Spectral solar irradiance data sets for selected terrestrial conditions

Solar Cells, 15 (1985) 365 - 391

365

SPECTRAL S O L A R I R R A D I A N C E DATA SETS F O R SELECTED T E R R E S T R I A L 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 presented for selected terrestrial conditions, along with a brief review of previous 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, p h o t o n flux density v e r s u s wavelength, and p h o t o n flux density v e r s u s p h o t o n energy.

1. Introduction Terrestrial solar spectral data are useful for the development and design of photovoltaic devices (cells, submodules, modules) and systems for terrestrial 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 o u t d o o r solar spectral distributions vary with atmospheric conditions and sun angle, the photovoltaic community often selects a representative spectral solar irradiance distribution so that solar cells can be compared on a c o m m o n 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 generated 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 ° from 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 c o m m o n l y 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 wavelengthdependent 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 (circumsolar radiation) was modeled and added to the direct beam values. The circumsolar c o m p o n e n t was approximated by assuming that it is equal to 50% of the radiation scattered out of the direct beam by aerosols. A comparison 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 overestimates 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 "~-

0.2

- - r - - - -f

0.6

]

T--] ~ ~ - - - - 7 - - ~ 1.0 1.4 1.8 2.2 Wavelength (,um)

2.6

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 parameters 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 a m o u n t and molecular absorber amount. The Monte Carlo m e t h o d 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 precipitable 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 calculations. 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 addition, 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. Comparisons 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. G e o m e t r y 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 Laboratory [21, 22], which shows that approximately 50% of the annual energy o u t p u t 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 ° tilted 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 p h o t o n 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 e x t e n d e d from the previous wavelength c u t o f f of 2.45 pm to 4.045 pm. This was done to a c c o u n t 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 between 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 o f 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 t he 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 generate new values for the relatively insignificant 2.45 to 4.045 #m region. 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 sets a r e 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 r e s h o w n in F i g . 2. The new integrals were calculated using three different integration techn 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

10

2100. ~l~ ~ A i r 1800 -~'E1500 1200

I ' V

I ~

Mass 0

08-I_

~

~ ~ ~

" ~ G l ° b a l ' 37° Tilt' Air Mass 1 5

;

"

.~_ 0.6-

, Air Mass 15

~

900

-

"~ 0.4-

6000.2300002

1.0

1.8 2.6 Wavelength (pm)

3.4

4.2

00.2

Fig. 2. Plots of three categories of spectral irradiance

vs.

1.0

1.8 2.6 Wavelength (pm)

3.4

42

wavelength.

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

TABLE l a Direct normal irradiance

~kia (pm)

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

vs.

wavelength spectrum (rectangular rule integration)

E~,ib (W m -2 pm -1 )

Eo .2kic (W m -2)

3.4 15.6 41.1 71.2 100.2 152.4 155.6 179.4 186.7 212.0 240.5 324.0 362.4 381.7 556.0 656.3 690.8

0.02 0.10 0.30 0.66 1.16 1.92 2.70 3.59 4.53 6.12 8.52 11.76 15.39 19.20 24.76 31.33 38.24

F;kid

~i a (pro)

Ehib (W m -2 pm -1)

Eo .ki c (W m - 2 )

Fkid

0.0000 0.0001 0.0004 0.0009 0.0015 0.0025 0.0035 0.0047 0.0059 0.0080 0.0111 0.0153 0.0200 0.0250 0.0322 0.0408 0.0498

0.9800 0.9935 1.0400 1.0700 1.1000 1.1200 1.1300 1.1370 1.1610 1.1800 1.2000 1.2350 1.2900 1.3200 1.3500 1.3950 1.4425

549.7 630.1 582.9 539.7 366.2 98.1 169.5 118.7 301.9 406.8 375.2 423.6 365.7 223.4 30.1 1.4 51.6

521.79 540.69 562.99 579.18 588.34 589.81 591.25 593.09 599.58 607.51 617.83 636.89 652.43 659.14 660.26 660.33 662.07

0.6793 0.7039 0.7329 0.7540 0.7659 0.7678 0.7697 0.7721 0.7806 0.7909 0.8043 0.8291 0.8494 0.8581 0.8596 0.8596 0.8619 (continued)

370 TABLE la

(continued)

hi

E;~i

E° "~.i

(pm)

( W m -2 pm--l)

(Wm

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 0.7180 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 0.8800 0.9050 0.9150 0.9250 0.9300 0.9370 0.9480 0.9650

641.9 798.5 956.6 990.8 998.0 1046.1 1005.1 1026.7 1066.7 1011.5 1084.9 1082.4 1102.2 1087.4 1024.3 1088.8 1062.1 1061.7 1046.2 859.2 1002.4 816.9 842.8 971.0 956.3 942.2 524.8 830.7 908.9 873.4 712.0 660.2 765.5 799.8 815.2 778.3 630.4 565.2 586.4 348.1 224.2 271.4 451.2

44.65 52.64 62.21 72.11 82.09 92.55 102.61 112.87 123.54 133.65 144.50 155.33 171.86 193.61 214.09 235.87 257.11 278.35 299.27 316.45 330.49 336.37 345.64 359.28 367.65 372.36 374.99 382.25 397.02 412.74 421.18 426.30 432.54 443.93 460.24 477.75 488.78 494.43 498.83 500.92 502.94 506.74 513.96

F)'i 2)

0.0581 0.0685 0.0810 0.0939 0.1069 0.1205 0.1336 0.1469 0.1608 0.1740 0.1881 0.2022 0.2237 0.2520 0.2787 0.3071 0.3347 0.3624 0.3896 0.4120 0.4302 0.4379 0.4500 0.4677 0.4786 0.4848 0.4882 0.4976 0.5169 0.5373 0.5483 0.5550 0.5631 0.5779 0.5992 0.6220 0.6363 0.6437 0.6494 0.6521 0.6547 0.6597 0.6691

hi

E hi

E° "~.i

(/lm)

( W i n -2 pm-1)

( W m --2)

1.4625 1.4770 1.4970 1.5200 1.5390 1.5580 1.5780 1.5920 1.6100 1.6300 1.6460 1.6780 1.7400 1.8000 1.8600 1.9200 1.9600 1.9850 2.0050 2.0350 2.0650 2.1000 2.1480 2.1980 2.2700 2.3600 2.4500 2.4940 2.5370 2.9410 2.9730 3.0050 3.0560 3.1320 3.1560 3.2040 3.2450 3.3170 3.3440 3.4500 3.5730 3.7650 4.0450

97.0 97.3 167.1 239.3 248.8 249.3 222.3 227.3 210.5 224.7 215.9 202.8 158.2 28.6 1.8 1.1 19.7 84.9 25.0 92.5 56.3 82.7 76.2 66.4 65.0 57.6 19.8 17.0 3.0 4.0 7.0 6.0 3.0 5.0 18.0 1.2 3.0 12.0 3.0 12.2 11.0 9.0 6.9

663.74 665.42 669.01 674.04 678.77 683.63 687.41 691.04 695.04 699.09 704.27 713.80 723.45 725.17 725.28 725.33 725.97 727.88 728.51 731.28 733.11 736.54 740.28 744.33 749.59 754.78 756.10 756.84 757.51 758.39 758.61 758.86 759.05 759.30 759.95 760.00 760.17 760.76 760.96 762.36 764.09 766.22 768.15

F~.i

0.8641 0.8663 0.8709 0.8775 0.8836 0.8900 0.8949 0.8996 0.9048 0.9101 0.9168 0.9292 0.9418 0.9440 0.9442 0.9443 0.9451 0.9476 0.9484 0.9520 0.9544 0.9589 0.9637 0.9690 0.9758 0.9826 0.9843 0.9853 0.9862 0.9873 0.9876 0.9879 0.9882 0.9885 0.9893 0.9894 0.9896 0.9904 0.9906 0.9925 0.9947 0.9975 1.0000

a)~i,wavelength. bEK. , spectral irradiance at wavelength )ki (centered at )~i and calculated using absorption 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. 1

.

371 TABLE lb Direct n o r m a l i r r a d i a n c e

vs. w a v e l e n g t h s p e c t r u m ( m o d i f i e d t r a p e z o i d a l i n t e g r a t i o n ) a

~'i

E~i

E° - hi

(pm)

(W m - 2 pm -1)

(W m - 2 )

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 0.7180 0.7244 0.7400 0.7525 0.7575 0.7625 0.7675 0.7800

3.4 15.6 41.1 71.2 100.2 152.4 155.6 179.4 186.7 212.0 240.5 324.0 362.4 381.7 556.0 656.3 690.8 641.9 798.5 956.6 990.8 998.0 1046.1 1005.1 1026.7 1066.7 1011.5 1084.9 1082.4 1102.2 1087.4 1024.3 1088.8 1062.1 1061.7 1046.2 859.2 1002.4 816.9 842.8 971.0 956.3 942.2 524.8 830.7 908.9

0.02 0.07 0.21 0.49 0.92 1.55 2.32 3.16 4.08 5.07 7.34 10.16 13.59 17.31 22.00 28.06 34.80 41.46 48.66 57.44 67.17 77.12 87.34 97.59 107.75 118.22 128.61 139.09 149.93 160.85 182.75 203.87 225.00 246.51 267.74 288.82 307.88 326.49 333.77 339.08 353.23 365.27 370.02 373.69 377.08 387.95

Fki

0.0000 0.0001 0.0003 0.0006 0.0012 0.0020 0.0030 0.0041 0.0053 0.0066 0.0095 0.0132 0.0177 0.0225 0.0286 0.0365 0.0453 0.0540 0.0633 0.0748 0.0874 0.1004 0.1137 0.1270 0.1402 0.1539 0.1674 0.1810 0.1951 0.2094 0.2379 0.2653 0.2928 0.3208 0.3485 0.3759 0.4007 0.4249 0.4344 0.4413 0.4597 0.4754 0.4816 0.4864 0.4908 0.5049

hi

Eki

E° "~'i

(pm)

(W m - 2 # m -1)

(W m - 2 )

Fki

0.9935 1.0400 1.0700 1.1000 1.1200 1.1300 1.1370 1.1610 1.1800 1.2000 1.2350 1.2900 1.3200 1.3500 1.3950 1.4425 1.4625 1.4770 1.4970 1.5200 1.5390 1.5580 1.5780 1,5920 1,6100 1.6300 1,6460 1,6780 1,7400 1.8000 1.8600 1.9200 1,9600 1,9850 2,0050 2.0350 2.0650 2,1000 2.1480 2.1980 2.2700 2.3600 2.4500 2,4940 2,5370 2.9410

630.1 582.9 539.7 366.2 98.1 169.5 118.7 301.9 406.8 375.2 423.6 365.7 223.4 30.1 1.4 51.6 97.0 97.3 167.1 239.3 248.8 249,3 222.3 227.3 210.5 224.7 215.9 202.8 158.2 28.6 1.8 1.1 19.7 84.9 25.0 92.5 56.3 82.7 76.2 66.4 65.0 57.6 19.8 17.0 3.0 4.0

526.06 554.26 571.10 584.69 589.33 590.67 591.68 596.73 603.46 611.28 625.26 646.96 655.80 659.60 660.31 661.57 663.06 664.46 667.11 671.78 676.42 681.15 685.87 689.01 692.95 697.31 700.83 707.53 718.72 724.33 725.24 725.32 725.74 727,05 728.15 729.91 732.14 734.57 738.39 741.95 746.68 752.20 755.68 756.49 756.92 758.34

0.6847 0.7214 0.7433 0.7610 0.7670 0.7688 0.7701 0.7767 0.7854 0.7956 0.8138 0.8421 0.8536 0.8585 0.8594 0.8611 0.8630 0.8648 0.8683 0.8744 0.8804 0.8866 0.8927 0.8968 0.9019 0.9076 0.9122 0.9209 0.9355 0.9428 0.9439 0.9441 0.9446 0.9463 0.9477 0.9500 0.9529 0.9561 0.9611 0.9657 0.9719 0.9790 0.9836 0.9846 0.9852 0.9870

(continued)

372 T A B L E l b (continued) ~i (pm)

0.8000 0.8160 0.8237 0.8315 0.8400 0.8600 0.8800 0.9050 0.9150 0.9250 0.9300 0.9370 0.9480 0.9650 0.9800

Eh i (Wm 2 p m 1) 873.4 712.0 660.2 765.5 799.8 815.2 778.3 630.4 565.2 586.4 348.1 224.2 271.4 451.2 549.7

E° "~-i ( W i n 2)

F~ i

}~i (pm}

405.77 418.46 423.74 429.30 435.95 452.10 468.04 485.65 491.62 497.38 499.72 501.72 504.45 510.59 518.10

0.5281 0.5446 0.5515 0.5588 0.5674 0.5884 0.6092 0.6321 0.6399 0.6474 0.6504 0.6530 0.6566 0.6646 0.6743

2.9730 3.0050 3.0560 3.1320 3.1560 3.2040 3.2450 3.3170 3.3440 3.4500 3.5730 3.7650 4.0450 4.0450

E~ i (Wm ~ p m 1) 7.0 6.0 3.0 5.0 18.0 1.2 3.0 12.0 3.0 12.2 11.0 9.0 6.9

Eo --h i ( W i n :)

F~ i

758.51 758.72 758.95 759.25 759.53 759.99 760.08 760.62 760.82 761.62 763.05 764.97 767.20 768.31

0.9872 0.9875 0.9878 0.9882 0.9886 0.9892 0.9893 0.9900 0.9902 0.9913 0.9932 0.9957 0.9986 1.0000

a F o r d e f i n i t i o n s see T a b l e l a . TABLE lc Direct n o r m a l irradiance vs. w a v e l e n g t h s p e c t r u m ( t r a p e z o i d a l i n t e g r a t i o n ) a ~-i (pm)

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

Eh i (Wm -2 pm -1) 3.4 15.6 41.1 71.2 100.2 152.4 155.6 179.4 186.7 212.0 240.5 324.0 362.4 381.7 556.0 656.3 690.8 641.9 798.5 956.6 990.8

Eo - h i ( W m -2)

Fh i

~,i (pm)

Eh i (W m - 2 p m -1)

E o - hi (W m - 2 )

Fh i

--

-0.0001 0.0002 0.0006 0.0012 0.0020 0.0030 0.0041 0.0053 0.0066 0.0095 0.0132 0.0177 0.0225 0.0286 0.0365 0.0453 0.0540 0.0634 0.0748 0.0875

0.9800 0.9935 1.0400 1.0700 1.1000 1.1200 1.1300 1.1370 1.1610 1.1800 1.2000 1.2350 1.2900 1.3200 1.3500 1.3950 1.4425 1.4625 1.4770 1.4970 1.5200

549.7 630.1 582.9 539.7 366.2 98.1 169.5 118.7 301.9 406.8 375.2 423.6 365.7 223.4 30.1 1.4 51.6 97.0 97.3 167.1 239.3

518.07 526.04 554.24 571.08 584.67 589.31 590.65 591.65 596.70 603.43 611.25 625.23 646.94 655.78 659.58 660.29 661.55 663.03 664.44 667.08 671.76

0.6753 0.6857 0.7224 0.7444 0.7621 0.7682 0.7699 0.7712 0.7778 0.7866 0.7968 0.8150 0.8433 0.8548 O.8598 0.8607 0.8623 0.8643 0.8661 0.8695 0.8756

0.05 0.19 0.47 0.90 1.53 2.30 3.14 4.05 5.05 7.31 10.13 13.57 17.29 21.98 28.04 34.77 41.44 48.64 57.41 67.15

373 TABLE l c

(continued)

hi (pm)

Ek i (W m -2 pro-l)

Eo -k i (W m -2)

Fk i

hi (pm)

Ek i (W m -2 pm -1)

Eo -k i (W m -2)

F~,i

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 0.7180 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 0.8800 0.9050 0.9150 0.9250 0.9300 0.9370 0,9480 0,9650

998.0 1046.1 1005.1 1026.7 1066.7 1011.5 1084.9 1082.4 1102.2 1087.4 1024.3 1088.8 1062.1 1061.7 1046.2 859.2 1002.4 816.9 842.8 971.0 956.3 942.2 524.8 830.7 908.9 873.4 712.0 660.2 765.5 799.8 815.2 778.3 630.4 565.2 586.4 348.1 224.2 271.4 451.2

77.09 87.31 97.57 107.73 118.20 128.59 139.07 149.91 160.83 182.73 203.84 224.97 246.48 267.72 288.80 307.85 326.47 333.75 339.06 353.21 365.25 370.00 373.66 377.05 387.93 405.75 418.43 423.72 429.28 435.93 452.08 468.01 485.62 491.60 497.36 499.69 501.70 504.42 510,56

0.1005 0.1138 0.1272 0.1404 0.1541 0.1676 0.1813 0.1954 0.2096 0.2382 0.2657 0.2932 0.3213 0.3490 0.3764 0.4013 0.4255 0.4350 0.4420 0.4604 0.4761 0.4823 0.4871 0.4915 0.5057 0.5289 0.5454 0.5523 0.5596 0.5682 0.5893 0.6100 0.6330 0.6408 0.6483 0.6513 0.6540 0.6575 0.6655

1.5390 1.5580 1.5780 1.5920 1.6100 1.6300 1.6460 1.6780 1.7400 1.8000 1.8600 1.9200 1.9600 1.9850 2.0050 2.0350 2.0650 2.1000 2.1480 2.1980 2,2700 2.3600 2.4500 2.4940 2.5370 2.9410 2.9730 3.0050 3.0560 3.13203.1560 3.2040 3.2450 3.3170 3.3440 3.4500 3.5730 3.7650 4.0450

248.8 249.3 222.3 227.3 210.5 224.7 215.9 202.8 158.2 28.6 1.8 1.1 19.7 84.9 25.0 92.5 56.3 82.7 76.2 66.4 65.0 57.6 19.8 17.0 3.0 4.0 7.0 6.0 3.0 5.0 18.0 1.2 3.0 12.0 3.0 12.2 11.0 9.0 6.9

676.40 681.13 685.84 688.99 692.93 697.28 700.81 707.51 718.70 724.30 725.21 725.30 725.72 727.02 728.12 729.89 732.12 734.55 738.36 741.93 746.66 752.18 755.66 756.47 756.90 758.31 758.49 758.70 758.93 759.23 759.51 759.97 760.05 760.59 760.80 761.60 763.03 764.95 767.17

0.8817 0.8878 0.8940 0.8981 0.9032 0.9089 0.9135 0.9222 0.9368 0.9441 0.9453 0.9454 0.9460 0.9477 0.9491 0.9514 0.9543 0.9575 0.9624 0.9671 0.9733 0.9805 0.9850 0.9860 0.9866 0.9884 0.9887 0.9889 0.9892 0.9896 0.9900 0.9906 0.9907 0.9914 0.9917 0.9927 0.9946 0.9971 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 T A B L E 2a Global irradiance rule i n t e g r a t i o n )

vs.

w a v e l e n g t h s p e c t r u m for a sun-facing, 37 ° tilted surface (rectangular

~i a (~um)

E~.ib (W m - 2 pm-1)

Eo .hi c (W m -2)

Fh i d

E~,ie (W m 2 pm-l)

E'o.hi e (W m- 2)

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 0.7180 0.7244 0.7400 0.7525 0.7575 0.7625 0.7675

9.2 40.8 103.9 174.4 237.9 381.0 376.0 419.5 423.0 466.2 501.4 642.1 686.7 694.6 976.4 1116.2 1141.1 1033.0 1254.8 1470.7 1541.6 1523.7 1569.3 1483.4 1492.6 1529.0 1431.1 1515.4 1494.5 1504.9 1447.1 1344.9 1431.5 1382.1 1368.4 1341.8 1089.0 1269.0 973.7 1005.4 1167.3 1150.6 1132.9 619.8 993.3

0.05 0.25 0.77 1.64 2.83 4.74 6.62 8.71 10.83 14.33 19.34 25.76 32.63 39.57 49.34 60.50 71.91 82.24 94.79 109.50 124.91 140.15 155.84 170.68 185.60 200.89 215.20 230.36 245.30 267.87 296.82 323.71 352.34 379.99 407.35 434.19 455.97 473.74 480.75 491.81 508.21 518.27 523.94 527.04 535.73

0.0000 0.0003 0.0008 0.0017 0.0029 0.0049 0.0069 0.0090 0.0112 0.0149 0.0201 0.0267 0.0339 0.0411 0.0512 0.0628 0.0746 0.0854 0.0984 0.1136 0.1296 0.1454 0.1617 0.1771 0.1926 0.2085 0.2233 0.2391 0.2546 0.2780 0.3080 0.3360 0.3657 0.3944 0.422S 0.4506 0.4732 0.4917 0.4989 0.5104 0.5274 0.5379 0.5438 0.5470 0.5560

9.5 42.3 107.8 181.0 246.9 395.4 390.2 435.4 439.0 483.8 520.4 666.4 712.7 720.9 1013.3 1158.4 1184.3 1072.1 1302.3 1526.3 1599.9 1581.3 1628.6 1539.5 1549.0 1586.8 1485.2 1572.7 1551.0 1561.8 1501.8 1395.8 1485.6 1434.4 1420.1 1392.5 1130.2 1317.0 1010.5 1043.4 1211.4 1194.1 1175.7 643.2 1030.9

0.05 0.26 0.80 1.70 2.94 4.92 6.87 9.04 11.24 14.87 20.07 26.73 33.86 41.07 51.20 62.79 74.63 85.35 98.37 113.64 129.63 145.45 161.73 177.13 192.62 208.49 223.34 239.07 254.58 278.00 308.04 335.96 365.67 394.36 422.76 450.61 473.21 491.65 498.93 510.41 527.43 537.87 543.75 546.97 555.99

F~ie

0.0000 0.0003 0.0008 0.0017 0.0029 00049 0.0069 0.0090 0.0112 0.0149 0.0201 0.0267 0.0339 0.0411 0.0512 0.0628 0.0746 0.0854 0.0984 0.1136 0.1296 0.1454 0.1617 0.1771 0.1926 0.2085 0.2233 0.2391 0.2546 0.2780 0.3080 0.3360 0.3657 0.3944 0.4228 0.4506 0.4732 0.4917 0.4989 0.5104 0.5274 0.5379 0.5438 0.5470 0.5560

375 TABLE 2a ;ki (pro)

(continued) Ek i (W m - 2

E~ .ki ( W m -~)

Fk i

~m -1) 0.7800 0.8000 0.8160 0.8237 0.8315 0.8400 0.8600 0.8800 0.9050 0.9150 0.9250 0.9300 0.9370 0.9480 0.9650 0.9800 0.9935 1.0400 1.0700 1.1000 1.1200 1.1300 1.1370 1.1610 1.1800 1.2000 1.2350 1.2900 1.3200 1.3500 1.3950 1.4425 1.4625 1.4770 1.4970 1.5200 1.5390 1.5580 1.5780 1.5920 1.6100 1.6300 1.6460 1.6780 1.740.0 1.8000 1.8600

1090.1 1042.4 818.4 756.5 883.2 925.1 943.4 899.4 721.4 643.3 665.3 389.0 248.9 302.2 507.7 623.0 719.7 665.5 614.4 397.6 105.0 182.2 127,4 326.7 443.3 408.2 463.1 398.1 241.1 31.3 1.5 53.7 101.3 101.7 175.5 253.1 264.3 265.0 235.7 238.4 220.4 235.6 226.3 212.5 165.3 29.6 1.9

553.44 572.21 581.91 587.77 594.97 608.15 627.02 647.25 659.88 666.31 671.30 673.63 675.87 680.11 688.23 697.11 718.70 744.15 762,58 772.52 774.10 775.65 777.62 784.65 793.29 804.52 825.36 842.28 849.51 850.68 850.75 852.56 854.31 856.07 859.84 865.15 870.18 875.34 879.35 883.16 887.35 891.59 897.02 907.01 917.10 918.87 918.99

0.5744 0.5938 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

f Ek i (Win-2 pm -1)

E o . ki ( W m -2)

i

1131.3 1081.8 849.4 785.1 916.6 960.1 979.1 933.4 748,7 667.6 690.5 403.7 258.3 313.6 526.9 646.6 746.9 690.7 637.6 412.6 109.0 189.1 132.2 339.1 460.1 423.6 480.6 413.2 250.2 32.5 1.6 55.7 105.1 105.5 182.1 262.7 274.3 275.0 244.6 247.4 228.7 244.5 234.9 220.5 171.6 30.7 2.0

574.37 593.85 603.91 610.00 617.47 631.15 650.73 671.73 684.83 691.51 696.69 699.11 701.43 705.83 714.26 723.47 745.88 772.29 791.42 801.74 803.37 804.98 807.03 814.32 823.29 834.94 856.57 874.13 881.64 882.85 882.93 884.81 886.62 888.44 892.36 897.87 903.08 908.45 912.61 916.56 920.91 925.31 930.95 941.31 951.78 953.62 953.74

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 T A B L E 2a (continued) )~i (tim)

1.9200 1.9600 1.9850 2.0050 2.0350 2.0650 2.1000 2.1480 2.1980 2.2700 2.3600 2.4500 2.4940 2.5370 2.9410 2.9730 3.0050 3.0560 3.1320 3.1560 3.2040 3.2450 3.3170 3.3440 3.4500 3.5730 3.7650 4.0450

Eki (Wm 2 ~ m - 1) 1.2 20.4 87.8 25.8 95.9 58.2 85.9 79.2 68.9 67.7 59.8 20.4 17.8 3.1 4.2 7.3 6.3 3.1 5.2 18.7 1.3 3.1 12.6 3.1 12.8 11.5 9.4 7.2

E ° " ~ki (Wm-2)

Fki

919.05 919.71 921.68 922.33 925.21 927.10 930.66 934.54 938.75 944.23 949.61 950.98 951.75 952.45 953.36 953.59 953.86 954.05 954.31 954.99 955.04 955.22 955.84 956.05 957.51 959.33 961.54 963.56

0.9538 0.9545 0.9565 0.9572 0.9602 0.9622 0.9659 0.9699 0.9742 0.9799 0.9855 0.9869 0.9877 0.9885 0.9894 0.9897 0.9899 0.9901 0.9904 0.9911 0.9912 0.9913 0.9920 0.9922 0.9937 0.9956 0.9979 1.0000

Eki (Win 2 p m - 1) 1.2 21.2 91.1 26.8 99.5 60.4 89.1 82.2 71.5 70.3 62.1 21.2 18.5 3.2 4.4 7.6 6.5 3.2 5.4 19.4 1.3 3.2 13.1 3.2 13.3 11.9 9.8 7.5

E ° " '~-i ( W i n 21

/~'~J

953.80 954.49 956.54 957.21 960.20 962.16 965.86 969.89 974.25 979.94 985.52 986.94 987.75 988.46 989.42 989.66 989.93 990.13 990.40 991.10 991.16 991.34 991.99 992.20 993.73 995.61 997.91 1000.00

0.9538 0.9545 0.9565 0.9572 0.9602 0.9622 0.9659 0.9699 0.9742 0.9799 0.9855 0.9869 0.9877 0.9885 0.9894 0.9897 0.9899 0.9901 0.9904 0.9911 0.9912 0.9913 0.9920 0.9922 0.9937 0.9956 0.9979 1.0000

ahi, wavelength. bEk. spectral irradiance at wavelength hi (centered at hl and calculated using absorption 1' data with 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 Eki, ~ E o. ~ hi, Fki, r as defined above but for the spectrum normalized 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 spectrum 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 irradiance. 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 irradiance vs. w a v e l e n g t h s p e c t r u m for a sun-facing, 37 ° tilted surface ( m o d i f i e d trapezoidal integration) a

~'i

E ~,i

Eo " ki

(pro)

(W m - 2 pm -1)

(Wm -2)

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 0.7180 0.7244 0.7400 0.7525 0.7575 0.7625 0.7675

9.2 40.8 103.9 174.4 237.9 381.0 376.0 419.5 423.0 466.2 501.4 642.1 686.7 694.6 976.4 1116.2 1141.1 1033.0 1254.8 1470.7 1541.6 1523.7 1569.3 1483.4 1492.6 1529.0 1431.1 1515.4 1494.5 1504.9 1447.1 1344.9 1431.5 1382~1 1368.4 1341.8 1089.0 1269.0 973.7 1005.4 1167.3 1150.6 1132.9 619.8 993.3

0.06 0.19 0.55 1.25 2.28 3.82 5.72 7.70 9.81 12.03 16.87 22.59 29.23 36.14 44.49 54.96 66.24 77.11 88.55 102.18 117.24 132.57 148.03 163.30 178.18 193.29 208.09 222.82 237.87 252.87 282.39 310.30 338.07 366.20 393.71 420.81 445.12 468.70 477.67 484.00 500.95 515.44 521.15 525.53 529.56

Fk i

0.0001 0.0002 0.0006 0.0013 0.0024 0.0040 0.0059 0.0080 0.0102 0.0125 0.0175 0.0234 0.0303 0.0375 0.0462 0.0570 0.0687 0.0800 0.0919 0.1060 0.1217 0.1376 0.1536 0.1694 0.1849 0.2006 0.2159 0.2312 0.2468 0.2624 0.2930 0.3220 0.3508 0.3800 0.4085 0.4366 0.4619 0.4863 0.4956 0.5022 0.5198 0.5348 0.5407 0.5453 0.5495

E~i

E'° " ki

(W m - 2 /~m -1)

(W m - 2 )

9.5 42.3 107.8 181.0 246.8 395.3 390.1 435.3 438.9 483.7 520.3 666.2 712.5 720.7 1013.1 1158.2 1184.0 1071.9 1302.0 1526.0 1599.6 1581.0 1628.3 1539.2 1548.7 1586.5 1484.9 1572.4 1550.7 1561.5 1501.5 1395.5 1485.3 1434.1 1419.9 1392.3 1130.0 1316.7 1010.3 1043.2 1211.2 1193.9 1175.5 643.1 1030.7

0.06 0.19 0.57 1.29 2.36 3.97 5.93 7.99 10.18 12.49 17.51 23.44 30.33 37.50 46.17 57.02 68.74 80.01 91.88 106.02 121.65 137.55 153.60 169.44 184.88 200.55 215.91 231.20 246.81 262.38 293.01 321.98 350.78 379.98 408.52 436.64 461.86 486.33 495.64 502.21 519.79 534.82 540.75 545.29 549.48

F~i

0.0001 0.0002 0.0006 0.0013 0.0024 0.0040 0.0059 0.0080 0.0102 0.0125 0.0175 0.0234 0.0303 0.0375 0.0462 0.0570 0.0687 0.0800 0.0919 0.1060 0.1217 0.1376 0.1536 0.1694 0.1849 0.2006 0.2159 0.2312 0.2468 0.2624 0.2930 0.3220 0.3508 0.3800 0.4085 0.4366 0.4619 0.4863 0.4956 0.5022 0.5198 0.5348 0.5407 0.5453 0.5495

(continued)

378 T A B L E 2b

(continued)

hi (pm)

E;~ i (W m - 2 #m -l)

E0 -~-i

0.7800 0.8000 0.8160 0.8237 0.8315 0.8400 0.8600 0.8800 0.9050 0.9150 0.9250 0.9300 0.9370 0.9480 0.9650 0.9800 0.9935 1.0400 1.0700 1.1000 1.1200 1.1300 1.1370 1.1610 1.1800 1.2000 1.2350 1.2900 1.3200 1.3500 1.3950 1.4425 1.4625 1.4770 1.4970 1.5200 1.5390 1.5580 1.5780 1.5920 1.6100 1.6300 1.6460 1.6780 1.7400 1.8000 1.8600

1090.1 1042.4 818.4 756.5 883.2 925.1 943.4 899.4 721.4 643.3 665.3 389.0 248.9 302.2 507.7 623.0 719.7 665.5 614.4 397.6 105.0 182.2 127.4 326.7 443.3 408.2 463.1 398.1 241.1 31.3 1.5 53.7 101.3 101.7 175.5 253.1 264.3 265.0 235.7 238.4 220.4 235.6 226.3 212.5 165.3 29.6 1.9

542.58 563.91 578.79 584.86 591.25 598.94 617.62 636.05 656.31 663.13 669.68 672.31 674.55 677.58 684.46 692.94 702.00 734.21 753.41 768.59 773.61 775.05 776.13 781.58 788.90 797.41 812.66 836.34 845.93 850.02 850.76 852.07 853.62 855.09 857.86 862.79 867.70 872.73 877.74 881.06 885.19 889.75 893.44 900.46 912.18 918.02 918.97

Fk i

(W m -2)

Eki (Wm-2 p m -1)

0.5630 0.5851 0.6006 0.6069 0.6135 0.6215 0.6409 0.6600 0.6810 0.6881 0.6949 0.6976 0.6999 0.7031 0.7102 0.7190 0.7284 0.7618 0.7817 0.7975 0.8027 0.8042 0.8053 0.8110 0.8186 0.8274 0.8432 0.8678 0.8777 0.8820 0.8828 0.8841 0.8857 0.8872 0.8901 0.8952 0.9003 0.9056 0.9108 0.9142 0.9185 0.9232 0.9270 0.9343 0.9465 0.9525 0.9535

1131.1 1081.6 849.2 785.0 916.4 959.9 978.9 933.2 748.5 667.5 690.3 403.6 258.3 313.6 526.8 646.4 746.8 690.5 637.5 412.6 108.9 189.1 132.2 339.0 460.0 423.6 480.5 413.1 250.2 32.5 1.6 55.7 105.1 105.5 182.1 262.6 274.2 275.0 244.6 247.4 228.7 244.5 234.8 220.5 171.5 30.7 2.0

Eo-hi (W m -2)

562.99 585.12 600.56 606.85 613.49 621.46 640.85 659.97 680.99 688.07 694.86 697.60 699.91 703.06 710.20 719.00 728.41 761.82 781.74 797.49 802.71 804.20 805.32 810.98 818.57 82'7.40 843.22 867.80 877.75 881.99 882.75 884.11 885.72 887.25 890.12 895.24 900.34 905.56 910.75 914.19 918.48 923.21 927.05 934.33 946.48 952.55 953.53

FK i

0.5630 0.5851 0.6006 0.6069 0.6135 0.6215 0.6409 0.6600 0.6810 0.6881 0.6949 0.6976 0.6999 0.7031 0.7102 0.7190 0.7284 0.7618 0.7817 0.7975 0.8027 0.8042 0.8053 0.8110 0.8186 0.8274 0.8432 0.8678 0.8777 0.8820 0.8828 0.8841 0.8857 0.8872 0.8901 0.8952 0.9003 0.9056 0.9108 0.9142 0.9185 0.9232 0.9270 0.9343 0.9465 0.9525 0.9535

379 TABLE 2b (continued) t

~,i ~m)

1.9200 1.9600 1.9850 2.0050 2.0350 2.0650 2.1000 2.1480 2.1980 2.2700 2.3600 2.4500 2.4940 2.5370 2.9410 2.9730 3.0050 3.0560 3.1320 3.1560 3.2040 3.2450 3.3170 3.3440 3.4500 3.5730 3.7650 4.0450 4.0450

Eh i (W m - 2 pm-1) 1.2 20.4 87.8 25.8 95.9 58.2 85.9 79.2 68.9 67.7 59.8 20.4 17.8 3.1 4.2 7.3 6.3 3.1 5.2 18.7 1.3 3.1 12.6 3.1 12.8 11.5 9.4 7.2

Eb - h i (W m - 2 )

Fhi

919.06 919.49 920.85 921.98 923.81 926.12 928.64 932.60 936.30 941.22 946.96 950.57 951.41 951,86 953.33 953.52 953.73 953.97 954.29 954.58 955.06 955.15 955.71 955.92 956.77 958.26 960.27 962.59 963.75

0.9536 0.9541 0.9555 0.9567 0.9586 0.9609 0.9636 0.9677 0.9715 0.9766 0.9826 0.9863 0.9872 0.9877 0.9892 0.9894 0.9896 0,9899 0.9902 0.9905 0.9910 0.9911 0.9917 0.9919 0.9928 0.9943 0.9964 0.9988 1.0000

l

I

Eki (W m - 2 pm -1)

Eo" ki (W m - 2 )

Fhi

1.2 21.2 91.1 26.8 99.5 60.4 89.1 82.2 71.5 70.2 62.0 21.2 18.5 3.2 4.4 7.6 6.5 3.2 5.4 19.4 1.3 3.2 13.1 3.2 13.3 11.9 9.8 7.5

953.63 954.07 955.48 956.66 958.55 960.95 963.57 967.68 971.52 976.62 982.57 986.32 987.19 987.66 989.19 989.38 989.60 989.85 990.18 990.48 990.98 991.07 991.66 991.88 992.75 994.30 996.38 998.79 1000.00

0.9536 0.9541 0.9555 0.9567 0.9586 0.9609 0.9636 0.9677 0.9715 0.9766 0.9826 0.9863 0.9872 0.9877 0.9892 0.9894 0.9896 0.9899 0.9902 0.9905 0.9910 0.9911 0.9917 0.9919 0.9928 0.9943 0.9964 0.9988 1.0000

aFor definitions see Table 2a. TABLE 2c Global irradiance vs. wavelength spectrum for a sun-facing, 37 ° tilted surface (trapezoidal integration)a

hi

Ehi

E o . hi

(pm)

(Win - 2 ) pm -1)

(Win -2)

0.3050 0.3100 0.3150 0.3200 0.3250 0.3300

9.2 40.8 103.9 174.4 237.9 381.0

0.13 0.49 1.18 2.21 3.76

Fhi

0.0001 0.0005 0.0012 0.0023 0.0039

E~i

E'~. hi

( W m -2 pm -1)

(Win -2)

9.6 42.4 107.9 181.2 247.2 395.8

0.13 0.51 1.23 2.30 3.91

F~i

0.0001 0.0005 0.0012 0.0023 0.0039

(continued)

380 T A B L E 2c ( c o n t i n u e d ) '~i (gm)

E~. i (Wm 2 ~ m 1)

E o -h i ( W r n 2)

F~ i

E~. i (Wm 2 pm--l)

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 0.7180 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 0.8800

376.0 419.5 423.0 466.2 501.4 642.1 686.7 694.6 976.4 1116.2 1141.1 1033.0 1254.8 1470.7 1541.6 1523.7 1569.3 1483.4 1492.6 1529.0 1431.1 1515.4 1494.5 1504.9 1447.1 1344.9 1431.5 1382.1 1368.4 1341.8 1089.0 1269.0 973.7 1005.4 1167.3 1150.6 1132.9 619.8 993.3 1090.1 1042.4 818.4 756.5 883.2 925.1 943.4 899.4

5.65 7.64 9.75 11.97 16.81 22.53 29.17 36.08 44.43 54.90 66.18 77.05 88.49 102.12 117.18 132.51 147.97 163.24 178.12 193.22 208.02 222.76 237.81 252.80 282.32 310.24 338.01 366.14 393.65 420.75 445.06 468.64 477.61 483.94 500.89 515.38 521.08 525.47 529.50 542.52 563.84 578.73 584.79 591.19 598.87 617.56 635.99

0.0059 0.0079 0.0101 0.0124 0.0175 0.0234 0.0303 0.0375 0.0462 0.0570 0.0688 0.0801 0.0919 0.1061 0.1217 0.1377 0.1537 0.1696 0.1850 0.2007 0.2161 0.2314 0.2471 0.2626 0.2933 0.3223 0.3512 0.3804 0.4090 0.4371 0.4624 0.4869 0.4962 0.5028 0.5204 0.5354 0.5414 0.5459 0.5501 0.5636 0.5858 0.6013 0.6076 0.6142 0.6222 0.6416 0.6607

390.6 435.8 439.5 484.3 520.9 667.1 713.4 721.6 1014.4 1159.7 1185.5 1073.2 1303.6 1528.0 1601.6 1583.0 1630.4 1541.1 1550.7 1588.5 1486.8 1574.4 1552.7 1563.5 1503.4 1397.3 1487.2 1435.9 1421.7 1394.0 1131.4 1318.4 1011.6 1044.5 1212.7 1195.4 1177.0 643.9 1032.0 1132.5 1083.0 850.3 786.0 917.6 961.1 980.1 934.4

Eo- hi ( W i n :)

5.87 7.94 10.13 12.44 17.46 23.40 30.3] 37.48 46.16 57.03 68.76 80.05 91.94 106.09 121.74 137.66 153.73 169.59 185.05 200.75 216.12 231.43 247.06 262.64 293.31 322.32 351.16 380.40 408.97 437.13 462.38 486.88 496.20 502.78 520.39 535.44 541.37 545.92 550.11 563.64 585.80 601.26 607.56 614.20 622.19 641.60 660.75

[ hi

0.0059 0.0079 0.0101 0.0124 0.0175 0.0234 0.0303 0.0375 0.0462 0.0570 0.0688 0.0801 0.0919 0.1061 0.1217 0.1377 0.1537 0.1696 0.1850 0.2007 0.2161 0.2314 0.2471 0.2626 0.2933 0.3223 0.3512 0.3804 0.4090 0.4371 0.4624 0.4869 0.4962 0.5028 0.5204 0.5354 0.5414 0.5459 0.5501 0.5636 0.5858 0.6013 0.6076 0.6142 0.6222 0.6416 0.6607

381 TABLE 2c (continued) ~,i (pm)

0.9050 0.9150 0.9250 0.9300 0.9370 0.9480 0.9650 0.9800 0.9935 1.0400 1.0700 1.1000 1.1200 1.1300 1.1370 1.1610 1.1800 1.2000 1.2350 1.2900 1.3200 1.3500 1.3950 1.4425 1.4625 1.4770 1.4970 1.5200 1.5390 1.5580 1.5780 1.5920 1.6100 1.6300 1.6460 1.6780 1.7400 1.8000 1.8600 1.9200 1.9600 1.9850 2.0050 2.0350 2.0650 2.1000 2.1480

Ek i ( W m -2 ~m -1) 721.4 643.3 665.3 389.0 248.9 302.2 507.7 623.0 719.7 665.5 614.4 397.6 105.0 182.2 127.4 326.7 443.3 408.2 463.1 398.1 241.1 31.3 1.5 53.7 101.3 101.7 175.5 253.1 264.3 265.0 235.7 238.4 220.4 235.6 226.3 212.5 165.3 29.6 1.9 1.2 20.4 87.8 25.8 95.9 58.2 85.9 79.2

Eo-~. i ( W m -2)

Fk i

656.25 663.07 669.61 672.25 674.48 677.51 684.40 692.88 701.94 734.15 753.35 768.53 773.55 774.99 776.07 781.52 788.84 797.35 812.60 836.28 845.87 849.96 850.69 852.00 853.55 855.03 857.80 862.73 867.64 872.67 877.68 881.00 885.13 889.69 893.38 900.40 912.11 917.96 918.91 919.00 919.43 920.78 921.92 923.74 926.06 928.58 932.54

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

t

Ek i (W m -2 pm -1)

Eo-~, i ( W m -2)

749.5 668.3 691.2 404.1 258.6 314.0 527.5 647.3 747.7 691.4 638.3 413.1 109.1 189.3 132.4 339.4 460.6 424.1 481.1 413.6 250.5 32.5 1.6 55.8 105.2 105.7 182.3 263.0 274.6 275.3 244.9 247.7 229.0 244.8 235.1 220.8 171.7 30.8 2.0 1.2 21.2 91.2 26.8 99.6 60.5 89.2 82.3

681.80 688.88 695.68 698.42 700.74 703.89 711.04 719.85 729.27 762.73 782.67 798.44 803.67 805.16 806.28 811.94 819.54 828.39 844.23 868.84 878.80 883.04 883.81 885.17 886.78 888.31 891.19 896.31 901.42 906.64 911.85 915.29 919.58 924.32 928.16 935.45 947.62 953.70 954.68 954.77 955.22 956.63 957.81 959.71 962.11 964.73 968.84

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 (pm)

EXi (Wm 2 pm 1)

2.1980 2.2700 2.3600 2.4500 2.4940 2.5370 2.9410 2.9730 3.0050 3.0560 3.1320 3.1560 3.2040 3.2450 3.3170 3.3440 3.4500 3.5730 3.7650 4,0450

68.9 67.7 59.8 20.4 17.8 3.1 4.2 7.3 6.3 3.1 5.2 18.7 1.3 3.1 12.6 3.1 ] 2.8 11.5 9.4 7.2

Eo- Xi ( W m 2)

FX i

936.24 941.16 946.90 950.51 951.35 951.80 953.27 953.45 953.67 953.91 954.23 954.51 954.99 955.08 955.65 955.86 956.70 958.20 960.21 962.53

0.9727 0.9778 0.9838 0.9875 0.9884 0.9888 0.9904 0.9906 0.9908 0.9910 0.9914 0.9917 0.9922 0.9923 0.9929 0.9931 0.9939 0.9955 0.9976 1.0000

E~ i (Win 2 pm 1) 71.6 70.3 62.1 21.2 18.5 3.2 4.4 7.6 6.5 3.2 5.4 19.4 1.4 3.2 13.1 3.2 13.3 11.9 9.8 7.5

Eo- h i (Win 2)

F~ i

972.69 977.80 983.76 987.51 988.38 988.85 990.38 990.57 990.80 991.05 991.38 991.67 992.17 992.27 992.85 993.07 993.95 995.50 997.59 1000.00

0.9727 0.9778 0.9838 0.9875 0.9884 0.9888 0.9904 0.9906 0.9908 0.9910 0.9914 0.9917 0.9922 0.9923 0.9929 0.9931 0.9939 0.9955 0.9976 1.0000

aFor definitions see Table 2a. 1600

/,4,,,

E1200 ~_~ 800o~

400 0

08

11 19 Wavelength (,urn)

27

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 d o 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 r e s u 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 (having t h e s p e c i f i e d w a t e r vapor and turbidity values) would not represent nature [ 23]. P h o t o n f l u x d e n s i t y v a l u e s 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 irrad i a n c e d a t a sets a r e g i v e n in T a b l e s 3 a n d 4 a n d p l o t t e d in Figs. 5 a n d 6.

383 TABLE 3 Direct n o r m a l p h o t o n flux d e n s i t y vs. w a v e l e n g t h X a n d p h o t o n energy ( e V ) s p e c t r u m ~,a (~tm)

Ephoto n b (eV)

E~ c ( W m - 2 p m -1)

Nph (~k)d (1016 c m - 2 s-I pm-1)

Nph ( e v ) e (1016 c m - 2 s-1 e V - 1 )

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 0.7180 0.7244 0.7400 0.7525 0.7575 0.7626 0.7675 0.7800

4.0651 3.9995 3.9360 3.8745 3.8149 3.7571 3.7011 3.6466 3.5938 3.5424 3.4440 3.3510 3.2628 3.1791 3.0996 3.0240 2.9520 2.8834 2.8178 2.7552 2.6953 2.6380 2.5830 2.5303 2.4797 2.4311 2.3843 2.3393 2.2960 2.2543 2.1752 2.1014 2.0325 1.9680 1.9075 1.8505 1.7969 1.7463 1.7268 1.7116 1.6755 1.6476 1.6368 1.6260 1.6154 1.5896

3.4 15.6 41.1 71.2 100.2 152.4 155.6 179.4 186.7 212.0 240.5 324.0 362.4 381.7 556.0 656.3 690.8 641.9 798.5 956.6 990.8 998.0 1046.1 1005.1 1026.7 1066.7 1011.5 1084.9 1082.4 1102.2 1087.4 10243 1088.8 1062.1 1061.7 1046.2 859.2 1002.4 816.9 842.8 971.0 956.3 942.2 524.8 830.7 908.9

0.052 0.243 0.652 1.147 1.639 2.532 2.624 3.071 3.243 3.735 4.359 6.035 6.933 7.494 11.196 13.546 14.606 13.895 17.687 21.670 22.944 23.613 25.277 24.793 25.842 27.386 26.478 28.946 29.424 30.517 31.202 30.423 33.434 33.684 34.740 35.286 29.844 35.827 29.526 30.734 36.172 36.226 35.929 20.144 32.095 35.688

0.004 0.019 0.052 0.095 0.140 0.222 0.238 0.286 0.311 0.369 0.456 0.666 0.807 0.919 1.445 1.837 2.078 2.072 2.762 3.539 3.916 4.207 4.697 4.801 5.211 5.745 5.775 6.558 6.920 7.446 8.176 8.541 10.034 10.783 11.838 12.776 11.460 14.567 12.277 13.008 15.976 16.545 16.628 9.446 15.248 17.512 (continued)

384 TABLE 3 )(pm)

0.8000 0.8160 0.8237 0.8315 0.8400 0.8600 0.8800 0.9050 0.9150 0.9250 0.9300 0.9370 0.9480 0.9650 0.9800 0.9935 1.0400 1.0700 1.1000 1.1200 1.1300 1.1370 1.1610 1.1800 1.2000 1.2350 1.2900 1.3200 1.3500 1.3950 1.4425 1.4625 1.4770 1.4970 1.5200 1.5390 1.5580 1.5780 1.5920 1.6100 1.6300 1.6460 1.6780 1.7400 1.8000 1.8600 1.9200

(continued) Ephoton (eV)

1.5498 1.5194 1.5052 1.4911 1.4760 1.4417 1.4089 1.3700 1.3550 1.3404 1.3332 1.3232 1.3079 1.2848 1.2652 1.2480 1.1922 1.1587 1.1271 1.1070 1.0972 1.0905 1.0679 1.0507 1.0332 1.0039 0.9611 0.9393 0.9184 0.8888 0.8595 0.8478 0.8394 0.8282 0.8157 0.8056 0.7958 0.7857 0.7788 0.7701 0.7606 0.7533 0.7389 0.7126 0.6888 0.6666 0.6458

EX

(W m 2 g m

873.4 712.0 660.2 765.5 799.8 815.2 778.3 630.4 565.2 586.4 348.1 224.2 271.4 451.2 549.7 630.1 582.9 539.7 366.2 98.1 169.5 118.7 301.9 406.8 375.2 423.6 365.7 223.4 30.1 1.4 51.6 97.0 97.3 167.1 239.3 248.8 249.3 222.3 227.3 210.5 224.7 215.9 202.8 158.2 28.6 1.8 1.1

1)

s 1 pm-l)

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

35.174 29.247 27.375 32.042 33.820 35.292 34.478 28.720 26.034 27.306 16.297 10.575 12.952 21.919 27.119 31.513 30.517 29.071 20.278 5.531 9.642 6.794 17.645 24.165 22.665 26.335 23.748 14.845 2.046 0.098 3.747 7.141 7.235 12.593 18.311 19.275 19.553 17.659 18.216 17.061 18.438 17.890 17.131 13.857 2.592 0.169 0.106

18.156 15.707 14.981 17.868 19.247 21.053 21.535 18.972 17.580 18.844 11.368 7.489 9.388 16.463 21.006 25.088 26.622 26.844 19.790 5.596 9.930 7.084 19.183 27.138 26.324 32.397 31.874 20.862 3.007 0.154 6.289 12.320 12.729 22.761 34.121 36.822 38.280 35.466 37.237 35.668 39.510 39.092 38.904 33.838 6.772 0.470 0.316

Nph()~)

(1016 cm z

385 TABLE 3

(pm)

1.9600 1.9850 2.0050 2.0350 2.0650 2.1000 2.1480 2.1980 2.2700 2.3600 2.4500 2.4940 2.5370 2.9410 2.9730 3.0050 3.0560 3.1320 3.1560 3.2040 3.2450 3.3170 3.3440 3.4500 3.5730 3.7650 4.0450

(continued) Ephoton (eV)

0.6326 0.6246 0.6184 0.6093 0.6004 0.5904 0.5772 0.5641 0.5462 0.5254 0.5061 0.4971 0.4887 0.4216 0.4170 0.4126 0.4057 0.3959 0.3929 0.3870 0.3821 0.3738 0.3708 0.3594 0.3470 0.3293 0.3065

Ek ( W m -2 pm -1)

19.7 84.9 25.0 92.5 56.3 82.7 76.2 66.4 65.0 57.6 19.8 17.0 3.0 4.0 7.0 6.0 3.0 5.0 18.0 1.2 3.0 12.0 3.0 12.2 11.0 9.0 6.9

Nph(k) (101~ cm -2 s-1 p m - l ) 1.944 8.484 2.523 9.476 5.853 8.743 8.240 7.347 7.428 6.843 2.442 2.134 0.383 0.592 1.048 0.908 0.462 0.788 2.860 0.194 0.490 2.004 0.505 2.119 1.979 1.706 1.405

Nph(eV) (1016 cm-2

s-1 eV-1) 6.023 26.961 8.181 31.651 20.129 31.096 30.662 28.628 30.870 30.740 11.823 10.707 1.989 4.131 7.468 6.611 3.476 6.237 22.974 1.603 4.162 17.781 4.555 20.341 20.372 19.502 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 p h o t o n flux density in either wavelength or energy intervals are given in Appendix B. The representation of the spectral data in units of p h o t o n 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 measurements to validate the modeled AM 1.5 spectral irradiance data sets and to further study the variation in AM 1.5 spectral irradiance (under cloudless

386

TABLE 4 Global p h o t o n flux d e n s i t y

vs.

w a v e l e n g t h ~ a n d p h o t o n energy E s p e c t r u m a

(/~m)

Ephoton (eV)

E~, (W m 2 p m 1)

Nph(~, ) (1016 em : s l p m 1)

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

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 0.7180 0.7244 0.7400 0.7525 0.7575 0.7625 0.7675 0.7800

4.0651 3.9995 3.9360 3.8745 3.8149 3.7571 3.7011 3.6466 3.5938 3.5424 3.4440 3.3510 3.2628 3.1791 3.0996 3.0240 2.9520 2.8834 2.8178 2.7552 2.6953 2.6380 2.5830 2.5303 2.4797 2.4311 2.3843 2.3393 2.2960 2.2543 2.1752 2.1014 2.0325 1.9680 1.9075 1.8505 1.7969 1.7463 1.7268 1.7116 1.6755 1.6476 1.6368 1.6260 1.6154 1.5896

9.2 40.8 103.9 174.4 237.9 381.0 376.0 419.5 423.0 466.2 501.4 642.1 686.7 694.6 976.4 1116.2 1141.1 1033.0 1254.8 1470.7 1541.6 1523.7 1569.3 1483.4 1492.6 1529.0 1431.1 1515.4 1494.5 1504.9 1447.1 1344.9 1431.5 1382.1 1368.4 1341.8 1089.0 1269.0 973.7 1005.4 1167.3 1150.6 1132.9 619.8 993.3 1090.1

0.141 0,637 1.648 2,809 3.892 6.329 6.341 7.180 7.346 8.214 9.087 11.960 13.136 13.637 19.661 23.038 24.126 22.361 27.794 33,316 35.698 36.051 37.920 36.591 37.569 39.255 37.462 40.431 40.626 41.666 41,523 39.945 43.958 43.833 44.776 45.256 37.826 45,356 35.194 36.663 43.484 43.586 43.201 23.791 38.377 42.803

0.011 0.049 0.132 0.232 0.332 0.556 0.574 0.669 0.705 0.812 0.950 1.321 1.530 1.673 2.537 3.124 3.433 3.335 4.340 5.441 6.092 6.423 7.047 7.086 7.575 8.235 8.170 9.160 9.555 10.166 10.881 11.215 13,193 14.032 15.258 16.385 14.525 18.441 14.633 15.517 19.205 19,906 19.993 11.156 18.233 21.004

387 TABLE 4

(continued)

~. (pro)

Ephoton

Eh.

(eV)

(W m - 2 p m - 1 )

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

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

0.8000 0.8160 0.8237 0.8315 0.8400 0.8600 0.8800 0.9050 0.9150 0.9250 0.9300 0.9370 0.9480 0.9650 0.9800 0.9935 1.0400 1.0700 1.1000 1.1200 1.1300 1.1370 1.1610 1.1800 1.2000 1.2350 1.2900 1.3200 1.3500 1.3950 1.4425 1.4625 1.4770 1.4970 1.5200 1.5390 1.5580 1.5780 1.5920 1.6100 1.6300 1.6460 1.6780 1.7400 1.8000 1.8600 1.9200 1.9600

1.5498 1.5194 1.5052 1.4911 1.4760 1.4417 1.4089 1.3700 1.3550 1.3404 1.3332 1.3232 1.3079 1.2848 1.2652 1.2480 1.1922 1.1587 1.1271 1.1070 1.0972 1.0905 1.0679 1.0507 1.0332 1.0039 0.9611 0.9393 0.9184 0.8888 0.8595 0.8478 0.8394 0.8282 0.8157 0.8056 0.7958 0.7857 0.7788 0.7701 0.7606 0.7533 0.7389 0.7126 0.6888 0.6666 0.6458 0.6326

1042.4 818.4 756.5 883.2 925.1 943.4 899.4 721.4 643.3 665.3 389.0 248.9 302.2 507.7 623.0 719.7 665.5 614.4 397.6 105.0 182.2 127.4 326.7 443.3 408.2 463.1 398.1 241.1 31.3 1.5 53.7 101.3 101.7 175.5 253.1 264.3 265.0 235.7 238.4 220.4 235.6 226.3 212.5 165.3 29.6 1.9 1.2 20.4

41.980 33.618 31.369 36.969 39.119 40.842 39.843 32.866 29.631 30.980 18.212 11.740 14.422 24.663 30.735 35.994 34.842 33.094 22.017 5.920 10.364 7.292 19.094 26.333 24.659 28.791 25.852 16.021 2.127 0.105 3.900 7.458 7.562 13.226 19.367 20.476 20.784 18.723 19.106 17.863 19.332 18.751 17.950 14.479 2.682 0.178 0.116 2.013

21.670 18.054 17.166 20.615 22.262 24.363 24.886 21.710 20.009 21.379 12.704 8.314 10.454 18.524 23.807 28.655 30.394 30.560 21.487 5.990 10.674 7.603 20.758 29.573 28.639 35.418 34.698 22.515 3.127 0.165 6.544 12.866 13.305 23.905 36.089 39.116 40.691 37.603 39.055 37.345 41.427 40.975 40.764 35.356 7.009 0.496 0.345 6.237

388 TABLE 4 (continued)

(pro)

Ephoton (eV)

1.9850 2.0050 2.0350 2.0650 2.1000 2.1480 2.1980 2.2700 2.3600 2.4500 2.4940 2.5370 2.9410 2.9730 3.0050 3.0560 3.1320 3.1560 3.2040 3.2450 3.3170 3.3440 3.4500 3.5730 3.7650 4.0450

0.6246 0.6184 0.6093 0.6004 0.5904 0.5772 0.5641 0.5462 0.5254 0.5061 0.4971 0.4887 0.4216 0.4170 0.4126 0.4057 0.3959 0.3929 0.3870 0.3821 0.3738 0.3708 0.3594 0.3470 0.3293 0.3065

Nph(~) (1016 c m -2 s lpm-:)

EX (W m- 2 pm-- l)

87.8 25.8 95.9 58.2 85.9 79.2 68.9 67.7 59.8 20.4 17.8 3.1 4.2 7.3 6.3 3.1 5.2 18.7 1.3 3.1 12.6 3.1 12.8 11.5 9.4 7.2

8.774 2.604 9.824 6.050 9.081 8.564 7.624 7.736 7.104 2.516 2.235 0.396 0.622 1.093 0.953 0.477 0.820 2.971 0.210 0.506 2.104 0.522 2.223 2.069 1.782 1.466

Nph(eV) (1016 cm : s l e V 1) 27.882 8.443 32.814 20.808 32.300 31.869 29.706 32.152 31.914 12.181 11.211 2.055 4.338 7.789 6.941 3.592 6.487 23.867 1.736 4.301 18.670 4.707 21.341 21.298 20.369 19.348

a F o r d e f i n i t i o n s see Table 3.

Air Mass q i

~

[' 41.~, ~ G l o b a l ,

4°4 J / N

37 ° Tilt,

~E 40-

A,rMass s

4 ~ ~['~.jj--Direct

~j

Normal, Air Mass15

>,

~

s

GIobal, 37 ° Tilt Air Mass 1 5 Direct Normal

/~

~ 30~

~_

g ~5

Mass 0

.g ~ 20

~o

,=-

~: Q_

~Air

.~

g 0

0.2

.

1.0

1.8 26 Wavelength (,um)

.

.

34

.

~5

42

0

03

0.9

15 2.t 27 33 Photon Energy (eV}

39

45

Fig. 5. P h o t o n flux d e n s i t y vs. w a v e l e n g t h k (Tables 3 a n d 4) for t h r e e categories o f solar irradiance. Fig. 6. P h o t o n flux d e n s i t y vs. p h o t o n energy E (Tables 3 a n d 4) for t h r e e categories of solar irradiance.

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 locations and a range of atmospheric conditions and air mass values. The longrange 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, A S T M Stand. E891-82, 1982 (American Society for Testing of Materials, Philadelphia, PA). 2 Standard for solar spectral irradiance tables at air mass 1.5 for a 37 ° tilted surface, A S T M Stand. E892-82, 1982 (American Society for Testing of Materials, Philadelphia, 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, Cleveland, 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 distribution, 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 calculations, 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 (Electromagnetic 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, Switzerland. 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 irradiance 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). Appendix A: integration techniques

a. R e c t a n g u l a r rule integration (see Tables l ( a ) and 2(a)) At end points first

AXl=~2--hl

last

AXN = ~kN

-

-

~'N-

1

w h e r e 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 other wavelengths k i + I - - ~'i

&hi -

I

2

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

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

1

2

(~i + 1 -- hi)

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 2+ E h l ) ( ~ 2 - kl)

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 p h o t o n 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 p h o t o n flux density per wavelength interval to p h o t o n flux per p h o t o n energy eV interval is given b y k N p h ( e V ) = Nph(}k)

Ephoton

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