 899 .4 636 .05 0 .6600 933 .2 659 .97 0 .6600 0 .9050 721 .4 656.31 0 .6810 748 .5 680 .99 0 .6810 0 .9150 643.3 663 .13 0 .6881 667 .5 688.07 0 .6881 0 .9250 665 .3 669 .68 0 .6949 690 .3 694 .86 0 .6949 0 .9300 389 .0 672 .31 0 .6976 403 .6 697 .60 0 .6976 0 .9370 248.9 674 .55 0 .6999 258.3 699.91 0 .6999 0 .9480 302.2 677 .58 0 .7031 313 .6 703 .06 0 .7031 0 .9650 507.7 684 .46 0 .7102 526.8 710 .20 0 .7102 0 .9800 623.0 692 .94 0 .7190 646.4 719 .00 0 .7190 0 .9935 719.7 702 .00 0 .7284 746 .8 728.41 0 .7284 1 .0400 665 .5 734 .21 0 .7618 690 .5 761 .82 0 .7618 1 .0700 614 .4 753 .41 0 .7817 637 .5 781 .74 0 .7817 1 .1000 397 .6 768 .59 0 .7975 412 .6 797 .49 0 .7975 1 .1200 105.0 773 .61 0 .8027 108.9 802.71 0 .8027 1 .1300 182.2 775 .05 0 .8042 189.1 804 .20 0 .8042 1 .1370 127 .4 776 .13 0 .8053 132.2 805 .32 0 .8053 1 .1610 326.7 781 .58 0 .8110 339.0 810 .98 0 .8110 1 .1800 443 .3 788 .90 0 .8186 460 .0 818 .57 0 .8186 1 .2000 408 .2 797.41 0 .8274 423 .6 82'7.40 0 .8274 1 .2350 463.1 812 .66 0 .8432 480 .5 843 .22 0 .8432 1 .2900 398.1 836 .34 0 .8678 413.1 867 .80 0 .8678 1 .3200 241.1 845 .93 0 .8777 250.2 877 .75 0 .8777 1 .3500 31.3 850 .02 0 .8820 32.5 881 .99 0 .8820 1 .3950 1.5 850 .76 0 .8828 1.6 882 .75 0 .8828 1 .4425 53.7 852 .07 0 .8841 55.7 884.11 0 .8841 1 .4625 101.3 853 .62 0 .8857 105.1 885 .72 0 .8857 1 .4770 101.7 855 .09 0 .8872 105.5 887 .25 0 .8872 1 .4970 175.5 857 .86 0 .8901 182.1 890 .12 0 .8901 1 .5200 253.1 862 .79 0 .8952 262.6 895 .24 0 .8952 1 .5390 264.3 867 .70 0 .9003 274.2 900 .34 0 .9003 1 .5580 265.0 872 .73 0 .9056 275.0 905 .56 0 .9056 1 .5780 235.7 877 .74 0 .9108 244.6 910 .75 0 .9108 1 .5920 238.4 881 .06 0 .9142 247.4 914 .19 0 .9142 1 .6100 220.4 885 .19 0 .9185 228.7 918 .48 0 .9185 1 .6300 235.6 889 .75 0 .9232 244.5 923.21 0 .9232 1 .6460 226.3 893 .44 0 .9270 234.8 927 .05 0 .9270 1 .6780 212.5 900 .46 0 .9343 220.5 934 .33 0 .9343 1 .7400 165.3 912 .18 0 .9465 171.5 946 .48 0 .9465 1 .8000 29.6 918 .02 0 .9525 30.7 952 .55 0 .9525 1 .8600 1.9 918.97 0 .9535 2.0 953 .53 0 .9535

TABLE 2b (continued)

379

t l I

~,i Eh i Eb - h i Fhi Eki Eo" ki Fhi ~ m ) (W m - 2 (W m - 2 ) (W m - 2 (W m - 2 )

pm-1) pm -1)

1.9200 1.2 919.06 0.9536 1.2 953.63 0.9536 1.9600 20.4 919.49 0.9541 21.2 954.07 0.9541 1.9850 87.8 920.85 0.9555 91.1 955.48 0.9555 2.0050 25.8 921.98 0.9567 26.8 956.66 0.9567 2.0350 95.9 923.81 0.9586 99.5 958.55 0.9586 2.0650 58.2 926.12 0.9609 60.4 960.95 0.9609 2.1000 85.9 928.64 0.9636 89.1 963.57 0.9636 2.1480 79.2 932.60 0.9677 82.2 967.68 0.9677 2.1980 68.9 936.30 0.9715 71.5 971.52 0.9715 2.2700 67.7 941.22 0.9766 70.2 976.62 0.9766 2.3600 59.8 946.96 0.9826 62.0 982.57 0.9826 2.4500 20.4 950.57 0.9863 21.2 986.32 0.9863 2.4940 17.8 951.41 0.9872 18.5 987.19 0.9872 2.5370 3.1 951,86 0.9877 3.2 987.66 0.9877 2.9410 4.2 953.33 0.9892 4.4 989.19 0.9892 2.9730 7.3 953.52 0.9894 7.6 989.38 0.9894 3.0050 6.3 953.73 0.9896 6.5 989.60 0.9896 3.0560 3.1 953.97 0,9899 3.2 989.85 0.9899 3.1320 5.2 954.29 0.9902 5.4 990.18 0.9902 3.1560 18.7 954.58 0.9905 19.4 990.48 0.9905 3.2040 1.3 955.06 0.9910 1.3 990.98 0.9910 3.2450 3.1 955.15 0.9911 3.2 991.07 0.9911 3.3170 12.6 955.71 0.9917 13.1 991.66 0.9917 3.3440 3.1 955.92 0.9919 3.2 991.88 0.9919 3.4500 12.8 956.77 0.9928 13.3 992.75 0.9928 3.5730 11.5 958.26 0.9943 11.9 994.30 0.9943 3.7650 9.4 960.27 0.9964 9.8 996.38 0.9964 4.0450 7.2 962.59 0.9988 7.5 998.79 0.9988 4.0450 963.75 1.0000 1000.00 1.0000

aFor definitions see Table 2a.

TABLE 2c

Global irradiance vs. wavelength spectrum for a sun-facing, 37 ° tilted surface (trapezoidal integration)a

h i Ehi E o . hi Fhi E~i E'~. hi F~i (pm) (Win -2) (Win -2) (Wm -2 (Win -2)

pm -1) pm -1)

0.3050 9.2 9.6 0.3100 40.8 0.13 0.0001 42.4 0.13 0.0001 0.3150 103.9 0.49 0.0005 107.9 0.51 0.0005 0.3200 174.4 1.18 0.0012 181.2 1.23 0.0012 0.3250 237.9 2.21 0.0023 247.2 2.30 0.0023 0.3300 381.0 3.76 0.0039 395.8 3.91 0.0039

(continued)

380

TABLE 2c ( c o n t i n u e d )

'~i E~. i E o -h i F ~ i E~. i E o - h i [ h i (gm) ( W m 2 (Wrn 2) ( W m 2 (Win :)

~m 1) pm--l)

0.3350 376.0 5.65 0.0059 390.6 5.87 0.0059 0.3400 419.5 7.64 0.0079 435.8 7.94 0.0079 0.3450 423.0 9.75 0.0101 439.5 10.13 0.0101 0.3500 466.2 11.97 0.0124 484.3 12.44 0.0124 0.3600 501.4 16.81 0.0175 520.9 17.46 0.0175 0.3700 642.1 22.53 0.0234 667.1 23.40 0.0234 0.3800 686.7 29.17 0.0303 713.4 30.3] 0.0303 0.3900 694.6 36.08 0.0375 721.6 37.48 0.0375 0.4000 976.4 44.43 0.0462 1014.4 46.16 0.0462 0.4100 1116.2 54.90 0.0570 1159.7 57.03 0.0570 0.4200 1141.1 66.18 0.0688 1185.5 68.76 0.0688 0.4300 1033.0 77.05 0.0801 1073.2 80.05 0.0801 0.4400 1254.8 88.49 0.0919 1303.6 91.94 0.0919 0.4500 1470.7 102.12 0.1061 1528.0 106.09 0.1061 0.4600 1541.6 117.18 0.1217 1601.6 121.74 0.1217 0.4700 1523.7 132.51 0.1377 1583.0 137.66 0.1377 0.4800 1569.3 147.97 0.1537 1630.4 153.73 0.1537 0.4900 1483.4 163.24 0.1696 1541.1 169.59 0.1696 0.5000 1492.6 178.12 0.1850 1550.7 185.05 0.1850 0.5100 1529.0 193.22 0.2007 1588.5 200.75 0.2007 0.5200 1431.1 208.02 0.2161 1486.8 216.12 0.2161 0.5300 1515.4 222.76 0.2314 1574.4 231.43 0.2314 0.5400 1494.5 237.81 0.2471 1552.7 247.06 0.2471 0.5500 1504.9 252.80 0.2626 1563.5 262.64 0.2626 0.5700 1447.1 282.32 0.2933 1503.4 293.31 0.2933 0.5900 1344.9 310.24 0.3223 1397.3 322.32 0.3223 0.6100 1431.5 338.01 0.3512 1487.2 351.16 0.3512 0.6300 1382.1 366.14 0.3804 1435.9 380.40 0.3804 0.6500 1368.4 393.65 0.4090 1421.7 408.97 0.4090 0.6700 1341.8 420.75 0.4371 1394.0 437.13 0.4371 0.6900 1089.0 445.06 0.4624 1131.4 462.38 0.4624 0.7100 1269.0 468.64 0.4869 1318.4 486.88 0.4869 0.7180 973.7 477.61 0.4962 1011.6 496.20 0.4962 0.7244 1005.4 483.94 0.5028 1044.5 502.78 0.5028 0.7400 1167.3 500.89 0.5204 1212.7 520.39 0.5204 0.7525 1150.6 515.38 0.5354 1195.4 535.44 0.5354 0.7575 1132.9 521.08 0.5414 1177.0 541.37 0.5414 0.7625 619.8 525.47 0.5459 643.9 545.92 0.5459 0.7675 993.3 529.50 0.5501 1032.0 550.11 0.5501 0.7800 1090.1 542.52 0.5636 1132.5 563.64 0.5636 0.8000 1042.4 563.84 0.5858 1083.0 585.80 0.5858 0.8160 818.4 578.73 0.6013 850.3 601.26 0.6013 0.8237 756.5 584.79 0.6076 786.0 607.56 0.6076 0.8315 883.2 591.19 0.6142 917.6 614.20 0.6142 0.8400 925.1 598.87 0.6222 961.1 622.19 0.6222 0.8600 943.4 617.56 0.6416 980.1 641.60 0.6416 0.8800 899.4 635.99 0.6607 934.4 660.75 0.6607

TABLE 2c (continued)

~,i Ek i (pm) (Wm -2

~m -1)

Eo-~. i (Wm -2)

Fk i t

Ek i (W m -2 pm -1)

Eo-~, i (Wm -2)

0.9050 721.4 656.25 0.6818 749.5 681.80 0.9150 643.3 663.07 0.6889 668.3 688.88 0.9250 665.3 669.61 0.6957 691.2 695.68 0.9300 389.0 672.25 0.6984 404.1 698.42 0.9370 248.9 674.48 0.7007 258.6 700.74 0.9480 302.2 677.51 0.7039 314.0 703.89 0.9650 507.7 684.40 0.7110 527.5 711.04 0.9800 623.0 692.88 0.7199 647.3 719.85 0.9935 719.7 701.94 0.7293 747.7 729.27 1.0400 665.5 734.15 0.7627 691.4 762.73 1.0700 614.4 753.35 0.7827 638.3 782.67 1.1000 397.6 768.53 0.7984 413.1 798.44 1.1200 105.0 773.55 0.8037 109.1 803.67 1.1300 182.2 774.99 0.8052 189.3 805.16 1.1370 127.4 776.07 0.8063 132.4 806.28 1.1610 326.7 781.52 0.8119 339.4 811.94 1.1800 443.3 788.84 0.8195 460.6 819.54 1.2000 408.2 797.35 0.8284 424.1 828.39 1.2350 463.1 812.60 0.8442 481.1 844.23 1.2900 398.1 836.28 0.8688 413.6 868.84 1.3200 241.1 845.87 0.8788 250.5 878.80 1.3500 31.3 849.96 0.8830 32.5 883.04 1.3950 1.5 850.69 0.8838 1.6 883.81 1.4425 53.7 852.00 0.8852 55.8 885.17 1.4625 101.3 853.55 0.8868 105.2 886.78 1.4770 101.7 855.03 0.8883 105.7 888.31 1.4970 175.5 857.80 0.8912 182.3 891.19 1.5200 253.1 862.73 0.8963 263.0 896.31 1.5390 264.3 867.64 0.9014 274.6 901.42 1.5580 265.0 872.67 0.9066 275.3 906.64 1.5780 235.7 877.68 0.9118 244.9 911.85 1.5920 238.4 881.00 0.9153 247.7 915.29 1.6100 220.4 885.13 0.9196 229.0 919.58 1.6300 235.6 889.69 0.9243 244.8 924.32 1.6460 226.3 893.38 0.9282 235.1 928.16 1.6780 212.5 900.40 0.9355 220.8 935.45 1.7400 165.3 912.11 0.9476 171.7 947.62 1.8000 29.6 917.96 0.9537 30.8 953.70 1.8600 1.9 918.91 0.9547 2.0 954.68 1.9200 1.2 919.00 0.9548 1.2 954.77 1.9600 20.4 919.43 0.9552 21.2 955.22 1.9850 87.8 920.78 0.9566 91.2 956.63 2.0050 25.8 921.92 0.9578 26.8 957.81 2.0350 95.9 923.74 0.9597 99.6 959.71 2.0650 58.2 926.06 0.9621 60.5 962.11 2.1000 85.9 928.58 0.9647 89.2 964.73 2.1480 79.2 932.54 0.9688 82.3 968.84

381

Fk i

0.6818 0.6889 0.6957 0.6984 0.7007 0.7039 0.7110 0.7199 0.7293 0.7627 0.7827 0.7984 0.8037 0.8052 0.8063 0.8119 0.8195 0.8284 0.8442 0.8688 0.8788 0.8830 0.8838 0.8852 0.8868 0.8883 0.8912 0.8963 0.9014 0.9066 0.9118 0.9153 0.9196 0.9243 0.9282 0.9355 0.9476 0.9537 0.9547 0.9548 0.9552 0.9566 0.9578 0.9597 0.9621 0.9647 0.9688

(conHnued)

382

TABLE 2c (continued)

hi EX i Eo- X i FX i E~ i Eo- h i F~ i (pm) (Wm 2 (Wm 2) (Win 2 (Win 2)

pm 1) pm 1)

2.1980 68.9 936.24 0.9727 71.6 972.69 0.9727 2.2700 67.7 941.16 0.9778 70.3 977.80 0.9778 2.3600 59.8 946.90 0.9838 62.1 983.76 0.9838 2.4500 20.4 950.51 0.9875 21.2 987.51 0.9875 2.4940 17.8 951.35 0.9884 18.5 988.38 0.9884 2.5370 3.1 951.80 0.9888 3.2 988.85 0.9888 2.9410 4.2 953.27 0.9904 4.4 990.38 0.9904 2.9730 7.3 953.45 0.9906 7.6 990.57 0.9906 3.0050 6.3 953.67 0.9908 6.5 990.80 0.9908 3.0560 3.1 953.91 0.9910 3.2 991.05 0.9910 3.1320 5.2 954.23 0.9914 5.4 991.38 0.9914 3.1560 18.7 954.51 0.9917 19.4 991.67 0.9917 3.2040 1.3 954.99 0.9922 1.4 992.17 0.9922 3.2450 3.1 955.08 0.9923 3.2 992.27 0.9923 3.3170 12.6 955.65 0.9929 13.1 992.85 0.9929 3.3440 3.1 955.86 0.9931 3.2 993.07 0.9931 3.4500 ] 2.8 956.70 0.9939 13.3 993.95 0.9939 3.5730 11.5 958.20 0.9955 11.9 995.50 0.9955 3.7650 9.4 960.21 0.9976 9.8 997.59 0.9976 4,0450 7.2 962.53 1.0000 7.5 1000.00 1.0000

aFor definitions see Table 2a.

1600 /,4,,,

E1200

~_~ 800- o ~

400

0 08 11 19 27

Wavelength (,urn)

Fig. 4. ( - - - - - - ) , AM 1.5 direct normal spectrum normalized to 1000 W m -2 by using a constant multiplier across all wavelengths. However, a change in atmospheric conditions, such as turbidity, is required to obtain an outdoor AM 1.5 direct normal spectrum with an integrated irradiance approaching 1000 W m 2 ( ) . A spectral shift is associated with the change in turbidity that is not reflected in the spectrum obtained by normalizing with a constant multiplier.

We do n o t r e c o m m e n d n o r m a l i z a t i o n o f t h e d i r e c t n o r m a l s p e c t r u m

(Fig. 4) t o 1 0 0 0 W m 2 b e c a u s e s i g n i f i c a n t s p e c t r a l d i s t o r t i o n w o u l d resu l t .

T h e r e s u l t a n t A M 1.5 d i r e c t n o r m a l s p e c t r u m (hav ing t h e s p e c i f i e d w a t e r

v a p o r a n d t u r b i d i t y va lues ) w o u l d n o t r e p r e s e n t n a t u r e [ 2 3 ] . P h o t o n f l u x d e n s i t y va lues c o r r e s p o n d i n g t o t h e A M 1.5 s p e c t r a l irra-

d i a n c e d a t a sets a re g iven in Tab les 3 a n d 4 a n d p l o t t e d in Figs. 5 a n d 6.

383

T A B L E 3

Direct no rma l p h o t o n f lux dens i ty vs. wavelength X and p h o t o n energy (eV) s p e c t r u m

~, a Ephoto n b E~ c Nph (~k) d Nph ( e v ) e (~tm) (eV) ( W m -2 p m -1) (1016 cm -2 (1016 cm -2

s - I p m - 1 ) s-1 e V - 1 )

0 .3050 4 .0651 3.4 0 .052 0 .004 0 .3100 3 .9995 15.6 0 .243 0 .019 0 .3150 3 .9360 41.1 0 .652 0 .052 0 .3200 3 .8745 71.2 1 .147 0 .095 0 .3250 3 .8149 100.2 1 .639 0 .140 0 .3300 3 .7571 152.4 2 .532 0 .222 0 .3350 3 .7011 155.6 2 .624 0 .238 0 .3400 3 .6466 179.4 3.071 0 .286 0 .3450 3 .5938 186.7 3 .243 0 .311 0 .3500 3 .5424 212.0 3 .735 0 .369 0 .3600 3 .4440 240.5 4 .359 0 .456 0 .3700 3 .3510 324.0 6 .035 0 .666 0 .3800 3 .2628 362.4 6 .933 0 .807 0 .3900 3 .1791 381.7 7 .494 0 .919 0 .4000 3 .0996 556.0 11 .196 1 .445 0 .4100 3 .0240 656.3 13 .546 1 .837 0 .4200 2 .9520 690.8 14 .606 2 .078 0 .4300 2 .8834 641.9 13 .895 2 .072 0 .4400 2 .8178 798.5 17 .687 2 .762 0 .4500 2 .7552 956 .6 21 .670 3 .539 0 .4600 2 .6953 990 .8 22 .944 3 .916 0 . 4 7 0 0 2 .6380 998.0 23 .613 4 .207 0 .4800 2 .5830 1046.1 25 .277 4 .697 0 .4900 2 .5303 1005.1 24 .793 4 .801 0 .5000 2 .4797 1026.7 25 .842 5.211 0 .5100 2 .4311 1066.7 27 .386 5 .745 0 .5200 2 .3843 1011.5 26 .478 5 .775 0 .5300 2 .3393 1084 .9 28 .946 6 .558 0 ,5400 2 .2960 1082 .4 29 .424 6 .920 0 .5500 2 .2543 1102 .2 30 .517 7 .446 0 .5700 2 .1752 1087.4 31 .202 8 .176 0 .5900 2 .1014 1 0 2 4 3 30 .423 8.541 0 .6100 2 .0325 1088 .8 33 .434 10 .034 0 .6300 1 .9680 1062.1 33 .684 10 .783 0 .6500 1 .9075 1061.7 34 .740 11 .838 0 .6700 1 .8505 1046 .2 35 .286 12 .776 0 .6900 1 .7969 859.2 29 .844 11 .460 0 .7100 1 .7463 1002 .4 35 .827 14 .567 0 .7180 1 .7268 816.9 29 .526 12 .277 0 .7244 1 .7116 842 .8 30 .734 13 .008 0 .7400 1 .6755 971.0 36 .172 15 .976 0 .7525 1 .6476 956.3 36 .226 16 .545 0 .7575 1 .6368 942 .2 35 .929 16 .628 0 .7626 1 .6260 524.8 20 .144 9 .446 0 . 7 6 7 5 1 .6154 830.7 32 .095 15 .248 0 .7800 1 .5896 908 .9 35 .688 17 .512

(continued)

384

TABLE 3 (continued)

)- Ephoton EX (pm) (eV) (W m 2 g m 1)

Nph()~) (1016 cm z s 1 p m - l )

Nph(eV) (1016 cm s 1 e V - 1 )

0 .8000 1 .5498 873.4 35 .174 18 .156 0 .8160 1 .5194 712.0 29 .247 15 .707 0 .8237 1 .5052 660 .2 27 .375 14.981 0 .8315 1 .4911 765 .5 32 .042 17 .868 0 .8400 1 .4760 799.8 33 .820 19 .247 0 .8600 1 .4417 815.2 35 .292 21 .053 0 .8800 1 .4089 778.3 34 .478 21 .535 0 .9050 1 .3700 630.4 28 .720 18 .972 0 .9150 1 .3550 565.2 26 .034 17 .580 0 .9250 1 .3404 586.4 27 .306 18 .844 0 .9300 1 .3332 348.1 16.297 11 .368 0 .9370 1 .3232 224.2 10 .575 7 .489 0 .9480 1 .3079 271.4 12 .952 9 .388 0 .9650 1 .2848 451 .2 21 .919 16 .463 0 .9800 1 .2652 549.7 27 .119 21 .006 0 .9935 1 .2480 630.1 31 .513 25 .088 1 .0400 1 .1922 582.9 30 .517 26 .622 1 .0700 1 .1587 539.7 29 .071 26 .844 1 .1000 1 .1271 366.2 20 .278 19 .790 1 .1200 1 .1070 98.1 5.531 5 .596 1 .1300 1 .0972 169.5 9 .642 9 .930 1 .1370 1 .0905 118.7 6 .794 7 .084 1 .1610 1 .0679 301.9 17 .645 19 .183 1 .1800 1 .0507 406 .8 24 .165 27 .138 1 .2000 1 .0332 375.2 22 .665 26 .324 1 .2350 1 .0039 423 .6 26 .335 32.397 1 .2900 0 .9611 365.7 23 .748 31 .874 1 .3200 0 .9393 223.4 14 .845 20 .862 1 .3500 0 .9184 30.1 2 .046 3 .007 1 .3950 0 .8888 1.4 0 .098 0 .154 1 .4425 0 .8595 51.6 3 .747 6 .289 1 .4625 0 .8478 97.0 7 .141 12 .320 1 .4770 0 .8394 97.3 7 .235 12 .729 1 .4970 0 .8282 167.1 12 .593 22.761 1 .5200 0 .8157 239.3 18.311 34.121 1 .5390 0 .8056 248 .8 19 .275 36 .822 1 .5580 0 .7958 249.3 19 .553 38 .280 1 .5780 0 .7857 222.3 17 .659 35 .466 1 .5920 0 .7788 227.3 18 .216 37 .237 1 .6100 0 .7701 210.5 17 .061 35 .668 1 .6300 0 .7606 224.7 18 .438 39 .510 1 .6460 0 .7533 215.9 17 .890 39 .092 1 .6780 0 .7389 202.8 17.131 38 .904 1 .7400 0 .7126 158.2 13 .857 33 .838 1 .8000 0 .6888 28.6 2 .592 6 .772 1 .8600 0 .6666 1.8 0 .169 0 .470 1 .9200 0 .6458 1.1 0 .106 0 .316

TABLE 3 (continued)

385

Ephoton Ek Nph(k) (pm) (eV) (Wm -2 pm -1) (101~ cm -2

s-1 p m - l )

Nph(eV) (1016 cm-2 s-1 eV-1)

1.9600 0.6326 19.7 1.944 6.023 1.9850 0.6246 84.9 8.484 26.961 2.0050 0.6184 25.0 2.523 8.181 2.0350 0.6093 92.5 9.476 31.651 2.0650 0.6004 56.3 5.853 20.129 2.1000 0.5904 82.7 8.743 31.096 2.1480 0.5772 76.2 8.240 30.662 2.1980 0.5641 66.4 7.347 28.628 2.2700 0.5462 65.0 7.428 30.870 2.3600 0.5254 57.6 6.843 30.740 2.4500 0.5061 19.8 2.442 11.823 2.4940 0.4971 17.0 2.134 10.707 2.5370 0.4887 3.0 0.383 1.989 2.9410 0.4216 4.0 0.592 4.131 2.9730 0.4170 7.0 1.048 7.468 3.0050 0.4126 6.0 0.908 6.611 3.0560 0.4057 3.0 0.462 3.476 3.1320 0.3959 5.0 0.788 6.237 3.1560 0.3929 18.0 2.860 22.974 3.2040 0.3870 1.2 0.194 1.603 3.2450 0.3821 3.0 0.490 4.162 3.3170 0.3738 12.0 2.004 17.781 3.3440 0.3708 3.0 0.505 4.555 3.4500 0.3594 12.2 2.119 20.341 3.5730 0.3470 11.0 1.979 20.372 3.7650 0.3293 9.0 1.706 19.502 4.0450 0.3065 6.9 1.405 18.542

ak, wavelength. bEphoton , energy of a photon at wavelength k. CEk, irradiance at wavelength ~,. dNph(~,), photon flux density per wavelength interval (pm) at wavelength k. eNph(eV), photon flux density per photon energy iriterval (eV) at wavelength k.

Methods used to convert the spectral irradiance data to photon flux density in either wavelength or energy intervals are given in Appendix B. The representation of the spectral data in units of pho ton flux density is useful for applications such as calculating the theoretical number of photons that can be collected as a function of photovoltaic material bandgaps.

6. Future work

SERI is currently collecting high-resolution spectral irradiance measure- ments to validate the modeled AM 1.5 spectral irradiance data sets and to further s tudy the variation in AM 1.5 spectral irradiance (under cloudless

386

T A B L E 4

Global p h o t o n flux dens i ty v s . wavelength ~ and p h o t o n energy E spec t rum a

Ephoton E~, Nph(~, ) (/~m) (eV) (W m 2 p m 1) (1016 em :

s l p m 1)

Nph(eV) (1016 cm s - l e V 1)

0 .3050 4 .0651 9.2 0 .141 0.011 0 .3100 3 .9995 40 .8 0 ,637 0 .049 0 .3150 3 .9360 103.9 1 .648 0 .132 0 .3200 3 .8745 174.4 2 ,809 0 .232 0 .3250 3 .8149 237.9 3 .892 0 .332 0 .3300 3 .7571 381.0 6 .329 0 .556 0 .3350 3 .7011 376.0 6 .341 0 .574 0 .3400 3 .6466 419 .5 7 .180 0 .669 0 .3450 3 .5938 423.0 7 .346 0 .705 0 .3500 3 .5424 466 .2 8 .214 0 .812 0 .3600 3 .4440 501.4 9 .087 0 .950 0 .3700 3 .3510 642.1 11 .960 1.321 0 .3800 3 .2628 686.7 13 .136 1 .530 0 .3900 3 .1791 694.6 13 .637 1 .673 0 .4000 3 .0996 976 .4 19.661 2 .537 0 .4100 3 .0240 1116 .2 23 .038 3 .124 0 .4200 2 .9520 1141.1 24 .126 3 .433 0 .4300 2 .8834 1033.0 22 .361 3 .335 0 .4400 2 .8178 1254 .8 27 .794 4 .340 0 .4500 2 .7552 1470.7 33 ,316 5.441 0 .4600 2 .6953 1541 .6 35 .698 6 .092 0 .4700 2 .6380 1523.7 36 .051 6 .423 0 .4800 2 .5830 1569.3 37 .920 7 .047 0 .4900 2 .5303 1483 .4 36 .591 7 .086 0 .5000 2 .4797 1492 .6 37 .569 7 .575 0 .5100 2 .4311 1529 .0 39 .255 8 .235 0 .5200 2 .3843 1431.1 37 .462 8 .170 0 .5300 2 .3393 1515 .4 40 .431 9 .160 0 .5400 2 .2960 1494 .5 40 .626 9 .555 0 .5500 2 .2543 1504 .9 41 .666 10 .166 0 .5700 2 .1752 1447.1 41 ,523 10 .881 0 .5900 2 .1014 1344 .9 39 .945 11 .215 0 .6100 2 .0325 1431 .5 43 .958 13 ,193 0 .6300 1 .9680 1382.1 43 .833 14 .032 0 .6500 1 .9075 1368 .4 44 .776 15 .258 0 .6700 1 .8505 1341 .8 45 .256 16 .385 0 .6900 1 .7969 1089 .0 37 .826 14 .525 0 .7100 1 .7463 1269 .0 45 ,356 18 .441 0 .7180 1 .7268 973.7 35 .194 14 .633 0 .7244 1 .7116 1005 .4 36 .663 15 .517 0 .7400 1 .6755 1167 .3 43 .484 19 .205 0 .7525 1 .6476 1150 .6 4 3 . 5 8 6 19 ,906 0 .7575 1 .6368 1132.9 43 .201 19 .993 0 .7625 1 .6260 619.8 23 .791 11 .156 0 .7675 1 .6154 993 .3 38 .377 18 .233 0 .7800 1 .5896 1090.1 42 .803 21 .004

T A B L E 4 (continued)

~. Ephoton Eh. (pro) (eV) (W m -2 p m -1 )

Nph(~') _ (1016 cm-~ s-1 p m - 1 )

Nph(eV) (I0 I~ cm-: s - I e V - 1 )

387

0 .8000 1 .5498 1042 .4 41 .980 21 .670 0 .8160 1 .5194 818.4 33 .618 18 .054 0 .8237 1 .5052 756 .5 31 .369 17 .166 0 .8315 1 .4911 883.2 36 .969 20 .615 0 .8400 1 .4760 925.1 39 .119 22 .262 0 .8600 1 .4417 943 .4 40 .842 24 .363 0 .8800 1 .4089 899 .4 39 .843 24 .886 0 .9050 1 .3700 721 .4 32 .866 21 .710 0 .9150 1 .3550 643.3 29.631 20 .009 0 .9250 1 .3404 665.3 30 .980 21 .379 0 .9300 1 .3332 389.0 18 .212 12 .704 0 .9370 1 .3232 248.9 11 .740 8 .314 0 .9480 1 .3079 302.2 14 .422 10 .454 0 .9650 1 .2848 507.7 24 .663 18 .524 0 .9800 1 .2652 623.0 30 .735 23 .807 0 .9935 1 .2480 719.7 35 .994 28 .655 1 .0400 1 .1922 665.5 34 .842 30 .394 1 .0700 1 .1587 614.4 33 .094 30 .560 1 .1000 1 .1271 397.6 22 .017 21 .487 1 .1200 1 .1070 105.0 5 .920 5 .990 1 .1300 1 .0972 182.2 10 .364 10 .674 1 .1370 1 .0905 127.4 7 .292 7 .603 1 .1610 1 .0679 326.7 19 .094 20 .758 1 .1800 1 .0507 443 .3 2 6 . 3 3 3 29 .573 1 .2000 1 .0332 408 .2 24 .659 28 .639 1 .2350 1 .0039 463.1 28.791 35 .418 1 .2900 0 .9611 398.1 25 .852 34 .698 1 .3200 0 .9393 241.1 16 .021 22 .515 1 .3500 0 .9184 31.3 2 .127 3 .127 1 .3950 0 .8888 1.5 0 .105 0 .165 1 .4425 0 .8595 53.7 3 .900 6 .544 1 .4625 0 .8478 101.3 7 .458 12 .866 1 .4770 0 .8394 101.7 7 .562 13 .305 1 .4970 0 .8282 175.5 13 .226 23 .905 1 .5200 0 .8157 253.1 19 .367 36 .089 1 .5390 0 .8056 264.3 20 .476 39 .116 1 .5580 0 . 7 9 5 8 265.0 20 .784 40 .691 1 .5780 0 .7857 235.7 18 .723 37 .603 1 .5920 0 .7788 238.4 19 .106 39 .055 1 .6100 0 .7701 220.4 17 .863 37 .345 1 .6300 0 . 7 6 0 6 235 .6 19 .332 41 .427 1 .6460 0 .7533 226.3 18.751 40 .975 1 .6780 0 . 7 3 8 9 212.5 17 .950 40 .764 1 .7400 0 .7126 165.3 14 .479 35 .356 1 .8000 0 .6888 29.6 2 .682 7 .009 1 .8600 0 .6666 1.9 0 .178 0 .496 1 .9200 0 . 6 4 5 8 1.2 0 .116 0 .345 1 .9600 0 . 6 3 2 6 20.4 2 .013 6 .237

388

T A B L E 4 ( c o n t i n u e d )

Ephoton EX (pro) (eV) (W m- 2 pm-- l)

Nph(~) Nph(eV) (1016 cm -2 (1016 cm : s l p m - : ) s l e V 1)

1 .9850 0 .6246 87.8 8 .774 27 .882 2 .0050 0 .6184 25.8 2 .604 8 .443 2 .0350 0 .6093 95.9 9 .824 32 .814 2 .0650 0 .6004 58.2 6 .050 20 .808 2 .1000 0 .5904 85.9 9 .081 32 .300 2 .1480 0 .5772 79.2 8 .564 31 .869 2 .1980 0 .5641 68.9 7 .624 29 .706 2 .2700 0 .5462 67.7 7 .736 32 .152 2 .3600 0 .5254 59.8 7 .104 31 .914 2 .4500 0 .5061 20.4 2 .516 12.181 2 .4940 0 .4971 17.8 2 .235 11 .211 2 .5370 0 .4887 3.1 0 .396 2 .055 2 .9410 0 .4216 4.2 0 .622 4 .338 2 .9730 0 .4170 7.3 1 .093 7 .789 3 .0050 0 .4126 6.3 0 .953 6.941 3 .0560 0 .4057 3.1 0 .477 3 .592 3 .1320 0 .3959 5.2 0 .820 6 .487 3 .1560 0 .3929 18.7 2.971 23 .867 3 .2040 0 .3870 1.3 0 .210 1 .736 3 .2450 0 .3821 3.1 0 .506 4.301 3 .3170 0 . 3 7 3 8 12.6 2 .104 18 .670 3 .3440 0 .3708 3.1 0 .522 4 .707 3 .4500 0 .3594 12.8 2.223 21 .341 3 .5730 0 .3470 11.5 2 .069 21 .298 3 .7650 0 .3293 9.4 1 .782 20 .369 4 .0450 0 .3065 7.2 1 .466 19 .348

aFor def in i t ions see Table 3.

Air Mass q .~

i ~ [' 41.~, ~ G l o b a l , 37 ° Tilt, ~E 40- 4°4 J / N A,rMass s 4 ~ ~ [ ' ~ . j j - - D i r e c t Normal, Air Mass15

~j ~ 30-

>, ~

~ ~o .g ~ 20

,=- ~_

g g ~5 0 . . . . ~5 0 ~: 0.2 1.0 1.8 26 34 42 Q_

Wavelength (,um)

~ A i r Mass 0

s GIobal, 37 ° T i l t

Air Mass 1 5 / ~ Direct Normal

03 0.9 15 2.t 27 33 39 45 Photon Energy (eV}

Fig. 5. P h o t o n f lux dens i ty vs. wavelength k (Tables 3 and 4) for th ree categories of solar i r radiance.

Fig. 6. P h o t o n flux dens i ty vs. p h o t o n energy E (Tables 3 and 4) for t h r ee categories of solar i r radiance.

389

sky conditions) that is due to different turbidities and water vapor amounts. Initial limited comparisons of modeled and measured data, shown in ref. 3, were favorable. Spectral solar irradiance data are also being used to validate a simple spectral irradiance model for cloudless skies developed by SERI [24] and to develop a cloud-cover modifier for the simple model.

Both the measured and the modeled spectral irradiance data will be used to study the performance of photovoltaic devices for particular loca- tions and a range of atmospheric conditions and air mass values. The long- range goal is to provide representative outdoor spectral h'radiance data sets that can be used to predict the hourly, daily, monthly and annual energy produced by any particular photovoltaic device at specific locations and atmospheric conditions.

References

i Standard terrestrial direct normal solar spectral irradiance tables for air mass 1.5, ASTM Stand. E891-82, 1982 (American Society for Testing of Materials, Philadel- phia, PA).

2 Standard for solar spectral irradiance tables at air mass 1.5 for a 37 ° tilted surface, ASTM Stand. E892-82, 1982 (American Society for Testing of Materials, Philadel- phia, PA).

3 R. E. Bird, R. L. Hulstrom and L. J. Lewis, Terrestrial solar spectral data sets, Sol. Energy, 30 (6) (1983) 563.

4 Terrestrial photovoltaic measurement procedures, ERDA/NASA/1022-77/16, NASA Tech. Memo. 73702, 1977 (National Aeronautics and Space Administration, Cleve- land, OH).

5 R. Matson, R. Bird and K. Emery, Terrestrial solar spectra, solar simulation and solar cell efficiency measurement, SERI Tech. Rep. 612-964, 1981, (Solar Energy Research Institute, Golden, CO).

6 ERDA/NASA Terrestrial Photovoltaic Workshop, NASA Lewis Research Center, Cleveland, OH, March, 1975.

7 H. Brandhorst, J. Hickey, H. Curtis and E. Ralph, Interim solar cell testing procedures for terrestrial applications, NASA Tech. Memo. X-71771, 1975 (National Aeronautics and Space Administration, Cleveland, OH).

8 M. P. Thekaekara, Survey of quantitative data on solar energy and its spectral dis- tribution, Cooperation M4diterran~enne Sous L'Energie Solaire, Conference, Dahran, Saudi Arabia, 1975.

9 M. P. Thekaekara, Extraterrestrial solar spectrum, 3000 - 6100 ~ at 1-~ intervals, Appl. Opt., 13 (3) (1974) 518.

10 Solar electromagnetic radiation, NASA Spec. Publ. 8005, 1971 (National Aeronautics and Space Administration, Cleveland, OH).

11 Standard solar constant and air mass zero solar spectral irradiance tables, ASTM Stand. E490-73a, reapproved 1981 ; Annual Book of ASTM Standards, 1982, Part 41 ; Annual Book of ASTM Standards, 1974, Part 41, pp. 609 - 615 (American Society for Testing of Materials, Philadelphia, PA).

12 ERDA/NASA Terrestrial Photovoltaic Measurements -- II Workshop, Baton Rouge, LA, November, 1976.

13 H. B. Curtis, The effect of atmospheric parameters on silicon cell performance, paper presented at ERDA/NASA Terrestrial Photovoltaic M e a s u r e m e n t s - II Workshop, Baton Rouge, LA, November, 1976.

390

14 P. J. Ireland, S. Wagner, L. L. Kazmerski and R. L. Hulstrom, A combined irradiance transmittance solar spectrum and its application to photovoltaic efficiency calcula- tions, Science, 204 (1979) 611.

15 D. Labs and H. Neckel, Transformation of the absolute solar radiation data into the international practical temperature scale of 1968, Sol. Phys., 15 (1970) 79 - 87.

16 R. E. Bird, Terrestrial solar spectral modeling, Sol. Cells, 7 (1983) 107. 17 R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz and J. S. Garing, Optical

properties of the atmosphere, 3rd Edn., Air Force Publ. AFCRL-72-0497, 1972, (Air Force Cambridge Research Laboratories, Bedford, MA).

18 E. P. Shettle and R. W. Fenn, Models of the atmospheric aerosol and their optical properties, Proc. AGARD Conf. 183: Optical propagation in the atmosphere (Elec- tromagnetic Wave Propagation Panel Symposium, Lyngby, l~enmark), 1975, pp. 2.1 - 2.16.

19 L. Elterman, UV visible and IR attenuation for altitudes to 50 km, Air Force Publ. AFCRL-68-0153, 1968 (Air Force Cambridge Research Laboratories, Bedford, MA).

20 Provided by C. D. FrShlich and C. Wehrli, World Radiation Centre, Davos, Switzer- land. Spectrum revised and extended by the work of H. Neckel and D. Labs, Improved data of solar spectral irradiance from 0.33 /~m to 1.25 pm, Sol. Phys., 74 (1) (1981) 231 - 249.

21 R. Ross, Photovoltaic electrical performance specification considerations, paper presented at the American Society for Testing and Materials Meeting, Lake Tahoe, NV, 1979.

22 C. C. Gonzalez and R. G. Ross, Performance measurement reference conditions for terrestrial photovoltaics, paper presented at the American Section of the International Solar Energy Society Annual Conference, Phoenix, AZ, 1980.

23 R. Bird, R. Hulstrom and C. Riordan, Normalization of direct beam spectral irra- diance data for photovoltaic cell performance analyses, Sol. Cells, 14 (1985)193 - 195.

24 R. Bird and C. Riordan, Simple solar spectral model for direct and diffuse irradiance on horizontal and tilted planes at the earth's surface for cloudless atmospheres, SERI Tech. Rep. 215-2436, 1984 (Solar Energy Research Institute, Golden, CO).

A p p e n d i x A: i n t e g r a t i o n t e c h n i q u e s

a. Rec tangular rule integration (see Tables l (a ) and 2(a)) At e n d p o i n t s

f irst A X l = ~ 2 - - h l

last AXN = ~k N - - ~ ' N - 1

where N is t h e n u m b e r o f w a v e l e n g t h s .

At o t h e r w a v e l e n g t h s

ki+ I - - ~'i I &hi -

2

M u l t i p l y AXi b y Ea~ to o b t a i n t h e i r r a d i a n e e in t he i n t e r v a l AXe.

b. Trapezoidal integrat ion (see Tables l (e ) and 2(c)) I r r a d i a n c e in t h e i n t e r v a l Aki ( for i = 1 to (N - - 1)) is

1 ( ~ i + 1 - - h i ) 2

391

c. Modified trapezoidal integration (see Tables l (b ) and 2(b ) and appendices of refs. 1 and 2)

Same as shown under point b for trapezoidal integration, except at endpoints

first 1 / 2 ( Ex2 + E h l ) ( ~ 2 - kl) 2 ,

last 1/2(EhN2EhN-I:)(kN--kN_I) Appendix B: conversion of spectral irradiance to photon flux density per wavelength k and per photon energy eV interval

Spectral irradiance may be converted to spectral photon flux density by the expression

Nph(k) = E(k) h--c

where Nph(k) = the number of photons per wavelength k interval, E ( k ) = spectral irradiance, h = Planck's constant = 6.626 176 × 10 -34 J s and c = speed of light = 2.997 924 58 X 1014 pm s -1.

Assuming (1 )E(k) is in units of W m -2 gm -1, (2) k is in units of pm and (3) the desired units for Nph(k) are Nph cm -2 s -1 ~m -1 , the conversion is

Nph(k) = 5.034 × 1014E(k) k

The conversion of spectral photon flux density per wavelength interval to photon flux per photon energy eV interval is given by

k Nph(eV) = Nph(}k)

Ephoton where Nph(eV) = photon flux density per energy interval (eV) in units of Nph cm -2 s -1 eV -1, Nph(k) = photon flux density per wavelength interval (pm) in units of Nph cm -2 s -1 pm -1, k = wavelength (#m), Ephoton = photon energy (eV) at wavelength ~(pm) = (hc/X)/(1 eV) and 1 eV = 1.602 189 2 × 10 -19 J.