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Direct Solar Spectral Irradiance Measurements and Updated Simple Transmittance Models

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Direct Solar Spectral Irradiance Measurements and Updated Simple Transmittance Models MAY 1997 DE LA CASINIERE ET AL. 509 Direct Solar Spectral Irradiance Measurements and Updated Simple Transmittance Models A. DE LA CASINIEÁ RE,A.I.BOKOYE, AND T. C ABOT IRSA/Universite Joseph Fourier, Grenoble, France (Manuscript received 11 December 1995, in ®nal form 15 June 1996) ABSTRACT A set of 509 direct solar irradiance spectra, carefully measured over one year, is checked against spectral irradiances computed from ®ve updated transmittance models. The wavelengths under investigation range from 290 to 900 nm, with a 5- or 10-nm step. The parameters explored include the solar altitude angle, with a range from 138 to 688, and the standard Linke turbidity factor, with a range from 2.0 to 6.0. Measurement devices and experimental processes are described in detail in the paper. The comparison between measured and computed values is carried out by means of the relative mean bias error and the mean absolute relative error. These coef®cients are applied to ultraviolet-B and ultraviolet-A total irradiances, and to visible and near-IR spectral irradiances. No clear and systematic sensitivity of the models or measurements to the solar altitude and the turbidity parameters is observed. Of the ®ve models tested, three of them give mean coef®cient values between 7% and 16% in UV bands and between 5% and 9% in visible or near-IR bands. Adjusting factors for the elimination of the systematic differences that occur between the measurements and the computation results of the models are proposed. Comparisons with a radiative transfer code tend to prove the competitiveness of so-called updated transmittance models, which are very fast, and they are particularly suitable when large amounts of data have to be processed. 1. Introduction phase function. Moreover, these sophisticated codes are not always easy to implement as far as long-term or The two main ways generally used to model the solar routine measurements (which require that very large beam spectral irradiance at the ground are the atmo- numbers of spectra be processed) are concerned. Al- spheric transmittance method and the radiative transfer though direct irradiance transmittance models are by method. In the former the atmosphere is merely taken de®nition less exact, they are very short codes, whose as a one-layer medium attenuating the extraterrestrial inputs are easily obtainable from ground data. The sim- solar irradiance by means of ®ve or more identi®ed plicity of the hypothesis adopted for conceiving such scattering and absorption processes. The latter takes into models leads to errors, whose magnitudes remain un- account the vertical inhomogeneity of the atmosphere, known until direct irradiances computed from this meth- dividing it into a series of superposed scattering and od are checked against reliable measurements. This is absorbing layers that exchange radiative energy between particularly true in the case of very turbid atmospheres. themselves. Because it uses fundamental properties of The present work compares some updated spectral gases and aerosols, models based on the radiative trans- transmittance models with accurate spectral measure- fer method are often labelled as ``rigorous.'' Atmo- ments. It is based on 1 year of measurements carried spheric transmittance±based models that are worked out out in the town of Grenoble (458129N, 58439E and by means of parameterizations, such as that in Leckner 210-m altitude) under various conditions of atmospheric (1978), are justly considered to be approximate. turbidity. This industrial town of the French Alps suffers To be accurately used, the so-called rigorous radiative from strong pollution episodes, due to its location in a transfer models require highly restrictive inputs, such bowl-shaped valley surrounded by groups of mountains as the ozone and water vapor pro®les, the air density rising up to between 1000 and 2200 m. The wavelengths pro®le, and the size and altitude distribution of aerosols explored range from 290 to 900 nm, with a 5- or 10-nm with single scattering albedo and asymmetry factor or step. 2. Spectral transmittance models a. Atmospheric transmittances Corresponding author address: Dr. Alain de La CasinieÁre, IRSA/ Universite Joseph Fourier, 17, Quai Claude Bernard, Grenoble 38 It is commonly considered that the solar beam, along 000, France. its path through the atmosphere, is partially absorbed q1997 American Meteorological Society Unauthenticated | Downloaded 10/01/21 06:57 AM UTC 510 JOURNAL OF APPLIED METEOROLOGY VOLUME 36 and scattered by air molecules and solid or liquid sus- Iqbal (1983); ma is the relative optical air mass for local pended particles, the latter of which are usually called conditions, which is commonly approximated by means aerosols. It is well known that molecular absorption is of the relation discontinuous (depending on the wavelength of the in- m 5 m p/p , (6) cident radiation), while absorption by aerosols may be a r o considered to be continuous. The spectral transmittance where p is the local pressure and po is the standard models of the direct solar irradiances generally take into pressure. account both of these depletion phenomena by means Using Young's (1981) determination of the depolar- of ®ve distinct spectral atmospheric transmittances, ization factor and Peck and Reeder's (1972) formula for which are denoted by tol, twl, tgl, trl, and tal. They the refractive index of air, Gueymard (1994) developed refer, respectively, to the ozone absorption, water vapor by means of a least squares curve ®tting technique the absorption, uniformly mixed gases absorption (carbon following expression of Rayleigh scattering transmit- dioxide, oxygen, nitrogen dioxide, etc.), molecular scat- tance: tering (Rayleigh scattering), and absorption and scat- tering by aerosols (the latter of which is called Mie 2m t 5 expa , (7) scattering). For solar altitude g the direct spectral irradi- rl 42 22 12a1234l1al1a1al ance on a horizontal plane is then simply expressed as where a1 5 117.2594, a2 521.3215, a3 5 3.2073 3 Ihl 5 EoIol(sing)toltwltgltrltal. (1) 24 25 10 , and a4 527.6842 3 10 if wavelength l is in microns. Equation (7) improves the widely used Leck- Here, Iol is the extraterrestrial normal spectral irra- ner's (1978) Rayleigh transmittance relation, written as diance for the mean sun±earth distance, and Eo is the correction to the actual sun±earth distance. Due to a t 5 exp(20.008735l24.08m ). (8) lack of updated values published in the open literature, rl a the Iol values used in the present study are those of the The well-known AngstroÈm turbidity coef®cients a WRC spectrum recommended by FroÈhlich and Wehrli and b remain of great interest for simple transmittance (see Iqbal 1983) and adopted by the World Meteoro- models, although they are often regarded as outmoded logical Organization in 1981. when considering problems of atmospheric radiative When applied to ozone absorption, Bouguer's clas- transfer. Since attenuation effects of scattering and ab- sical attenuation law gives sorption by dust are dif®cult to separate, A. AngstroÈm proposed the following aerosol transmittance formula: tol 5 exp(2kollomo), (2) 2a tal 5 exp(2bl ma). (9) where kol is the ozone spectral absorption coef®cient, lo (cm NTP) is the amount of ozone, and mo is the The parameter b, which may vary from 0.0 to 0.5, relative optical mass for ozone. Although slightly de- is an index of the amount of aerosols present in a vertical pendent on temperature, the kol coef®cients are assumed column of the atmosphere. The parameter a is a reliable here to be constant, and the values chosen are those index of the size distribution of these aerosols (at least reported by Iqbal (1983) from Leckner (1978) and Vi- for particles of radii ranging from 0.1 to 1.0 mm), as groux (1953). indicated by the nephelometer measurements of Charl- Since the relative optical ozone mass mo is dif®cult son (1972). Generally, a has values of between 0.5 and to evaluate accurately, it is replaced by the relative optical 2.5, with a constant value of 1.3 being commonly used, air mass mr that Young (1994) wrote for sea level as as suggested by AngstroÈm. 2 mr 5 (1.002432 sin g 1 0.148386 sing 1 0.0096467) b. AngstroÈm coef®cients 3(sin32g 1 0.149864 sin g 1 0.0102963 sing 21 Several methods may be used to determine the co- 1 0.000303978) . (3) ef®cient b and even the coef®cient a. However, the Following Leckner (1978), the transmittances of wa- respective values obtained are different enough to lead ter vapor and of uniformly mixed gases are respectively to signi®cant discrepancies in Ihl values when the latter given by are reconstituted by means of Eq. (1). From the point of view of spectral solar irradiance modeling, the suit- t 5 exp[20.2385k wm (1 1 20.07k wm )20.45] wl wl r wl r able a, b couple is obviously that that results in the best (4) ®t between calculated and measured spectra when mea- and surements are presumed accurate. In the present study, ®ve distinct methods for deter- t 5 exp[21.41K m (1 1 118.93K m )20.45], (5) gl Gl a Gl a mining b and a were selected. Three of them only re- where w is the precipitable water. Here, kwl is the water quire knowledge of the direct solar total irradiance data, vapor absorption coef®cient and KGl is the mixed gases while the other two need one or two spectral irradiance absorption coef®cient, values of which are reported by measurements. Unauthenticated | Downloaded 10/01/21 06:57 AM UTC MAY 1997 DE LA CASINIERE ET AL.
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