UPDATED TRANSMITTANCE FUNCTIONS FOR USE

Proceedings of the 23rd American Solar Energy Society Annual Conference, San Jose, CA, June 1994

UPDATED TRANSMITTANCE FUNCTIONS FOR USE IN FAST SPECTRAL DIRECT BEAM IRRADIANCE MODELS

C. Gueymard Florida Solar Energy Center 300 State Road 401 Cape Canaveral, FL 32920

ABSTRACT

New spectral transmittance functions are introduced for the main extinction processes in the atmosphere for shortwave direct beam radiation: Rayleigh scattering, aerosol extinction, and absorption by ozone, uniformly mixed gases, water vapor, and NO2. The latter extinction effect (in the UV and visible) is introduced for the first time in a simple spectral model. Along with an improved extraterrestrial solar spectrum at 1 nm intervals below 1700 nm, these functions constitute a spectral radiation model called SMARTS2. It can be easily compared to measured data when using its circumsolar correction and smoothing functions. A preview of broadband applications of this new model is also provided, through the derivation of improved estimates of the luminous efficacy used in daylighting calculations. 1. INTRODUCTION

Spectral solar irradiance models are needed in a variety of applications spread among different disciplines such as atmospheric sciences, biological sciences and energy technologies (PV systems, high performance glazings, daylighting, selective coatings, etc.). Two types of spectral irradiance models may be used to predict or analyze solar radiation at the Earth’s surface: sophisticated rigorous codes and simple transmittance parameterizations. A well known example of the first kind is the LOWTRAN family, which originated more than 20 years ago. It has been recently supplanted by an even more detailed code called MODTRAN [1]. Such a model considers that the atmosphere is constituted of different layers, and uses reference or measured vertical profiles for its gaseous and aerosol constituents. Because of the detailed inputs needed, execution time, and some output limitations, MODTRAN is not an appropriate code for all applications, particularly in engineering. Most

of the latter needs are presently fulfilled by parameterized models which are relatively simple compared to MODTRAN. Most of the simple models that have appeared in the literature since the early '80s [2-8] are based on Leckner’s landmark contribution [9]. For computerized calculations, SPCTRAL2 [10], based on [2, 3], and SUNSPEC [11], based on [5], are frequently used. (SUNSPEC is being revised in accordance with the algorithms presented here.) They are both based on Leckner’s functions, at least for the determination of water vapor, mixed gases, and ozone absorptances. Much fundamental knowledge on gaseous absorption has been added since Leckner’s contribution, so that a detailed reexamination of his approach appears now justified. Furthermore, data of higher spectral resolution is now available, improving accuracy in those spectral regions where gaseous absorption changes rapidly, as will be shown. This paper will present SMARTS2, an extensive revision of the algorithms used to calculate direct beam radiation with SMARTS, a spectral model that was presented recently [5]. In short, the main objectives and achievements of this study are: • Introduce new transmittance functions for all the atmospheric extinction processes • Add nitrogen dioxide (NO 2) to the list of absorbers, for the first time in this type of model • Derive very accurate absorption coefficients from recent spectroscopic data • Improve the spectral resolution of calculations • Improve the extraterrestrial spectrum • Add the capability to estimate the circumsolar enhancement factor for comparison with pyrheliometric data • Add the flexibility to smooth the output data using a Gaussian filter function.

Because of the complexity of its algorithms and space limitation, only an outline of the derivation will be given, as well as limited comparisons with MODTRAN2 and experimental data to assess its performance. Details of the derivation of SMARTS2 may be found in [12]. Finally, an application of this model in daylighting calculations is outlined in Section 7, while other applications are detailed in [13].

3. INDIVIDUAL TRANSMITTANCES

2. MODEL STRUCTURE AND SOLAR SPECTRUM

Under cloudless sky conditions, direct beam radiation constitutes the major part of the incoming shortwave radiation. Moreover, its measurement can be used to derive information on atmospheric conditions (e.g., gaseous abundance and turbidity) by comparison with model calculations run backwards. (Such a technique based on the present work is being developed [14].) For these reasons, all that follows is concerned with direct beam radiation. However, SMARTS2 also has provision to calculate diffuse radiation on a horizontal or tilted plane, using the methodology described in [12]. The beam irradiance received at ground level by a surface normal to the sun rays (or “beam normal irradiance”) at wavelength λ is given by: Ebnλ = Eonλ TRλ Taλ Tgλ Toλ Tnλ Twλ

SPCTRAL2. This certainly gives a rather high resolution for engineering use, but the model output (transmittances and irradiance) can be downgraded afterwards according to the user’s needs (see Section 5). The different optical masses, which play a key role in the transmittance functions, have already been described [5, 16].

(1)

where Eonλ is the extraterrestrial irradiance corrected for the actual sun-earth distance and the other terms are the transmittances for the different extinction processes considered here: Rayleigh scattering, aerosol extinction, and absorption by uniformly mixed gases, ozone, NO 2, and water vapor, respectively. Note that NO2 absorption in the UV and visible is introduced here for the first time in a simple spectral irradiance model. It is not even considered yet in MODTRAN2. (The latest version used here was kindly provided in August 1993 by Jim Chetwynd, Phillips Lab.) Whereas SMARTS1 used the WRC85 spectrum [15], SMARTS2 uses a slightly modified spectrum, at 1 nm intervals between 280 and 1700 nm, and at 5 nm intervals between 1700 and 4000 nm. The total irradiance is 1350.0 W/m2, compared to 1349.5 W/m2 for the WRC85 spectrum, for a solar constant of 1367 W/m2. This new spectrum is justified because (i) Some problems were discovered in the WRC85 spectrum, including an anomalous dip in the 920980 nm range [personal communications with Claus Fröhlich, 1992, and Eric P. Shettle, 1993]; (ii) New high altitude balloon and satellite data have been published recently, particularly in the UV. The new spectrum has a total of 1881 wavelengths, compared to 545 wavelengths for the spectrum used in SMARTS1 and 122 wavelengths used in

• Rayleigh scattering: The Rayleigh optical depth has been recalculated from its theoretical expression, using Young’s determination of the depolarization factor [17] and Peck & Reeder’s formula [18] for the spectral variation of the refractive index. A least-squares curve fitting technique was used to develop the following equation: TRλ = exp[-mR P / (a1 λ4 + a2 λ2 + a3 + a4 λ−2)]

(2)

where m R is the optical air mass, P is the ratio of the site pressure to the standard value (1013.25 mb), a1= 117.2594, a2=-1.3215, a3=3.2073E-4 and a4=-7.6842E-5. Eqn. (2) fits the basic spectral calculations with an average deviation of less than 0.01%. • Ozone absorption: The Bouguer law is used to describe ozone absorption, i.e. Toλ = exp(-mo uo Aoλ)

(3)

where mo is the ozone optical mass, uo its reduced pathlength (in atm-cm), and Aoλ its spectral absorption coefficient. Ozone absorbs strongly in the UV, moderately in the visible, and slightly in the near infrared. In the UV (HartleyHuggins bands), recent spectroscopic data [19-21] were smoothed to 1 nm resolution for the region 280–365 nm. The basic absorption coefficients are for a reference temperature of 228 K and a temperature correction is applied (if λ