Reference Spectral Distributions

From the discussion in the preceding Sections, even without addressing the influence of clouds, it is clear that the terrestrial solar spectrum is highly variable. So, how can we relate the spectral responses and spectral optical properties of materials to each other when this variability is present? The answer is to establish a standard spectral distribution with which to compute performance. Then comparisons can be made based on standard set of conditions. Furthermore, if measurements are made under conditions, deviations from the standard conditions can be computed, documented, and in most cases corrected or scaled to the reference conditions.

Several national and international consensus standards organizations, such as the American Society for Testing and Materials (ASTM) and the International Standards Organization (ISO) have adopted a reference standard extraterrestrial spectral distribution (ASTM E490-00a), and terrestrial reference spectral distributions for direct beam and total hemispherical (on a 37° tilted south facing surface) spectra at a prescribed air mass of 1.5 (ASTM G173-03).21011

The extraterrestrial reference spectral distribution was assembled from a number of recent diverse space-based (satellite) measurement sources. The ETR reference spectrum is normalized to a total integrated irradiance of 1366.1 Wm-2.

The terrestrial reference spectra required a more extensive set of criteria to be met. Specifically, a set of reasonable conditions that could occur rather commonly in nature should be used. The conditions for the terrestrial reference spectra were chosen to meet the following criteria:12

• Air mass 1.5 represents the condition where approximately 1/2 of the total available solar energy is available for air masses greater than and less than this condition, respectively.

• For solar thermal and photovoltaic systems using flat plate collectors, energy collection is optimized for collectors tilted south (in the northern hemisphere) at approximately the latitude of the site.

• The mean latitude of the contiguous 48 United States is approximately 37° North.

• Standard test conditions prescribed in photovoltaic standards require a total hemispherical irradiance on flat plate collectors of 1000 Wm-2 (a value that can obtained on a clear day around noon).

• Concentrating solar collector systems that utilize the direct beam radiation would be more likely deployed in areas with relatively low aerosol optical depth, to maximize direct beam utilization.13

• The terrestrial reference should be easily reproducible, preferably by a simple (but accurate) model calculation, and the model should be easily maintained and updated, and in the public domain.14

• The terrestrial reference spectrum should have uniform wavelength increments for ease of computation and comparison with measured spectral data.

These criteria resulted in the choice of a relatively simple, but accurate spectral model of Gueymard (SMARTS: Simple Model for Atmospheric Transmission of Sunshine) to compute the reference standard terrestrial spectra.7

The philosophy behind the SMARTS model is to parameterize the band model transmittance functions used by a very complex (50,000 line of FORTRAN code and about 200 subroutines) MODTRAN (MODerate resolution TRANSmittance) code15 developed by the Air Force Geophysics Laboratory, for the most important at-

Table 1. Transmission expressions developed for SMARTS model.

Absorption Mechanism

Transmittance Expression

Rayleigh Scattering Ozone

Nitrogen Dioxide (NO2)

Tr(X) = exp{(P/Po)/[a0(X/Xo)4+a1(X/Xo)+a2+a3(X/Xo)-2]} To(X) = exp [-mo uo Ao(X) ]

Mixed and Trace Gases Water Vapor Aerosol

Tn(X) = exp [-m. un An(X) ] Tg(X) = exp [-( mg ug Ag(X))]

Tw(X) = exp[-( mw uw)Bw(X)Bm(X)Bp(X)Baw(X) Aw(X)] Ta(X) = exp [-ma ß (X/X1)-a]_

mospheric constituents, at a resolution of 0.5 nm in the ultraviolet less than 400 nm, 1 nm between 400 nm and 1700 nm, and 5 nm between 1700 nm and 4000 nm. These parameterized transmittance functions were developed to account for Rayleigh scattering (Tr), ozone (To), mixed gas (Tg), nitrogen dioxide (Tn), water vapor (Tw), and aerosol (Ta) transmission of the direct beam irradiance using Eq. 3:

at each wavelength (X, in nm), where E is the terrestrial spectral irradiance, Eo is the extraterrestrial spectral irradiance, and the spectral transmittances are defined above. Table 1 summarizes the form of transmittance functions developed for the SMARTS model.

Table 1 expression parameters are; P = station pressure, Po = standard pressure, ai = fitting coefficients, m = air mass correction for path length, u = absorber abundances, A = absorption coefficients, a = absorber/wavelength dependent, Bs = water vapor band, airmass, and pressure scaling factors, ai Pi, = Angstrom parameters, i = 1 for X < 500 nm, i = 2 for X > 500 nm,* X1: Reference wavelength (usually 1000 nm or 1 |im)

Figures 16 and 17 show percent difference between SMARTS MODTRAN results and one of many comparisons of measured and SMARTS spectral data. Agreement within the uncertainty limits of spectral irradiance measurements (1% in the visible, and 3% to 5% in the ultraviolet and infrared), is achieved.

Version 2.9.2 of the SMARTS spectral model used to generate the spectral reference standard, the users manual for the model, and a list of references, can be downloaded free of charge from the National Renewable Energy Laboratory Renewable Resource Data Center at the following URL: http://rredc.nrel.gov/solar/models /SMARTS/. A CD-ROM adjunct to the ASTM G-173-03 standard, with a copy of the model, manual, and reference material is available for purchase from ASTM.

The SMARTS input file is a straightforward assembly of fifteen to twenty parameters arranged as in a stack of input cards. Table 2 is an annotated input file used to generate the ASTM G173 standard spectra on a 37° tilted south facing plane. Note that we do not show all possible input combinations.

Figures 18 and 19 portray the ETR and terrestrial standard reference spectra.

The common assumption the a1 = a2 = a can lead to errors for the urban, maritime, and rural aerosol profiles. The Angstrom exponents are determined as a function of aerosol type and relative humidity (cf. Appendix B of Gueymard.)7

Astm Not Stack
Fig. 16. Percent difference between MODTRAN and SMARTS spectral results, for ASTM reference spectra conditions. Largest differences due to SMARTS trace gases.
Air Mass Factor Spectrum
Fig. 17. SMARTS model results (lines) and measurements (symbols) at 5 nm resolution for 3 air masses at NREL, Sep 18, 2001.

Table 2. SMARTS version 2.9 input file for ASTM reference spectra G173-03.

Card ID

Value

Parameter/Description/Variable name

2 2a

7 7a

10b 10c 11

12 12a 12b 12c

13 13a

16 17 17a

ASTM_G 173_Std_Spectra 1

USSA

370 1

S&F_RURAL 0

0.084 38

38 37 180 280 4000 1.0 1367.0

Comment line

Pressure input mode (1 = pressure and altitude): ISPR

Station pressure (mb) and altitude (km): SPR, ALT

Standard Atmosphere Profile Selection (1 = use default atmosphere): IATM1 Default Standard Atmosphere Profile: ATM (one of eleven choices, including user defined)

Water vapor input (1 = default from Atmospheric Profile):

IH2O (may be user specified) Ozone calculation (1 = default from Atmospheric Profile): IO3

(may be user specified) Pollution level mode (1 = standard conditions/no pollution):

IGAS (for 10 pollutant gases) Carbon monoxide volume mixing ratio (ppm): qCO2 Extraterrestrial spectrum (1 = SMARTS/Gueymard): ISPCTR (one of seven choices)

Aerosol profile to use: AEROS (one of 10 choices, including user specified)

Specification for aerosol optical depth/turbidity input (0 = AOD

at 500 nm): ITURB Aerosol optical depth @ 500 nm: TAU5

Far field spectral Albedo file to use (38 = Light Sandy Soil):

IALBDX (on of 40 choices, including user defined) Specify tilt calculation (1 = yes): ITILT

Albedo and Tilt variables—Albedo file to use for near field,

Tilt, and Azimuth: IALBDG, TILT, WAZIM Wavelength range—start, stop, mean radius vector correction, integrated solar spectrum irradiance: WLMN, WLMX, SUNCOR, SOLARC Separate spectral output file print mode (2 = yes): IPRT: Spectral & broadband files Output file wavelength—Print limits, start, stop, minimum step size: WPMN, WPMX, INTVL Number of output variables to print: IOTOT (up to 32)

Code relating output variables to print (8 = Hemispherical tilt, 9 = direct normal + circumsolar): OUT(8), OUT(9) [up to 32 spectral parameters available for output] Circumsolar calculation mode (1 = yes): ICIRC Receiver geometry—Slope, View, Limit half angles: SLOPE, APERT, LIMIT

Smooth function mode (0 = none): ISCAN (Gaussian and triangle filter shapes can be specified) Illuminance calculation mode (0 = none): ILLUM (Luminance and efficacy may be selected)

UV calculation mode (0 = none): IUV (UVA, UVB, action weighed dosages available) Solar geometry mode (2 = Air Mass): IMASS (zenith and azimuth, date/time/lat/long available) Air mass value: AMASS

Renewable Resource Data Center Spectral
Fig. 18. ASTM E490-00a extraterrestrial reference spectrum. The actual spectral data go out to 100,000 nm (100 microns). Inset shows details in the 250 nm to 2000 nm region.

1.80

1.80

Astm G173 Picture

0 500 1000 1500 2000 1500 3000 3500 4000

Wavelength (nm)

0 500 1000 1500 2000 1500 3000 3500 4000

Wavelength (nm)

Fig. 19. ASTM G173-03 Terrestrial reference spectra for Air Mmass 1.5, conditions specified in Table 2.

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