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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 13Њ to 68Њ, 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 (45Њ12ЈN, 5Њ43ЈE 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
᭧1997 American Meteorological Society
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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 ϭ 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 o, w, g, r, and a. 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 Ϫm ϭ expa , (7) scattering). For solar altitude ␥ the direct spectral irradi- r 42 Ϫ2 a1234ϩaϩaϩa ance on a horizontal plane is then simply expressed as where a1 ϭ 117.2594, a2 ϭϪ1.3215, a3 ϭ 3.2073 ϫ Ih ϭ EoIo(sin␥)owgra. (1) Ϫ4 Ϫ5 10 , and a4 ϭϪ7.6842 ϫ 10 if wavelength is in microns. Equation (7) improves the widely used Leck- Here, Io 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 ϭ exp(Ϫ0.008735Ϫ4.08m ). (8) lack of updated values published in the open literature, r a the Io values used in the present study are those of the The well-known AngstroÈm turbidity coef®cients ␣ WRC spectrum recommended by FroÈhlich and Wehrli and  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: o ϭ exp(Ϫkolomo), (2) Ϫ␣ a ϭ exp(Ϫ ma). (9) where ko is the ozone spectral absorption coef®cient, lo (cm NTP) is the amount of ozone, and mo is the The parameter , 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 ko coef®cients are assumed column of the atmosphere. The parameter ␣ 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 m), as groux (1953). indicated by the nephelometer measurements of Charl-
Since the relative optical ozone mass mo is dif®cult son (1972). Generally, ␣ 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 ϭ (1.002432 sin ␥ ϩ 0.148386 sin␥ ϩ 0.0096467) b. AngstroÈm coef®cients ϫ(sin32␥ ϩ 0.149864 sin ␥ ϩ 0.0102963 sin␥
Ϫ1 Several methods may be used to determine the co- ϩ 0.000303978) . (3) ef®cient  and even the coef®cient ␣. 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 Ih 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- ϭ exp[Ϫ0.2385k wm (1 ϩ 20.07k wm )Ϫ0.45] w w r w r able ␣,  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- ϭ exp[Ϫ1.41K m (1 ϩ 118.93K m )Ϫ0.45], (5) g G a G a mining  and ␣ were selected. Three of them only re- where w is the precipitable water. Here, kw is the water quire knowledge of the direct solar total irradiance data, vapor absorption coef®cient and KG is the mixed gases while the other two need one or two spectral irradiance absorption coef®cient, values of which are reported by measurements.
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1) METHOD L T Ϫ 0.1 Ϫ (␥ ϩ 85) 1  ϭ L . (13) The L of method L stands for ``Louche±Bird.'' With []39.5 exp(Ϫw) ϩ 47.4 16 ϩ 0.22w the help of the Bird and Hulstrom (1981a,b) parame- terization of the direct solar total irradiance, Louche et al. (1987) obtained the following explicit expression for 4) METHOD U : The U in method U stands for ``two usual wave- 1 C lengths.'' The two parameters  and ␣ can be simul-  ϭ ln , (10) taneously determined by using a dual-wavelength sun- mD A B a Ϫ Ј photometer. Such a device actually measures the beam where spectral irradiances I1 and I2 at the two wavelengths and , where molecular absorption is either absent I 1 2 A ϭ n , or weak. The values considered as the two usual wave- 0.975EIo scowgr lengths are 1 ϭ 0.38 m and 2 ϭ 0.50 m. Conse- quently,  and ␣ may be easily obtained by solving the B 0.12445 0.0162, Јϭ ␣ Ϫ following system of equations:
C ϭ 1.003 Ϫ 0.125␣, Ϫ␣ I1 ϭ EoIo1r1exp(Ϫ1 ma) D ϭ 1.089␣ ϩ 0.5123. (11) and Here, I is the normal total irradiance, which may be n I ϭ E I exp[Ϫ Ϫ␣ m ]. (14) measured either directly by means of a pyrheliometer 2 o o2 r2 2 a or indirectly by using a pyranometer and a diffusometer; Nevertheless, the ␣ and  values depend signi®cantly
Isc is the solar constant, and o, w, g, and r are the on the choice of the wavelength pair (1, 2). Further- total atmospheric transmittances of the Bird and Hul- more, the two usual wavelength values given above are strom (1981a,b) formulation summarized by Iqbal not the best for calculating realistic aerosol transmit- (1983) as parameterization model C. When the value of tances, as was observed by Cachorro et al. (1987). the AngstroÈm coef®cient ␣ is known,  can be calcu- By assuming that ␣ ϭ 1.3, the parameter  can be lated from Eqs. (10) and (11) using the measured In determined alone from a single-wavelength sunphoto- value and an assessed value for the atmospheric pre- meter. It can even be directly obtained at ϭ 1 m, in cipitable water. which case ␣ plays no part in the calculations; however, the measurement device used in this study cannot reach this wavelength. 2) METHOD I
The I of method I stands for ``IRSA Research Team.'' 5) METHOD G Grenier et al. (1994) developed a new coef®cient stan- dardized at an air mass of 2, nearly independent of the The G in method G stands for ``Gueymard.'' From relative optical air mass and referred to as TLAM2, from unpublished spectral measurements, Bird (1984) ob- a spectral model of Linke's turbidity factor TL. The TL served that turbidity versus wavelength often exhibits values classically obtained from In measurements can a curvelike relationship on a log±log plot. As a result, be converted into TLAM2 by means of an algorithm. Fur- he introduced the following multiterm formulation for thermore, these authors proposed a polynomial for con- aerosol transmittance: verting T into when precipitable water w can be Ϫ␣ LAM2  ϭ exp(Ϫ nm ), (15) assessed, which is expressed as a n a where n and ␣n are constants whose values change at 13 ϭ 0.5 m. Nicholls (1984) simultaneously derived ϭb(w)(jiT ) . (12) ij LAM2 the dependence of the parameter ␣ on the wavelength. iϭ0[]jϭ0 More recently, in the beam spectral irradiance model
The coef®cients bij are calculated with ␣ ϭ 1.3 and called SMARTS2, Gueymard (1993a, 1994) expressed lo ϭ 3 mm. the turbidity as Eq. (15) using, as Bird (1984) did, two
different values for ␣: ␣1 for Ͻ 0.5 m and ␣2 for Ͼ 0.5 m. On the other hand,  is taken as independent 3) METHOD D of wavelength and is derived from The D in method D stands for ``Dogniaux.'' Dogniaux  ϭ 0.5␣2 . (16) (1975) developed the following relationship, reported 5 by Page (1986), from a statistical analysis of the many The determination of 5, the aerosol optical thickness  values determined in meteorological stations (by at 0.5 m, requires a beam spectral irradiance mea- means of pyrheliometers ®tted with standard color ®lters surement. Typical values of coef®cients ␣1 and ␣2 are such as OG1, RG2, and RG 8): presented in Table 1; these were obtained by linearly
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TABLE 1. Typical values of coef®cients ␣1 and ␣2 used in TABLE 2. Number of spectra respectively recorded in the various method G. classes with the corresponding mean solar altitude angle in degrees (in parentheses). Humidity T 0% 50% 70% 90% 99% LAM2 ␥ 2.0±3.0 3.0±4.0 4.0±5.0 5.0±6.0 ␣1 0.933 0.932 0.928 0.844 0.659
Rural ␣2 1.444 1.441 1.428 1.377 1.134 10Њ±20Њ 24 (17.6) 13 (17.1) 0 0
␣1 0.822 0.827 0.838 0.779 0.492 20Њ±30Њ 77 (25.3) 22 (24.7) 8 (27.1) 0
Urban ␣2 1.167 1.171 1.186 1.256 1.127 30Њ±40Њ 39 (34.4) 49 (35.4) 8 (36.1) 10 (36.3)
␣1 0.468 0.449 0.378 0.232 0.107 40Њ±50Њ 23 (45.6) 36 (45.5) 18 (44.7) 11 (45.6)
Maritime ␣2 0.626 0.598 0.508 0.246 0.053 50Њ±60Њ 16 (53.1) 34 (54.5) 29 (54.6) 9 (55.6)
␣1 1.010 1.008 1.005 0.911 0.797 60Њ±70Њ 0 26 (64.9) 38 (64.6) 19 (64.5)
Troposphere ␣2 2.389 2.379 2.357 2.130 1.962
a very sensitive function of coef®cient . Thus in Eq.
®tting the spectral aerosol coef®cients of four aerosol (1), the transmittance a may be considered as the gov- types (rural, urban, maritime, and tropospheric) used in erning term, while o, r, w, and g, whose variations Shettle and Fenn's (1979) MODTRAN code for relative with time are generally weak or limited to narrow wave- humidities between 0% and 99%. length bands, may be regarded as secondary terms. Therefore, the direct solar spectral irradiance models of transmittance tested here have a common part, which c. Description of the models is the product EoIo(sin␥)owgr calculated from Atmospheric turbidity is a highly variable parameter Eqs. (2), (4), (5), and (7), and a separate part, which is that depends on location and season. As an example, a. The latter is respectively obtained by means of the the Linke's turbidity factor in the town of Grenoble may ®ve distinct methods described above. The model using vary over the year between 2 and 6. Moreover, aerosol method L, for example, is simply referred to as model optical thickness is, over the wavelength range studied, L and so on.
FIG. 1. RMBE and MARE variations as functions of solar altitude angle for models L, I, D, U, and G in the UVB band.
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FIG. 2. RMBE and MARE variations as functions of solar altitude angle for models L, I, D, U, and G in the UVA band.
3. Measurement devices and processes The variations of the c(␥, ) factor with ␥ and were The spectral measurements were carried out using as previously determined by means of laboratory optical receiver of the solar radiations an axisymmetrical ¯at- methods for 16 angles of incidence between 0Њ and 80Њ plate UV diffuser, namely the 200±1100-nm Opal sold (within an error of 0.1Њ) and for 123 wavelengths rang- , ) mea- by the ®rm Oriel. This diffuser, whose receiving face ing from 290 to 900 nm. Four series of c(␥ surements were carried out over 2 years; the mean dis- is horizontal and may be shaded with a moving disk, crepancies observed in the respective results were only collects the solar radiation coming down from 2 sr. The collected ¯ux is transmitted by a 3-m-long UV optic 1%, and the maximum differences obtained reached 2%. ®ber bundle cable to the inlet slit of a double mono- The calibration coef®cient values at normal inci- ), were determined using a 250-W halogen chromator ®tted with two holographic gratings and a dence, k(0, lamp as a standard, operated with a regulated power photomultiplier detector. The spectral range under in- supply. Unfortunately, it turned out that calibration re- vestigation is 290±900 nm, with a step width of 5 nm. sults were sensitive to the temperature level of the de- Since a diffuser is never fully cosine true, a correction tection device. Therefore a systematic study of k(0, ) factor called spectral relative cosine response has to be as a function of such temperatures was undertaken, lead- applied to the electric signal V(␥) yielded by the pho- tomultiplier detectors (de La CasinieÁre et al. 1995). This ing to the following corrective algorithm: factor is de®ned as the ratio k(0, )/k(, ) for a beam k(0, ) ϭ A(t)k(0, )ref ϩ B(t), (18) angle of incidence . The terms k(0, ) and k( , ) are where k(0, ) is a ®xed reference, while A(t) and B(t) the angular coef®cients of calibration corresponding to ref are linear functions of temperature, valid between 20Њ the angles of incidence 0 and , respectively. Conse- and 30ЊC. No signi®cant aging effect could be detected quently the spectral relative cosine response is depend- on k(0, ) values over the 1-yr measurements. ant on the solar height angle and, therefore, is referred ␥ In Eq. (17), V (␥) is indirectly determined by assum- , ). The horizontal direct spectral irradiance to as c(␥ ing it to be the difference of the two respective signals may thus be written as obtained when simultaneously measuring global and
Ih ϭ k(0, ) V(␥)/c(␥, ). (17) diffuse horizontal spectral irradiances. Because such si-
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FIG. 3. RMBE and MARE variations as functions of solar altitude angle for models L, I, D, U, and G in the VIS band. multaneous measurements are impossible to carry out itable water content of the atmosphere. The equations with one spectral chain only, the global signal is re- used are those recommended by Gueymard (1993b): placed by the mean value of the two global signals w ϭ 0.1H (19) supplied just before and after the diffuse measurement. w v Diffuse spectral irradiance measurements are carried out and using the moving disk, which shades the diffuser with Hw ϭ 0.4976 ϩ 1.5265t ϩ exp(13.6897t Ϫ an 11Њ aperture angle cone in the sun direction. 14.9188t3), (20) The solarimeters used for total irradiance measure- ments are class 1 Kipp and Zonen pyranometers (type where the precipitable water w is in centimeters and the CM 11). These pyranometers were carefully calibrated surface water vapor density v is in grams per cubic simultaneously at the same site. The reference used was meter. Here, Hw is the apparent water vapor scale height a CM 11 previously checked by the French National (km) and t is the ratio of the ambient temperature (K) Meteorology Department in the Radiometric Center of to 273.15. Carpentras. The total direct irradiance is then deter- The amount of atmospheric ozone is obtained from mined by taking the difference between simultaneous Dobson's spectrometer measurements made at the total global and total diffuse irradiance measurements. Haute-Provence Observatory (OHP), which is located The latter is done by means of a shadow ring and by about 150 km from the Grenoble site. using a correction factor based on a clear-sky radiance distribution model (Page 1986) to take into account the 4. Methods of analysis anisotropy of sky radiance. From total direct irradiance data, it is possible to calculate Linke's turbidity factor a. Statistical tests and to determine, by means of methods L, I, or D, the To compare the measured values of direct horizontal  AngstroÈm coef®cient for ␣ ϭ 1.3. spectral irradiance with those that are computed by Ambient temperature and relative humidity at the sur- means of models L, I, D, U, and G, one of two methods face are also recorded with probes to assess the precip- is used, depending on the wavelength bands considered.
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FIG. 4. RMBE and MARE variations as functions of solar altitude angle for models L, I, D, U, and G in the NIR band.
In the ultraviolet-B(UVB) band (0.28±0.32 m) the and ``mixed gases'' cause considerable discontinuous spectral signals are generally very weak in the lower absorptions, Ih has rather slow variations as a function wavelengths. To avoid the risk of working with data that of . Consequently applying the above two tests directly may be too inaccurate, it was decided to study only the to the discrete spectral irradiances appeared to be con- total irradiance of this band (W mϪ2). The same was sistent. Thus, for N distinct spectra with n spectral ir- applied to the ultraviolet-A (UVA) band (0.32±0.39 radiances in the given band, the ``mean'' RMBE and m). Considering a set of N distinct spectra, the fol- the mean MARE can be expressed, as percentages, as lowing relation for the classical relative mean bias error follows: (RMBE), de®ned as a percentage, can be used: 100Nn 1 I Ϫ I 100 N B Ϫ B RMBE ϭ hcij hmij (23) ci mi RMBE ϭ , (21) Nni1 j1 I ϭϭ hmij NBiϭ1 mi and where Bmi and Bci are, respectively, the measured and computed UVB or UVA band total irradiances. To assess 100Nn 1 I Ϫ I the mean discrepancies between computed and mea- MARE ϭ hcij hmij . (24) sured total irradiances, the following relation for the Nniϭ1jϭ1ΗΗ Ihmij mean absolute relative error (MARE) is used: In our experiment n ϭ 60 for the visible band (VIS) 100 N B Ϫ B and n ϭ 13 for the near-infrared band cut at 0.90 m MARE ϭ ci mi . (22) (NIR). Here, Ihmij and Ihcij are the measured and the NBi1ΗΗ ϭ mi computed direct horizontal spectral irradiances, respec- In the visible band (0.39±0.77 m), as well as in the tively, which are numbered as j in the considered band near-infrared band (0.77±0.90 m), the signals supplied and belong to the spectrum number i. Although RMBE are suf®ciently high to generally produce accurate re- and MARE deal with spectral irradiances, they also pro- sults. Except in the few narrow bands where water vapor vide an assessment of the discrepancies between mea-
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FIG. 5. RMBE between pyranometric measurements and integrated spectra of L, I, D, U, and G models and new models (i.e., with adjusting factors). sured and computed total irradiances of VIS and NIR ferences are a sure indication of their irrelevance. As bands. the bandpass of glass dome pyranometers is approxi- To summarize, while MARE and MARE give the mean mately 0.3±3.0 m, they are generally calibrated with absolute differences between the measurements and com- a corrected coef®cient to take into account the overall putation results of the models, RMBE and RMBE quan- solar spectrum. The computed spectrum was integrated tify the tendency of these various models to either un- at up to 10.0 m (the part of the solar constant corre- derestimate or overestimate the experimental results. sponding to higher wavelengths is only 0.05% of the Thus, when only occasional irradiance spectra are need- total). ed, the models to be used for predicting the measurements are those with the lowest MARE or MARE values. Con- versely, for predicting the measured long-term spectral 5. Results irradiations, which necessarily involve a great number of a. Class by class results irradiance spectra, the most suitable models are those with the lowest RMBE or RMBE values. The present work was carried out with a total of 509 direct irradiance spectra recorded over 1 year (from May 1994 to April 1995). The solar altitude angle ␥ ranged b. Test of irrelevance from 13Њ to 68Њ, and the standard Linke turbidity factor
In addition to this, a test of irrelevance may be carried TLAM2 varied from 2.0 to 6.0. out on the computed direct spectral irradiances. Such a To compare the measurements with the model results, test merely consists of comparing the direct total irra- 24 distinct spectrum classes were established, depending diance measured using the two pyranometers with that on solar altitudes and on standard turbidity values. The obtained by integrating the calculated spectra over the ␥ ranges considered were, respectively, 10Њ±20Њ,20Њ± same wavelength range. Because computed spectra may 30Њ,30Њ±40Њ,40Њ±50Њ,50Њ±60Њ, and 60Њ±70Њ, while be distorted, a close coincidence cannot irrefutably those of TLAM2 were 2.0±3.0, 3.0±4.0, 4.0±5.0, and 5.0± prove that the tested models are good. But large dif- 6.0. Table 2 gives the number N of spectra recorded in
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FIG. 6. RMBE, MARE, RMBE, and MARE values over all recorded spectra, independant of solar altitude angle and turbidity. New MARE and MARE values (i.e., with adjusting factors). each class and, in parentheses, the mean solar altitude ly in¯uenced by solar altitude, at least over the tested value ␥ of the N spectra in the considered class. When range. Identical conclusions may be drawn about the the number N was too low (Ͻ5), the corresponding class possible dependence of these factors on the turbidity was not taken into account and N was replaced by a level. On the other hand, a rough hierarchy is observed zero in the table. between the various models concerning their ability to Values of RMBE and MARE or of RMBE and MARE predict the measurements as they were obtained: model for the ®ve models are given in Figs. 1±4. These values D outputs are always far from the experimental data, were calculated for the four TLAM2 ranges in each one while the other four give almost the same results. of the UVB, UVA, VIS, and NIR bands de®ned above, The irrelevance test results presented in Fig. 5 show and they are presented as a function of ␥. Taking, for that the RMBE of integrated spectra versus pyrano- example, the graphs 2.0 Ͻ TLAM2 Ͻ 3.0 in Figs. 1±4, metric data does not exceed 5% for models L and I, each point at 20ЊϽ␥Ͻ30Њ was calculated using N ϭ which is quite satisfactory. The values of this coef®cient 77 spectra, as shown in Table 2 (which also gives the are between 5% and 10% for model G, they range from common abscissa of these points, ␥ ϭ 25.3Њ). In the 5% to 15% for model U, and are lower than 20% for UVB band the mean values of measured spectral irra- model D. diances may sometimes fall below 5 W mϪ2 mϪ1. Therefore, to avoid any possibly inaccurate results, some classes (which generally correspond to low solar b. Results for all classes heights) were not taken into account. In this way, the To clarify the hierarchy observed, an analysis of all total number of useful spectra was reduced to 424 for the spectra recorded is presented in Fig. 6 for the UVB, the UVB study. UVA, VIS, and NIR bands. The main conclusions that The RMBE, MARE, RMBE, and MARE variations can be drawn are as follows. plotted in Figs. 1±4 do not reveal a clear and systematic sensitivity to ␥. Thus it can be seen that neither the R Of the three models requiring only total irradiance quality of measurements nor the model results is strong- data input (L, I, and D), model L best predicts the
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FIG. 7. Samples of measured and predicted irradiance spectra (models L, I, and G) for various solar altitude angles and various turbidity values.
measured long-term spectral irradiations in the four c. Adjusting factors bands considered; for occasional irradiance spectra Due to the great number of spectra used for carrying models, L and I may be considered to be fairly equiv- out the above study, RMBE and RMBE values obtained alent. In any case, model D is not suitable. in Fig. 6 may be regarded as systematic differences R Models G and U, which require, respectively, one and between measurements and model results. Consequent- two pieces of spectral irradiance data as input, are ly, UVB and UVA direct total irradiances computed almost equivalent for predicting occasional measure- from the various models will more closely approach the ments of irradiance, but when long-term irradiation measured irradiances when multiplied by the factor (1 predictions are needed, model G gives closer results Ϫ RMBE/100). The same is true for computed spectral than model U in all bands. R irradiances of VIS and NIR bands if they are multiplied Except in the NIR band, model G appears to be the by the factor (1 Ϫ RMBE/100). Table 3 gives these best of the ®ve models for both irradiance and irra- adjusting factors for the ®ve models in the four consid- diation prediction. ered wavelength bands. The new MARE and MARE Nevertheless, it can be seen that the results given by values (reported in Fig. 6) thus obtained when using models L and I are not so far from those of models G such factors show that the outputs of all models are or U. Since the spectral irradiance measurements needed improved, even those of model D, which become sur- by models G and U are generally more dif®cult and prisingly good. In so far as using Table 3 factors is justi®ed (as suggested by the improvement also ob- expensive to obtain than total irradiance measurements, served in Fig. 5 on irrelevance tests), the new conclu- L and I actually remain quite competitive models. Figure sions to be drawn are as follows. 7 shows some examples of typical spectra of direct hor- izontal irradiance measured over the four ranges of R The three models L, I, and D, which require only total
TLAM2 values and the corresponding spectra predicted by irradiance data as input, give equivalent results. means of models L, I, and G. R Models G and U, which need one and two spectral
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TABLE 3. Adjusting factors to be applied to computed irradiances to eliminate the systematic differences observed between the mea- surements and the results of the various models. Model L I DUG UVB 1.08 1.14 0.79 1.14 0.96 UVA 1.07 1.13 0.82 1.05 0.97 VIS 1.02 1.05 0.87 0.93 0.96 NIR 0.99 1.01 0.91 0.91 0.96
irradiance measurements, respectively, are almost al- ways equivalent and are the best ones.
6. Measurements and radiative transfer codes The ambition behind the present study is mainly to assess the differences to be expected between trans- mittance models that require very simple inputs and careful measurements. One of these models, at least, was checked successfully against radiative transfer codes such as BRITE and LOWTRAN 7 (Gueymard 1993). Therefore, as the ®ve models tested give roughly similar results, there must not be any important dis- crepancies between radiative transfer code results and the measurements made. Nevertheless, few systematic comparisons between the so-called rigorous codes and measured spectra have been undertaken up to now (Ca- chorro et al. 1994). A quick test was thus achieved using an upgraded version of the 5S radiative transfer code developed by the Laboratoire d'Optique AtmospheÂrique (Tanre et al. 1990) and widely used in France. Ten mea-
sured spectra belonging to the class (␥ ϭ 40Њ±50Њ, TLAM2 ϭ 3.0±4.0), which correspond to typical conditions, were checked against this code in the range of 320±900 nm (5S was not designed for the UVB). The required inputs were aerosol optical depth at 550 nm, atmo- spheric water vapor, and ozone contents. The results shown in Fig. 8 on one hand con®rm that 5S code and measurements are in good agreement (RMBE and MARE Ͻ 5%), and on the other hand they prove that the transmittance models tested are quite competitive.
7. Conclusions Despite their simplicity, updated transmittance mod- els of direct solar spectral irradiances are able to provide results that are reasonably close to very careful mea- surements carried out by means of expensive devices. For example, for the three models L, I, and G, the FIG. 8. RMBE, MARE, RMBE, and MARE values over ten spectra MARE corresponding to total UVB and UVA irradi- of the class (␥ ϭ 40Њ±50Њ and TLAM2 ϭ 3.0±4.0) for new models L, I, D, U, and G (i.e., with adjusting factors) and 5S radiative transfer ances ranged from 7% to 16%, while the MARE ob- code. served on spectral irradiances in VIS and NIR bands was between 5% and 9%. If one uses the adjusting factor values proposed in section 4, the MARE or MARE rates are signi®cantly reduced for all models, with the new
Unauthenticated | Downloaded 10/01/21 06:57 AM UTC 520 JOURNAL OF APPLIED METEOROLOGY VOLUME 36 values ranging from 4% to 14% in the UV bands and in Los Angeles smog aerosol. J. Colloid Interface Sci., 39, 240± from 4% to 8% in the VIS and NIR bands. 265. de La CasinieÁre, A., T. Cabot, and S. Benmansour, 1995: Measuring In the end, with transmittance models such as L, I, diffuse solar irradiance with non-cosine ¯at-plate diffusers. Sol. or D, which require only classical meteorological data Energy, 54, 173±183. as inputs, accurate solar spectra are made available in Dogniaux, R., 1975: Variations geÂographiques et climatiques des ex- a simple form to users that are not specialists of solar positions eÂnergeÂtiques solaires sur des surfaces reÂceptrices hor- izontales et verticales. Tech. Rep. Misc. B38, Institut Royal MeÂ- spectral measurements. Furthermore, such models are teÂorologique, Uccle, Belgium. [Available from Kon. Meteo In- so fast that they enable a quite inexpensive processing stitute, Ringlaan 3, 1180 Brussels, Belgium.] of very large numbers of spectra. These features open Grenier, J. C., A. de La CasinieÁre, and T. Cabot, 1994: A spectral new prospects in biology and agronomy, where contin- model of Linke's turbidity factor and its experimental implica- tions. Sol. Energy, 52, 303±313. uous solar spectral measurements would have to be Gueymard, C., 1993a: Development and performance assessment of made to investigate, for example, the long-term radia- a clear sky spectral radiation model. Proc. Solar'93-22 d ASES tion effects on vegetation in critical zones such as moun- Conf., 433±438. tains and deserts; the same is true in medicine, where , 1993b: Atmospheric turbidity and precipitable water data for Canada. 19th Annual Conf., Solar Energy Society of Canada, people's exposure to the sun has to be better controlled Quebec, Canada, L7±L12. to avoid serious health problems in the future. , 1994: Updated transmittance functions for use in fast spectral direct beam irradiance models. Proc. 23d ASES Conf., San Jose, CA, ASES, 1±6. Acknowledgments. J. Fourier-Grenoble I University Iqbal, M., 1983: An Introduction to Solar Radiation. Academic Press, has to be thanked for its indirect but highly effective 390 pp. support. In addition we wish to acknowledge Dr. J. Len- Leckner, B., 1978: The spectral distribution of solar radiation at oble and Dr. M. Fily of Centre Nationale de la Recherche earth's surfaceÐElement of a model. Sol. Energy, 20, 143±150. Louche, A., M. Maurel, G. Simonnot, G. Peri, and M. Iqbal, 1987: Scienti®que (France) for their help, particularly in using Determination of AngstroÈm's turbidity coef®cient from direct the 5S code. total solar irradiance measurements. Sol. Energy, 38, 89±96. Nicholls, R. W., 1984: Wavelength-dependent spectral extinction of atmospheric aerosols. Appl. Opt., 23, 1142±1143. REFERENCES Page, J. K., 1986: Prediction of Solar Radiation on Inclined Surfaces. Solar Energy R&D in the European Community Series F, Solar Radiation Data, Vol. 3, D. Reidel, 459 pp. Bird, R. E., 1984: A simple solar-spectral model for direct-normal Peck, E. R., and K. Reeder, 1972: Dispersion of air. J. Opt. Soc. and diffuse horizontal irradiance. Sol. Energy, 32, 461±471. Amer., 62, 958±962. , and R. L. Hulstrom, 1981a: Direct insolation models. Trans. Shettle, E. P., and R. W. Fenn, 1979: Models of the aerosols of the ASME J. Sol. Energy Eng., 103, 182±192. lower atmosphere and the effects of humidity variations on their , and 1981b: A simpli®ed clear sky model for direct and optical properties. Air Force Geophysics Lab., Rep. AFGL-TR- diffuse insolation on horizontal surfaces. SERI/TR, 642±761. 79-0214, Air Force Geophysics Laboratory, Hanscom Air Force [Available from Solar Energy Research Institute, Golden, CO Base, MA, 94 pp. 80401.] TanreÂ, D., C. Deroo, P. Duhaut, M. Herman, J. J. Morcrette, J. Perbos, Cachorro, V. E., and J. L. Casanova, 1987: The in¯uence of AngstroÈm and P. Y. Deschamps, 1990: Description of a computer code to parameters on calculated direct solar spectral irradiances at high simulate the satellite signal in the solar spectrum: The 5S code. turbidity. Sol. Energy, 39, 399±407. Int. J. Remote Sens., 11, 569±668. , A. M. de Frutos, P. Utrillas, and J. A. Martinez-Lozano, 1994: Vigroux, E., 1953: Contribution aÁl'eÂtude expeÂrimentale de l'absorp- Measurement and modelled data of solar spectral global, direct, tion de l'ozone. Ann. Phys., 8, 709±762. and diffuse radiation at Valencia (Spain). Proc. SPIE, 2309, 306± Young, A. T., 1981: On the Rayleigh-scattering optical depth of the 317. atmosphere. J. Appl. Meteor. 20, 328±330. Charlson, R. J., 1972: Multiwavelength nephelometer measurements , 1994: Air mass and refraction. Appl. Opt., 33, 1108±1110.
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