measuring spectral diffuse solar irradiance with non-cosine flat-plate diffusers

Pergamon

0038-092X( 94)00123-5

Solar Energy, Vol. 54, No. 3, pp. 173-182, 1995 Copyright 0 1995 Elsevier Science Ltd Printed in the USA. All rights reserved

0038-092X/95 $9.50 + .OO

MEASURING SPECTRAL DIFFUSE SOLAR IRRADIANCE WITH NON-COSINE FLAT-PLATE DIFFUSERS

A. DE LA CASINIERE, * T. CABOT, and S. BENMANSOUR * * Equipe de Recherche I.R.S.A.-UniversitC Joseph Fourier, 17, Quai Claude Bernard, 38 000 Grenoble,

France * *Institut de Gtnie MCcanique-U.S.T.H.B., BP 32, El-Alia Bab-Ezzouar, AlgCrie

Abstract-In spectral diffuse solar irradiance measurements, when diffusing devices used are neither perfectly Lambertian nor have an ideal cosine response, significant errors may spoil the collected data. An optical method permits the determination of a spectral correction factor (SCF) which fully compensates for the diffusers’ imperfection when the sky radiance is isotropic. A study of the errors introduced when using such a isotropic SCF in anisotropic radiance conditions is presented for two common flat-plate diffusers fitted with a shadow-ring or a tracking disk. The wavelength band explored is 0.29-0.90 pm and the clear sky radiance model used is Kittler’s. The relevance of several diffuse irradiance spectra measured on clear sky days with isotropic SCF is analysed by comparison with Brine-Iqbal model spectra and total diffuse measurements. A remarkable coherence is found for small solar zenith angles when using a tracking disk and a diffuser with an isotropic SCF smaller than 1.2.

1. INTRODUCTION

Since the diffuse solar radiation reaching the earth’s surface accounts for about 50% of the global solar radiation, the spectral diffuse solar irradiance, in many applications, has to be evaluated with the same accuracy as the spectral direct irradiance. Further, because the scattering by air molecules and aerosol is predominant in short wave radiation, many authors (Shettle and Green, 1974; Chai and Green, 1976; Garrison et al., 1978; Bird et al., 1982) observed the primary importance of the diffuse solar component in the UV spectral range. Although the phenomenon of atmospheric scattering was elucidated many years ago, few spectral diffuse solar irradiance measurements are available in the literature. Such measurements are dif- ficult because the scattered radiation arrives from the whole sky dome within a solid angle of 2~ sr and is anisotropic.

A diffuse solar irradiance measuring system basi- cally consists of a receiver and a detector. The role of the receiver is to collect the diffuse sky dome radiation and transmit it to the detector. The role of the detector is to convert the radiation to an electrical signal. In spectroradiometers, the solar radiation flux received has to impinge on the inlet slit of the detector at normal incidence. Therefore, the receiver is fitted with a diffusing device which mixes the radia- tions from the whole sky dome so that the flux enter- ing the slit at normal incidence does not depend, for a given horizontal diffuse irradiance, on the sky radiance anisotropy.

Ideally, such a diffusing device is both Lam- bertian and cosine-true. In this case, when the diffuser is irradiated by direct beams, the ratio of the

* ISES member.

spectral irradiance on its inlet face to that on its outlet face is invariant with respect to the angle of incidence of the beams. Because ideal diffusers don’t exist, a preliminary optical characterization has to be done with a view to apply a suitable correction factor to measurements. As good cosine diffusers are generally good Lambertian diffusers too, the cosine response is the predominant factor of the characterization.

Integrating spheres which are considered as nearly ideal diffusers may be used in spectrophotometric measurements as described by Kondratyev (1969). However, integrating spheres are expensive, bulky, and the transmittance is low; further, the receiving surface which is merely a circular hole, cannot fully accept a 27r sr incident flux and must be protected by a silica dome in routine measurements. Although less ideal than spheres, flat-plate diffusers are more commonly used. Their main advantages are low cost and higher transmittance. In addition, they are generally suitable for outdoor measurements.

This work is a study of methods of measuring spectral solar diffuse irradiances by using flat-plate diffusers which are neither perfectly Lambertian nor cosine-true in conditions of clear sky and anisotropic radiance.

2. THEORETICAL FORMULATION

2.1 The spectral relative cosine response An axisymmetrical flat-plate diffuser (D) is used

as receiver of a spectral diffuse irradiance measuring system. Let dE,(O) be the monochromatic irradiance (W me2 pm-’ ) on (D) from a small sized source (S ) the beams of which form an angle of incidence 0 with the (D) axis. The monochromatic angular response of

173

174 A. DE LA CASINIERE, T. CABOT, and S. BENMANSOUR

the detector is d Vh( 0) and the monochromatic irradi- ante may be expressed as:

dE,(8) = k(0, X)dV,(B) (1)

where k( 8, A) is the angular coefficient of calibration of the measuring system, which is generally a function of A. Assuming that (S) is on the (D) axis and remains at the same distance from (D), the monochromatic h-radiance becomes dE,( 0) = dE,( Q)/cos 19 while the angular response and the coefficient of calibration are respectively dV,( 0) and k( 0, A). Using the Grainger et al. ( 1993) definition of the spectral relative angular response as A(0, A) = dV,(B)ldV,(O), the spectral relative cosine response may be written as a function of 0 and A:

c(e, A) = k(O, A)/&@, A) = A(& A)/COS 0 (2)

If the diffuser (D) were ideal, c(e, A) would re- main equal to one independent of the angle of incidence and of the wavelength.

2.2 The spectral correction factor The whole sky vault may be considered as an ex-

tended radiation source of which the spectral normal radiant intensity-or spectral normal radiance-is Ih(e, 4) (W mm2 sr-’ pm-‘). The normal sky radiance depends generally on 8 and 4 which are respectively the zenith angle and the azimut defining the direction as observed from (D) . If the sky dome portion in the (0, 4) direction is considered as a small-sized plane radiation source, the diffuser (D) assumed to be horizontal would receive the spectral diffuse irradiance (W mm2 pm-‘):

d2Dhx(B, 4) = Ih(O, 4)sin 0 cos tided4 (3)

Consequently the spectral diffuse irradiance on (D) from the whole sky dome may be expressed as:

rr/2 2s Dhk =

s s d’Dhx(& 4)

8=0 Cp=o

s

al2 = sin e cos e

8=0 V

2n

I,(e,4)& de (4) fp=O 1

If d2Vk(0, 4) is the spectral angular response of the detector for the irradiance d2Dhk(0, I$), then with the help of eqns ( 1) and (2) one may derive:

k(O, A)d2V,(& 4) = c(e, A)d’Dh,(@, 4) (5)

Assuming that the spectral angular response is an additive quantity, the electrical signal yielded by the detector for the spectral diffuse irradiance Dhx is:

n/2 2n

v, = ss d2vk(e, 4) (6) e=o +=o

For shading (D) from direct solar radiation, the receiver has to be fitted with a mask which cuts off a part of the diffuse sky radiation. This may be taken into account by writing the sky radiance as the product ~(0, +)Ix(O, 4) where e(0, I#J) equals zero or one depending on whether the sky direction (0, 4) is cov- ered by the shading mask or not. From eqns (3), (5), and (6) we obtain:

s

s/2

k(0, A)V, = c(e, A)sin e cos e .9=0

2ri X

V 0, 4)I,(e, 4)d4 de (7)

+=0 1 By dividing eqn (7) by eqn (4) one gets:

where

Dh, = C(A)k(O, A)V, (8)

n/2 2a

C(A) = s

sin 8 cos e V

ue, 4)& de 8=0 #=O 1

U 7T/2 X c(e, A)sin e cos e

8=0

2a -I X

[J de, wde, w4 de 1 I (9)

+=0

Although C(A) is assumed to be constant by authors as DeLuisi and Harris (1983) it may depend quite significantly on the wavelength; for this reason it is called here the spectral correction factor (SCF) of the diffuser. Equation (9) is a general form of the SCF which may be more or less simplified depending on the method employed for measuring Dh,. When using a shadow-ring as described in classical Drum- mond study (1956), the SCF has to keep the above general form and is denoted by Co(A); the subscript 0 means that with such a method a part of the sky vault is necessarily occulted; if the sky radiance is isotropic that is if Ih( 0, 4) is constant independent of the direction (0, +), eqn (9) may be simplified and the ‘SCF is denoted by Co(A) . If the diffuse h-radiance on (D) is obtained with the aid of a small tracking disk such that E( 0,+) may be considered equal to one irrespective of the direction (0, 4)) the SCF is written C,(A) for anisotropic sky radiances and C,(A) for isotropic conditions; the subscript F means that this method leaves the sky vault completely free. In the last case, eqn (9) may be extensively simplified and C,(A) becomes equal to one if c(e, A) is equal to one: that is if (D) is an ideal diffuser.

Measuring spectral diffuse solar irradiance 175

literature. The performances of several of them were compared recently by Ineichen et al. ( 1994). A model for directional spectral radiance was also proposed by Justus and Paris ( 1985), whereas Siala and Hooper ( 1990) have developed a semi-empirical model of the total diffuse sky radiance. From all these models, the Kittler model, described by Page ( 1986)) was pre- ferred because of its simplicity. This model deals with total luminances which we substituted here, failing anything better, by spectral radiances. Because the present study is only an estimate, the errors introduced in this way are considered tolerable. For any wavelength, the modified Kittler relationship is then given as:

SCF

1.3

(Dl 1

I”* -7s’

1.25

200 300 400 500 600 700 800 h(nm)

Fig. 1. Spectral variations of isotropic and anisotropic SCF for (Dl ) when using a tracking disk (solar zenith angle H*

step width IO”).

3. STUDY OF THE SPECTRAL CORRECTION FACTOR

3.1 Measuring the spectral relative cosine response The present study of the spectral correction factor

is based on the optical features of two real flat-plate axisymmetrical UV diffusers refered to as (Dl) and (D2). These diffusers were bought from the Oriel Company within a 2 year time period. Although they bear the same name, “200 to 1100 nm Opal,” their properties are significantly different. They are not perfectly Lambertian, but according to the manufacturer they are far superior to ground quartz. The inlet of the detector is the input face of a three meter UV fiber optic cable. The diffuse flux collected by the diffuser is transmitted by the fiber to the inlet slit of a double monochromator fitted with two holographic gratings and a photomultiplier detector. The spectral range under investigation is 290-900 nm with a step width of 5 nm.

In order to determine the spectral relative cosine responses ~(0, A) for (Dl) and (D2), two xenon lamps of 100 W and 250 W operated by a suitable regulated power supply were used as small-sized radiation sources. The diffuser mounting permitted the adjustment and the selection of 16 different angles of incidence 0 ranging from 0” to 80”, within an error of 0.1”. Measurements with another type of detector have shown that the ~(0, h ) values do not depend on the optical properties of the diffusers alone, but are char- acteristic of the whole measurement system. Further- more, operating temperature and detector ageing may play a quite significant role. The spectral relative cosine responses of (Dl ) and (D2) were determined at an ambient temperature of about 20°C.

I,(@, f$)&(O. 0) = (0.91 + 10emi” + 0.45 cos’ 7)

X(1-e- “12’cMH)[(0.91 + 10ee3”* + 0.45 cos’Q*)

X (1 - e-““)I-’ (10)

Equation ( 10) is valid for relatively clear sky conditions and for Linke Turbidity factors below 5. Ix(O, 0) is the monochromatic zenith radiance; n is the angle (in radian) between the sky dome portion in the considered direction (8, 4) and the centre of the solar disk; and H* is the zenith angle of the sun (in radian)

3.3 The spectral correction factor for tracking disk methods

According to section 2.2, the SCF suitable for measurements of Dh, by means of a tracking disk (or any method which leaves the sky vault completely free) is C,(h) or C,(h) depending on the sky radiance isotropy. The variations of these SCFs which were computed from eqns (9) and (10) for the diffusers (Dl ) and (D2) are shown, respectively, in Figs. 1 and 2 as function of the wavelength A (from 290 to 900 nm). The thick lines represent the Cr( A) variations while the thin lines correspond to C,(A) which depends, according to eqn (lo), on the solar zenith angle

SCF (DZ) 1.8 ’

‘Ha = 75 IL I I i I

,!

1.7 }

1.6 !

1.5

HI i

3.2 The sky dome radiance model For assessing the effects on the SCF values of the

radiance anisotropy of the sky dome, an approach for cloudless conditions only was considered. Many models of total diffuse sky luminance may be found in the

1.4 I ) ! ‘,- :’

200 300 400 500 600 700 800 )c(nm)

Fig. 2. Spectral variations of isotropic and anisotropic SCF for (D2) when using a tracking disk (solar zenith angle B*

step width 10”).

176 A. DELA CASINIERE,T. CABOT,~~~ ~.BENMANSOUR

sDhJDh, (%) 15 I I

rI

I I I H* - 75 " - Dl

'k.. ___..._____ ,,2

--. 10-- i... -..../-.. .____._ . . . . . . . . r _...... “.f*.‘..__...‘._... _...:

‘.._ -- .,... ___.____ . .._- -o--_..-.-.. - sm... .- .___..I ._..._ _..* .

ll* -75 d...._ .-..____.__.____._.__.__.-._._.._...-...-_..____.~.._...._..~

_________.-~..-.---....-......___,____._._________. .._. _ ___._.._.. -

-5 e* _ I5 ‘J_ __--- ---------- ---.---._. ____.__.__. ___._.-..- _.__... ~_~t_‘L 1 ~~q---~~p_ f~ _f~ Y--~

200 300 400 500 600 700 800 h.hn)

Fig. 3. Errors of tracking disk measurements with (Dl ) and (D2) when using isotropic SCF (solar zenith angle 0* step

width 10’).

0*. Because the C,(X) values observed are closer to one in Fig. 1 than in Fig. 2, diffuser (Dl) can be considered more “ideal” than diffuser (D2).

The variations versus A of the ratios [C,(X) - -- Cr(X)]/Cr(A) are plotted in Fig. 3. Following eqn (8), these ratios also represent the relative difference SDhJDhh between the Dhx values obtained on the assumption that the sky radiance is isotropic and the values obtained by means of eqn ( 10). Table 1 shows that the mean values of these relative differences may attain 5% for (Dl ) and exceed 10% for (D2), depending on the solar zenith angle.

3.4 The spectral correction factor for shadow-ring methods

When using a shadow-ring for measuring the solar diffuse irradiance, a corrective coefficient must be applied in order to take into account the diffuse radiation cut off by the ring. This coefficient is, in fact, a geo- metrical correction which generally implies perfect isotropy of the sky dome radiance. In spite of such a disadvantage, shadow-rings are commonly used because of their simplicity, reliability, and low cost. It is, therefore, important to study their effect on the SCF in both cases of isotropic and anisotropic sky radiances. The ring considered here is the widely used Kipp & Zonen CM 1 1 / 12 1 diffuser. The dimensions of this diffuser are 570 mm inner diameter, 620 mm outer diameter, and 55 mm width.

In the isotropy hypothesis, the SCF is written C,(A) according to section 2.2 and depends on the ring position, that is on the site latitude cp and on the

solar declination S. Figure 4 shows the variations with wavelength of this SCF which were computed from eqn (9) for (Dl ) and (D2), with various S values and for the four Northern latitudes 35”, 45”, 55”, and 65”.

When the sky radiance is anisotropic, the SCF which is denoted by Co(A) has to be computed from eqns (9) and ( 10). In addition to cp and 6, the SCF is then dependent on the solar zenith angle 8*, as C,(A). Because a presentation with A as variable would need too many graphs, the ratios [C,(A) - - - Co(A)]/Co(A) were calculated only for one center wavelength of the spectral range involved, that is for A = 595 nm. These ratios are plotted versus the solar declination for the above four Northern latitudes in Fig. 5. As in section 3.3, they represent the relative difference GDhJDhk between Dhk obtained with the hypothesis of an isotropic sky radiance and Dhh obtained from eqn ( 10). The 6DhklDhx values are lowest in June, independent of the solar zenith angle, for Northern latitudes lower than 55”. A solar zenith angle of about 30” at all latitudes and in seasons where such an occurrence is possible, provides almost zero values using the Kittler model. The highest values are observed for cp = 65” which is the highest latitude considered. As they rise about 10% for (Dl) and 16% for (D2), these values are significantly larger than the differences observed when a tracking disk method is used. It is expected that the above results would not be drastically modified for any other wavelength of the studied spectrum.

4. THE RELEVANCE OF SPECTRAL DIFFUSE

IRRADIANCE MEASUREMENTS

4.1 Assessing the relevance of spectral difSuse irradiance data

Many spectral diffuse irradiance measurements were performed on perfectly clear sky days with (D 1) and (D2), using the ~(0, A) and k(0, A) values obtained from the optical methods described in sections 2 and 3. If there are no means to reliably know the accuracy of spectral solar it-radiance measurements, some methods exist which permit one to assess their relevance.

A first method consists of comparing the total diffuse irradiance measured by means of a shaded pyranometer to that obtained by integrating the diffuse spectra over the wavelength. It is obvious that a good coincidence cannot constitute an irrefutable proof of good quality, on the other hand a significant difference is a sure indication that there is some problem. The

Table 1. Mean relative errors introduced in Dhh measured by a tracking disk method when assuming isotronic sky vault radiance

Solar Zenith Angle 0*

Dl (%) D2 (%)

75” 65” 55” 45” 35” 25” 15”

-4.9 -3.9 -2.6 -1.4 -0.3 +0.6 +1.3 -10.5 -8.8 -6.3 -3.5 -0.6 +2.1 +4.4


co ( %I 1.9 I I I

I+ 23.4j” 35” dorth laJ:..__ . . .._..._ ’ i

,..,..... -...: 1.8 -- ',,

*.... *......_---~...,~~ /..---- :>* +

. . -0" *-L..*.*._*_... **--.*

.*...._........."'".i., ~_.....__..._.: :

. ..? . ...-...* ::*..

/_.......d /.,..d.-.3

23.45" ..-....__........_1"'-"" r

i 3 1.1 -

200 300 400 500 600 700 800 h(nm)

co (1) co (A) 1.9 I

55” ljorth lie. ’ 1.9 -A ; + 65” North Ibt.

---

1.8 ._.____.. *.........-..z_ ___.....--*-.- . _I

1.2 i C- 23.45+---" v

,,, ~~~.~_~~~_~~~

200 300 400 500 600 700 800 hhrn)

1.7

1.6

1.5

1.4

1.3s 0' -

200 300 400 500 600 700 800 h(t'NTI) 200 300 400 500 600 700 800 hhn)

Fig. 4. Spectral variations of SCF for (Dl ) and (D2) when using a shadow-ring.

bandpass of pyranometers is approximately 0.3-3.0 pm; so they are generally calibrated with a corrected coefficient in order to take into account the overall solar spectrum. Consequently, the monochromatic irradiances which were measured here from 0.29 to 0.90 ,um, have to be extended by means of a suitable model up to about 10.0 pm.

The Brine-Iqbal clear sky model ( 1983) was chosen as a second method to fit the measured spectral diffuse irradiances to those calculated for identical atmospheric conditions. In this model Dhh is considered to be the sum of three terms DhRh, DhAh, and DhMMh which are the spectral horizontal diffuse irradi- antes due to Rayleigh scattering, aerosol scattering, and multiple reflections between ground and atmosphere.

DhRh = 0.5Zhx( 1 - 7,k)/rrh

Dh,, = F,w,Zh,( 1 - 7,J/7,i

DhMi = (Ih, + DhRh -t DhAh)

x PxaP*J(l - PkaPd (11)

The coefficients pia and pks are the atmospheric

and ground diffuse albedos, respectively. Because the influence of phc is generally weak, this albedo was considered here as constant independent of the wavelength and taken equal to 0.2. Values of pka were assessed by the authors of this paper from the following integral:

s

n/Z P Xa = p&sin 28 d8 (12)

8=0

where p$ is the atmospheric direct albedo which is expressed by Brine-Iqbal as:

P6 = Tok7wh~gh[O.5(1 - 7rkbak

+ (1 - Fc)wo(l - ~G,)TAI (13)

The term Ih, is the spectral horizontal direct irradi- ante defined as:

Ih, = E,l,,,cos O*rrhrahrohrwhrgh (14)

Zox is the spectral extraterrestrial normal irradiance for mean sun-earth distance (WRC spectrum), and

A. DE LA CASINIERE, T. CABOT, and S. BENMANSOUR

aDh,/Dh, (%) 6DhJDhA (%)

-4 /’ “’ ” ” ““~’ ” “’ !“’ ““‘i”“’ ” / -25 -15 -5 5 15 8(") -25 -15 -5 5 15 b(O)

SDhx/Dh,, (%) 6Dh/Dhl, (%) 16 i,, ,,I~ I, 11, .. ,,~ ,I,,’ I~,.,, 1

A 16 ~8 178 '1 ~~~~~~~~~,~~~~~,~~i~~~~~~~~~i~~,~~~~~~ 1 fjr _

_.....-- 7~~~?'......""""""---........_~~ e* ?? 75".....""'

.---. -.-.......__*__*__

L 65' ..*.......*-

12A- _ . . .._....... - . . . . . . .._ __..

,.. . . . ..?%...-_--

- ni ,... .--

: “L as- Norm lat. L I_ b3- Norm Iat 1

-4 I1 ‘,‘,‘~,, “““/“,“““I”“,“,‘j”“‘,“‘/ -4 i”“““‘I”“““‘ll”“““~““““L/““““’

-25 -15 -5 5 15 a(") -25 -15 -5 5 15 6(O)

Fig. 5. Errors of shadow-ring measurements with (Dl) and (D2) when using isotropic SCF (8* = solar zenith angle).

E, is the correction to this distance. T,~, raX. T,,~, rWh, and rgh are spectral atmospheric transmittances which refer respectively to molecular scattering, absorption, and scattering by aerosol, ozone absorption, water vapor absorption, and mixed gas absorption. These rela- tionships following Leckner’s formulation ( 1978) are given in the Appendix. The transmittance rah is expressed as:

r*h = exp( -PA-%,) (15)

where m, is the altitude-corrected relative optical air mass m, given in the Appendix according to Kasten and Young (1989). The well-known Angstrom turbidity coefficient fi was derived from equations proposed recently by Grenier et al. (1994) on the basis of pyranometric measurements and for a mean value of LY equal to 1.3. The reduced thickness of ozone (NTP) and the thickness of precipitable water vapor which are needed to calculate the transmittances T,,~ and rWx were obtained by analysis of direct spectral it-radiances.

w, and F, refer to aerosol only. The first coefficient is the so-called single-scattering albedo, that is the fraction of the incident energy scattered to the total

attenuated energy. Because its values are generally unknown, it was used here as adjustable parameter. The coefficient F,, which is called forward scatterance, is the fraction of forward scattering to total scattering. It was assessed from a function of solar zenith angle 0* based on Robinson’s data reported by Iqbal (1983):

F, = 0.95 + 1.0 10-38* - 7.0 10-58*2 (16)

4.2 The measuring system The diffuse solar radiation receiver of the measur-

ing system, which was fitted with (Dl ) or with (D2), was located on the roof of a building of the Grenoble University in France (45” 11’ North latitude, 5” 43 ’ East longitude, 240 m in altitude). The first shading device used was a Kipp & Zonen ring as described in section 3.4 and, later, a tracking disk. The detector was the double monochromator system used for de- termining c( 8, A) as described in section 3.1. A 3 meter, UV fiber optic cable connected the outdoor radiation receiver with the indoor detection device. Its transmittance was found to be quite insensitive to bends or loops of a radius down to 9 cm.


Dh ,(W/m ‘pm) f/m 2pm) Dh, 500

400

300

200

100

0

i -4 ---+_ +

D 1 i 10/03/93

(isotropi+d SCF

03 03 04 05 06 07 0 8 1 (pm )

500

400

300

200

100

0

t-

(isotropip/ SCFJ

02 03 04 05 0.6 0.7 08 h(v)

Dh, (V 500

400

300

200

100

0

V/m ‘urn) Dh I (W/m ‘l&m)

/‘_I I t t 1 Dl 10/03/93 :

(isntropital SCF)’

I I I I I

i I ! Dl 1 o/03/93

(isotropi+?l SCF)

500

400

300

200

100

0

” 02 03 04 05 06 0.7 08 A(I

Dh A( W/m 2pm) 500 ! I I I I I

D2 o&3/07/93 (r.wtropiCal SCF)

1‘ r n) m)

V/m ‘urn)

I I : D2 08/0~7/93

(isowJpicjal SCF)

0.2 03 04 05 06 07 06 Awn)

400

300

200

100

0

\

02 03 04 05 0.6 0 7 08 k(pm)

Dh &( W/m 2w 1 500 j I I I

D2 : 08/Oj7/93 (isotropital SCFJ

02 03 0.4 0 5 0.6 0.7 0.8 k(pm ) 0.2 0.3 0.4 0.5 0.6 0.7 06 k(vm)

Fig. 6. Diffuse irradiance spectra run on two clear sky days with (Dl ) and (D2) fitted with a shadow-ring (O* = solar zenith angle).

A. DE LA CASINIERE, T. CABOT, and S. BENMANSOUR

0.2 0.3 0.4 0.5 0.6 0.7 0.8 k(pm) 0.2 0.3 0.4 0.5 0.6 0.7 0.8 h.(pm)

Fig. 7. Diffuse irradiance spectra run on a clear sky day with (Dl ) fitted with a tracking disk (O* = solar zenith angle).

The calibration coefficients k(0, A) were deter- ring in extreme conditions, Fig. 6 shows a set of spec- mined for (Dl ) and (D2) by means of a 100 W or a tra run with the “good” diffuser (Dl ) on a day of 200 W standard xenon lamp. It is commonly recom- the “worst” period (10/03/93), and another spectra mended to use standard irradiances which are on the set run with the “bad” diffuser (D2) on a day of the same level as the irradiances to be measured. Conse- “best” period (08/07/93). The thick lines are the quently, a 1000 W lamp would have been more suit- measured spectra and the thin lines are the correspond- able in the UV band. ing spectra computed from the Brine-Iqbal model.

Measurements of total diffuse irradiance were carried out simultaneously with spectral measurements, by means of a CM 11 Kipp & Zonen pyranometer fitted with a Kipp & Zonen shadow-ring identical to that described in section 3.4.

Figure 7 shows spectra obtained by means of (D 1) on another clear day (25105194) but using the tracking disk method which leads to better results- according to section 3-than the shadow-ring method when adopting the isotropy hypothesis.

4.3 Test runs in clear sky conditions Because the radiance ratios obtained from eqn ( 10)

are rather rough estimates, it was thought more suitable to determine the spectral diffuse irradiances by -- using the “isotropic” SCFs, C,,(A) and C,(X).

According to Fig. 5 which concerns shadow-ring methods, the discrepancies between Dhh values determined from eqn ( 10) and from the isotropy hypothesis are at a minimum in June and at a maximum in Febru- ary at Grenoble latitude. For illustrating the perfor- mance of (Dl) and (D2) when fitted with a shadow-

Table 2 gives the values of 0*, p, F,, wO, Dh( P), and LX (I) for the above spectra. The w, values chosen are those which best fit the Brine-Iqbal model to the measured spectra; Dh( P) are the pyranometer measurements of the total diffuse irradiance; and D/r(l) are the integrals of the spectral data (which were measured from 0.29 to 0.90 pm and were calculated from the Brine-Iqbal model up to 10.0 pm).

Significant variations of SCF and k(0, A) were observed with changes in temperature of the detection device and with the aging of the measurement system. This phenomenon which may introduce an important


Table 2. Data corresponding to diffuse spectra measured with (Dl) and (D2) by means of a shadow-ring (SR) or of a tracking disk (TD) on selected three clear sky days

l9* (“) FC wo

Dh(P) Dh(J) (W/m’) (W/m’)

(Dl) + SR 74.2 0.14 0.64 1.00 86 90 ( 1 O/03/93) 65.0 0.12 0.72 1.00 119 124 lo = 0.31 cm 57.3 0.10 0.78 0.95 130 135 w = 1.4 cm 51.6 0.11 0.82 0.90 146 151

(D2) + SR 61.9 0.18 0.74 0.85 146 134 (08/07/93) 49.5 0.13 0.83 0.65 131 126 li, = 0.32 cm 35.2 0.13 0.90 0.58 137 142 w = 1.5 cm 24.7 0.15 0.93 0.61 172 167

(Dl) + TD 62.1 0.095 0.74 0.60 90 79 (25/05/94) 48.3 0.075 0.83 0.60 98 91 1, = 0.35 cm 38.2 0.065 0.89 0.60 103 98 w = 2.5 cm 29.7 0.070 0.92 0.60 108 107

lo is the ozone layer thickness and w is the reduced precipitable water; O*, p, F, and wg are the solar zenith angle, the Angstrom turbidity coefficient, the forward scatterance, and the single-scattering albedo, respectively; Dh(P) is pyranometer measurement of the total diffuse irradiance and Dh(I) is the integral of the corresponding spectral diffuse it-radiance data.

inaccuracy in Dh, determination, leads us to estimate

the mean relative difference between Dh( P) and

D/r(l) due to the various possible errors to be 8%. The [LX(P), LX(Z)] pairs reported in Table 2 can then be considered as equally coherent independent of the solar zenith angle and of the the day of the year. In other words, the pyranometer comparison does not permit one to distinguish, with respect to accuracy, between the measurements carried out on the 3 selected days. Nevertheless, it gives a positive indication concerning the relevance of the SCF and k( 0, A) values used.

Figures 6 and 7 clearly demonstrate that the smaller the solar zenith angle, the better the fit between measurements and model. For the shadow-ring method used on the 2 chosen days this fit appears rather bad when 60” < B*, acceptable when 50” < 8* < 60”, and rather good (at least up to 0.70 pm) when 0* < SO”. For the tracking disk method, the fit follows a similar pattern and becomes even excellent when 8* < 40”. Two main reasons may explain such poor spectra fit for large 0* values-observed again when using anisotropic SCF: The first reason is the significant elevation of the mountains surrounding the measuring site (whereas the model implicitly supposes a free horizon); and the second reason lies in the model itself which straightforwardly gives Dhh = 0 when 0* = 90”, and therefore, is not likely to be suited for low solar elevations. An additional reason for these discrepancies could be the simplifying hypothesis- adopted de facto by Grenier et al. ( 1994) -that coefficient cy is not dependent on the average size of aerosol, and that coefficient 0 does not vary as a function of wavelength.

According to Figs. 3 and 5, the lowest differences between isotropic and anisotropic SCF are observed for 15” < 0* < 4.5”. Because these values are also the ones that give the best fit between model and measurements, the spectral diffuse irradiances ob-

tained at small zenith angles are likely the most accu- rate.

5. CONCLUSION

When measuring spectral diffuse solar irradiances, the diffusing device used in the radiation receiver is allowed to yield a imperfect cosine response. How- ever, a previous optical study has to be performed in order to determine the SCF of the diffuser. With regard to errors caused by sky radiance anisotropy when assuming isotropy, a tracking disk used as a shading device gives significantly better results than a simple shadow-ring. Further, it appears preferable to use a diffuser for which the SCF remains, in isotropic conditions, smaller than 1.2. Finally, unless a l-2% preci- sion of the SCF and/or k(0, X) values is ensured, no correction of measured data by means of a suitable clear sky radiance model seems to be justified. The coherence of spectral measurements and the Brine- Iqbal model values observed for solar zenith angles smaller than 40” is remarkable. It is concluded, therefore, that this simple model, when used together with

pyranometer diffuse measurements, would permit a

rough calibration of spectral diffuse irradiance mea-

surement systems.

Acknowledgments-This work was partly funded by the French ADEME (Agence de 1’Environnement et de la Mai- trise de l’Energie, Delegation Regionale Rhone-Alpes) and by the University Joseph Fourier of Grenoble, France. One of the authors, S. Benmansour, worked on this project while on a postdoctoral fellowship from the French Government to whom he would like to express his gratitude.

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measuring spectral diffuse solar irradiance with non-cosine flat-plate diffusers

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