~ms&eric E~~ironmem Vol. 16 No. 9. pi. 22374244 1982 tlW+4981/82/092237_oI WJ3.oOP

Primed in Gtw Britain. Q1982PapwmPlCD~.

SOLAR IRRADIANCE SPECTRUM AT MADRID

A. PONS and A. CORR~NS lnstituto de Optica, Scrrano, 121, Nadrid-6, Spain

(First received 15 July 1981 and infiMlfom 12 h’owmber 1981)

Abstract-An experimental study of the qcctrum of direct solar irradiiaa in Madrid on ckar days has been made. The expression

W= (l/s)r,(~)expt-~(~)~~,)~(ccw~,)[1+~~,(0.13~,,, -%I~

is proposed to describe more realistically the real direct solar spectral irradiance in Madrid.

INTRODUCTION

In a previous paper (Corr6ns and Pons, 1979), we described an experimental v ttomeasurethe solar irradiance global, direct and diffuse, by means of optical fibers and silicon detectors. The system con- tinuo~y measures the incident solar radiation with- out direct exposure of the photosensitive elements to the incident solar energy.

In that paper we announced the installation of similar radiometers with interference filters, to record points of the solar spectrum. With these spectral measurements we shall try to get an expression close to the real spectrum of direct solar irradiance received in Madrid (latitude: 40”, barometric height 6OOm, dry continental climate, with a great number of clear days with urban pollutants). This expression would be useful to applications such as calorimetry, with natural light, photometry and solar energy technologies.

THEORY

It is well known (~~~~rn and Rodhe, 196Q Shaw, 1976) that measurements of attenuated direct solar radiation by pyrheliometers are subject to errors due to the presence of diffuse sky radiation within the detector’s field of view. The amount of diffuse radi- ation depends on the instrument aperture and the characteristics (amount and kind) of the scatterers in the atmosphere.

Diffuse radiation consists of singly and multiply scattered radiation. Under moderately clear sky con- ditions, this diffuse radiation is single scattering by aerosols and molecules and multiple scattering by molecules (Box and Deepak, 19794 b). Foilowing the perturbation approach (Deirmendjian, 1970), we assume here that the multip~ scattering ~nt~butions due to aerosols are negligible.

Then the total spectral irradiance I(L) at wavelength E. measured by the receiver, is composed of contri- butions 1&A) due to attenuated, direct solar radiation,

and I&,%) due to diffuse sky radiance, entering the detector’s field of view.

r(n) = i,(n) + i&&),

where ldir is given by Bouguer’s law

(1)

f&(A) = (l/S&(& exp (- $1) =%k (2)

where I,(A) is the incident solar radiation outside the atmosphere, 9, is the solar zenith angle, S is a factor that take into account the distance sun-earth, and T is the total optical thickness due to molecular scattering, rM; aerosol scattering, TV and to the different atmos- pberic absorption components (in this work water- vapor absorption, ‘I, and ozone absorption, 50,. The absorption due to other atmospheric components like Or, COI, etc. has not been taken into account). I, is given by (Box and Deepak, 1979a, b; Green et al., 1971)

+ rh&h& (3)

with ~~ the aerosol optical depth, tM the effective molecular optical depth, including molecular multipk and singk scattering. To do that is implicit the assumption that the shape of the angular distribution of the multiply scattered light is similar to that of the singly scattered Rayleigh contribution (Box and Deepak, 1979). For moderately clear skies, this is a reasonably accurate appro~tion. Lp and LM are the error factors for extinction measurements due to aerosol and molecular forwardscattering, respectively. In fact they are a hemispheric integral of the scattering phase function (Box and Deepak, 1979a,b; Deepak and Box, 1978a,b). By substitution of expression (2) and (3) in (1)

I(A) = (l/S)I,(1)exp(-r(d)sec9,)

(1+=6,(r,L,+rMLM)J. (4)

On average, the diffuse radiation contributes roughly 5% to the total, because most solar radiometers have a small view ozone angle. Thus in

2237 *E 1*:= - M

2238 A. PONS and A. CORR~NS

general it is not necessary to introduce this correction. But, when spectral solar radiometry is performed to determine the aerosol optical thickness and the tur- bidity factor of the atmosphere the results obtained from such measurements may have large errors.

To apply this expression to the experimental measurements we shall make another approximation. This involves the neglect of the scattering contribution of molecules relative to that of the aerosol. As the aerosol particles are much larger than air molecules, they scatter most of the radiation in the near forward direction. For this reason, the major contribution to the diffuse radiation that we detect simultaneously with the direct solar radiation is aerosol scattering. Thus errors due to molecular scattering may be neglected, unless the aerosol optical depth is exception- ally low (Box and Deepak, 1979a, b).

Then the total irradiance recorded by the detector will be

I(4 = (l/S)f,(ntexp(-t(l)sec8,)

II +s=Ur&,)}. (5)

MEASUREMENT SYSTEM

The measurement system is identical to that de- scribed in (Corr&rs and Pans, 1979X with only one difTerence. At the interface of the fiber and diode there is an interference filter to isolate a narrow spectral band.

Five identical systems have been constructed. Each radiometer head has a different interference filter, with tranamittanee peaks at 505,605,700,800 and 904 nm. The bandwidth is about 15 nm.

The spectral response of each measurement system has been measured in absolute values by comparing it with an electrically calibrated standard radiometer (Geist and Blevin, 1973), using a technique of direct substitution with an instrument described elsewhere (Corrbns and Carteras, 1977). The estimated accuracy of this calibration is f 2 %. The estimated accuracy of the our spectral irradiance measurements is f 3 % as described before (Corrons and Pons, 1979).

We have chosen for aerosol size dist~butions, a power-law size distribution, which leads, as is well known (Junge, 1963; McCartney, 1976) to power-law behavior for f, as a function of A, fp=/l.d-*, 1 in pm. The wavelength exponent is characteristic of mean spectrum of distribution of aerosols diameter and B represent the mean number of particulates by cm’. Then the expression (5) will be

r(4 = (l/S)l,(~)exp(-r(;cfsecB,f

with our measurement systems, we obtain information about the real spectrum of solar irradiance received in Madrid, and thus, we can calculate the factors a, /? and L, for the atmospheric conditions of Madrid on

moderately clear days. Thus we can verify whether (6) agrees with the real spectrum of the solar irradiance received at Madrid.

MEASUREMENTS AND CALCULATIONS

To determine the values of direct spectral solar irradiance, continuous measurements of global and diffuse spectral it-radiance have been made. To obtain the diffuse spectral irradiance we have shaded the entrance aperture of the instrument against direct irradiation by means of black circular plates, subtend- ing a half angle of 8” from the entrance aperture. Thus, by making a simple subtraction, we have the direct solar irradiance received by a detector having a receiver with a cone half angle of 8”. During the measurements the angle is constant.

To determine the values of r(& the Raykigh optical thickness reported by Frblich and Shaw (1980), the data developed for ozone absorption by Elterman, (1968) and the water-vapor absorption of Gates and Harrop (1%3) has been used.

By substitution of experimental values of! (1) in (6) and with a least squares fitting procedure, the values of a, /I and L, were obtained, which approximate the theoretical model of the real direct spectral irradiance in Madrid. A value of w = 2Omm ~r~~bk water content), usual to Madrid’s atmosphere in clear days, has been taken.

From the results obtained, we have taken L, = 0. I3 as the mean value for the Madrid atmosphere. As the view cone angle was constant, we can assume that the variation of L, around 0.13, has been due to aerosol’s varhtion in amount and kind during the time for the different sets of mutants.

We have also found a variation of fl between 0.08 and 0.18 for very or moderately clear days, respectively, and of a between 2 and 1 with a mean value of 1.5.

These are the upper and lower limits of observed values to e and b. All possible combinations between a and fi values are not valid. With some of them zI to the shortest wavelengths can be excessively large, and the approximation assumed, to neglect the multiple scat- tering contribution due to aerosols, may lead to errors, which may require a much more complete and com- plicated analysis.

Moreover, in this work, we restrict our calculations to consider single scattering by particulates, because, in spite of finding some values of T, (505) slightly higher than 0.2 (upper limit obtained by Box and Deepak as quite accurate using the perturbation technique) the obtained deviation between theoretical and experimen- tal values is within the usual error percentage for the proposed applications above, (see Tables 1 and 2).

A comparison has been made between values of direct spectral irradiance obtained from the experimen- tal measurements with the experimental arrange- ment, and with the values calculated from the theoret- ical model. That is shown in Tables 1 and 2: In Table 1

Solar b-radiance spectrum at Madrid 2239

Table 1. Comparison of values of the direct spectral irradiance on a horizontal plane: (a) as measured with the experimental arrangement and (b) as calculated from the theoretical model, for 6 June 1979 in Madrid

# I Experimental Theoretical difference (nm) (W me2 nm-‘) (Wm-2nm-‘) ( S”)

47” 505 0.790 0.797 -0.9 ‘I 605 0.811 0.806 +0.6 I(, 700 0.786 0.768 + 2.2 ** 800 0.567 0.571 - 1.7 1, 904 0.306 0.308 - 0.8

59 505 1.015 1.027 - 1.2 ,* 605 1.032 1.010 +2.1 7, 700 0.954 0.934 -l-2.1 1, 800 0.718 0.715 + 0.4 >, 904 0.402 0.409 - 1.7

68.4” 505 1.106 1.122 - 1.4 v 605 1.091 1.102 - 1.0 11 700 1.054 1.021 +3.1 -1 800 0.809 0.780 + 3.5 11 904 0.444 0.453 - 2.0

# is the solar etevation angle.

Table 2. Comparison of value9 of the direct spectral irradiaoce on a horizontal plane (a) ss mured with the experimental arrangement and (b) as calculated from the theoretical model, for 5 Dacembcr 1979 in Madrid

505 605

tz 904

z: 700 800 904

Experimental Theoretical Difference (Wm-” run-‘) (Wm-*run-‘) ( %I

0.467 0.475 - 1.8 0.520 0.514 + 1.1 0.526 0.521 + 0.9 0.384 0.406 + 5.0 0.315 0.307 + 2.3 0.163 0.167 - 2.8 0.2011 0.207 +0.3 0.244 0.238 + 2.6 0.193 0.194 -0.3 0.157 0.163 - 3.8

$ is the soIar elevation angk.

the values for a very typical summer day, in which the solar elevation has its maximum variation, and in Table 2 for a typical winter day, in which the solar elevation has its minimum variation. The graphical representation of these values can be seen in Figs 1 and 2, respectively. Also in the figures are shown the values of a, /I and LP for these days.

Finally in agreement with these rest&s, we propose the following expression, that is more close to real direct solar spectral irmdiance reoeived in Madrid, for the case of moderately clear skies.

~0s 0, is introduced to reduce the spectral irradiance to the horizontal plane.

CONCLUSIONS

A set of five radiometers has been constructed, in order to record points of the solar spectral it-radiance, using detector elements that are not directly exposed to solar radiation.

The 0 and jI factors, of Madrid’s atmosphere have been obtained, for the time of the spectral measure- ~~~~~~~~&~~e~~~a~t~ variation range.

Fiiy with the experimental spectral measurc- ments we have obtained the mean values of the parameters for a theoretical model which provides an expression for the real direct spectral solar irmdiamz received in Madrid, but only for the case of moderately clear skies In other cases, the approximations assumed are not ensef and the molecular contribution to fo~~t~~g radiation and the multiple scatter-

2240 A. PONS and A. CORR~NS

.cp*47* -#*59* a = 1.75 &0.08 a l I.?5 8.0.08

Lp=O.i8 Lp=O.i3

6 June 1979

i I i 1 1 I 9 0.4 05 06 a7 a8 eke

Wowlength, pm

Fig. 1. Gn~reprrrcnctionof~lwrofdirtarpsctnli~Ou~rodwith the -roar&l l rrangamant, and A as cakuIated from the t&x&al model.

5, wcember-1979

(P*31* a ’ 2 /3*0.08 LfPO.18

13” om

#f= 210

a*l.5#*0.12

Lp*O. 13

IS” 25”

I I I I

as 0~3 0.7 aa

Wovelength, pm

Fig.2 Gmphiml~ofvalwsofdiractymcrnl imdiancK0aanuMurcdwitbtl%exprrhratr1amBgv-

mvnt, and A as &toil from tbc tbawctial model.

Fr6lich C. and !&aw G. E (1990) Nvw wtion of 2% scattaring in tbv tarmatM l tnM@aea A&. Opt.

Ga&D.~.andHuropW.J.(1%3)Snfnradvrrrroririollof the atmo@Ma to so& ratli&a Appi. opt. & 8tl?-8!x

Geist J. and BIavia W. R. (1973) w-s&&I&d null radiomvterbaauI upooatldaMallyc&eata&pyro&c- tric detector. Appl. Opt. It, 2532-2f35.

Green A. E: S., Dmpak A. aad Lipofsky 8. J. (1971) lntcrpncltion of thv sun.8 auraok baavd 08 uwrpbcric aerosol mod&. A&. or. 12,126~1279.

Jungc C. E (lW3) Air C-y ral mivity. Acadvmic, Nvw York.

McGutncy E. J. (1976) Opics of the Atmosphere. Wiky, New York.

Shaw G. E. (1976) Pweoph. Birkbauscr, Basei.

ing conwibution due to aerosols have to be taken into uxount.

AcluovlrlgnnmrtTbc au&on are very gmaful to E. F. ZakwakioftbaNationIBureauofof (U.S.A.) sod W. Buddv of tbc National Raarch Gnu4 (thtadaf for thvir very uovful commcnb end suggestians.

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