The contribution of the solar aureole to the measurements of pyrheliometers

Solar Energy, Vol. 18, pp. 343-348. Pergamon Press 1976. Printed in Great Britain

THE CONTRIBUTION OF THE SOLAR AUREOLE TO THE MEASUREMENTS OF PYRHELIOMETERSt THOMAS H. JEYS and LORIN L. VANT-HULL Solar Energy Laboratory, University of Houston, Houston, TX 77004,U.S.A.

(Received 31 July 1975) Al~'traet--The fraction of the intensity measured by a currently manufactured Eppley Normal Incidence Pyrheliometer (N.I.P.), within three annular regions of the solar aureole, has been determined during 8 days. This fraction was determined by measuring the adjusted voltage difference between the N.I.P. and a modified N.I.P., dividedby a corrected output voltageof the N.I.P. The fraction of intensity within the aureole was generallyfound to have little effect on the intensity measured by the N.I.P., even on hazy days. The data taken indicates a linear relationship between the fraction of the direct beam intensity scattered into the aureole and the total extinction coefficient of the atmosphere.

l. INTRODUCTION

in turn, are practically attainable only by actual measurements of the angular brightness of the solar aureole at particular wavelengths. In general, past consideration of circumsolar radiation has centered around obtaining atmospheric particle distributions. The concern over the contribution of the solar aureole to pyrheliometric measurements, and the general lack of approproate data or calculations of this effect, have prompted the experiment discussed in this paper. Measurements of the intensity of the circumsolar radiation in three annular regions about the sun along with the pyrheliometric and pyrometric measurements have been taken under both clear and hazy sky conditions. In addition, measurements of the atmospheric turbidity taken concurrently with the scattering measurements are presented. The measurements taken on hazy days should be of particular interest to those who anticipate large amounts of circumsolar radiation on these days.

The intensity of direct~ terrestrial solar radiation is a key factor in determining how much energy may be gathered by concentrating systems of solar energy collection. Presently, the regularly available data on the direct beam intensity is collected by Eppley Normal Incidence Pyrheliometers with full viewing apertures of about 5.72°. Since the Sun's disk represents a full angle of about 0.53°, the pyrheliometric measurements include more than just the direct beam intensity. Exactly how much more is included in the pyrheliometric measurements is dependent on the brightness of the solar aureole out to 2.86° from the Sun's center. This brightness is dependent on the amounts and sizes of scattering material through which the beam must travel. The solar aureole or circumsolar radiation is a result of the small angle forward scattering of solar radiation by atmospheric particles whose dimensions are comparable to the wavelengths scattered (Mie scattering). Very little data exists on the brightness of the solar aureole as a function of the angle from the center of the Sun. What data does exist is typically at a particular wavelength and taken on days with clear stable atmospheres [1--4]. Efforts to calculate the brightness distribution of the solar aureole have also been confined to particular wavelengths[5, 6]. Additionally, these calculations require knowledge of atmospheric particle size and height distributions, which,

2. EXPERIMENTALMETHOD

?Work supported in part by a grant from NSF/RANN. Presented at the I.S.E.S. Intemationai Solar Energy Congress and Exposition, Los Angeles, California (28 July-ll Aug. 1975). SAIl radiation within 0.27° from the Sun's center is considered direct beam radiation. §Turbidity is here defined as z (A) = -(l/M) Iog,o(I(A)/lo0t)) - rR(A) where M I0t) Io(A) •R00

is the relative air mass; is the intensity at wavelength, A; is the extraterrestrial intensity at wavelength, ;t; and is the scattering coefficient of air molecules at wavelength, A.

Two Eppley Normal Incidence Pyrheliometers [7] were used to measure the direct beam plus partial circumsolar radiation intensities. These pyrheliometers are mounted on an Eppley Equatorial Mount[7] in order to track the sun's movement across the sky. An Eppley Black and White Pyranometer [7] (Model No. 8--48) measured the total insolation incident on a horizontal plane, while the atmospheric turbidity[8]§ at 505 nm and 380nm was measured by a Volz type sunphotometer [8]. These instruments, except for the sunphotometer, were connected to a twelve channel Philips Modular Multi-Point Recorder (PM 8235) [9] which was able to record the signals of each instrument sequentially (3 sec intervals) and on differing ranges. The Eppley Normal Incidence Pyrheliometer (N.I.P.) has a light sensitive receiver (radius = 4.25 mm) located at one end of a tube 20.6 cm long with an aperture stop of 1.03 cm radius at the other end. This geometry results in a full angle field of view for the center of the receiver of about 5.72°. The field of view was modified on one N.I.P.

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T.H. JEYSand L. L. WANT-HULL

344

by attaching three brass collimator tubes to the Schott adjusted voltage difference on the most sensitive range glass filter wheel, without the filters inserted, which is (1 mV full scale) of the Philips Recorder and hence obtain supplied with the N.I.P. The three tubes have lengths of maximum resolution. The following variables are defined in order to clarify 8.6, 20.6 and 20.6 cm and aperture stops of diameters 1.03, 1.03 and 0.725 cm, respectively. The various tubes when how the fraction of the intensity measured by the N.I.P., in front of the N.I.P. produced full angle fields of view of within the three annular regions, was determined (see Fig. 4.04, 2.86 and 2.020. These fields of view could easily be 2). obtained by rotating the filter wheel until the appropriate tube was in front of the N.I.P. (see Fig. 1). V = the voltage output of the N.I.P. The difference of measured intensity between the V~ = the voltage output of the modified N.I.P. where i N.I.P. viewing a circle about the Sun of 2.86° angular indicates which collimator tube is limiting the radius, and the modified N.I.P. viewing a circle about the field of view (i = 0 - 3 , when i = 0 there is no tube) Sun of 2.02° angular radius, results in the intensity of an X = the potentiometric division factor annular region with angular radii of 2.02 and 2.860. By taking the difference between the intensity measurements X . V, =the adjusted voltage of the modified N.I.P. VAo=the adjusted voltage difference between the of the N.I.P. and the modified N.I.P. with any one of the N.I.P. and the modified N.I.P. when both see the three collimator tubes limiting its field of view, the same section of the sky about the Sun intensity of three annular regions about the Sun can be & = the change in the adjusted voltage difference due determined. The angular radii of these annular regions to a change in the field of view of the modified are: 2.02 and 2.86°; 1.43 and 2.86°; and 1.01 and 2.86°. The N.I.P. by collimator tube i. intensity of these regions was anticipated to be relatively AV, = the change in the voltage output of the modified small compared to the intensity measured by either the N.I.P. due to a change in its field of view by the N.I.P. or the modified N.I.P. and hence, the difference in collimator tube i. measurements was made electronically in order to obtain as much resolution as possible. From these definitions it can be seen that when the N.I.P. The calibrations of the N.I.P. and the modified N.I.P. were widely different, producing a large difference in their and the modified N.I.P. view the same section of the sky voltage outputs. To compensate for this voltage differV-XVo= VAo (1) ence, the large voltage was potentiometrically divided until the difference was less than 0.2 mV when the N.I.P. and the modified N.I.P. viewed the same solid angle about and when the ith tube limits the field of view of the the sun. This resulted in the ability to measure the modified N.I.P. V- XE

= VAo+ &

or since VI=Vo-AV~

then V-X(Vo-AVO

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which with the use of 1 reduces to X A V~ = ,3,

and dividing by X V o = V - VAo produces

Fig. 1.

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Fig. 2. Circuit diagram depicting how the intensity of various annularrings,about the Sun, were measured.

Measurementsof pyrheliometers where AE/Vo= the percentage of the N.I.P. measurement within the annular regions defined by the difference of the fields of view of the N.I.P. and the modified N.I.P. The actual measured quantities were: V, VAoand V~o+ & from which AV~[Vo was found as shown above. The amount of time required to measure both the intensities in each annular region about the Sun, and the atmospheric turbidity at 505 nm and 380 run was about 10 min. This restricted the days on which data could be taken to those with either no clouds or, at worst, where clouds passed in front of the Sun every 15 min. Since days conforming to these requirements are relatively rare in Houston, data was obtainable on only 8 days from April to July 1975. 3. RESULTS

Reducing the field of view of the N.I.P. is feasible by either addition of a collimator tube, the reduction of the aperture diameter, or by a combination of both. The effects of either or both alternatives are two-fold. First, constriction of the field of view of the N.I.P. obviously requires a greater steering accuracy for the N.I.P. to maintain the Sun in its field of view. Second, a large decrease in the field of view could result in a significant change in the intensity distribution on the N.I.P.s receiver. Because N.I.P.s are calibrated with a uniform intensity distribution incident on their receiver, any significant change in this uniformity would effectively change the N.I.P.s calibration in an unknown way. Measurements under these circumstances are meaningless. A lower limit of the intensity incident on the edge of the receiver divided by the intensity incident on the center of the receiver for most N.I.P. geometries may be obtained by assuming that the field of view is uniformly bright. Table 1 shows that the lower limit of this ratio remains essentially equal to one for the geometries considered, meaning that the intensity distribution on the receiver is uniform. However, when N.I.P. geometries restrict the field of view of the receiver to such an extent that not all points on the receiver are able to see the entire solar disk, the result is a non-uniform intensity distribution on the receiver (e.g. The second entry in Table 1). As mentioned

345

before, this would cause an effective change in the calibration of the H.I.P. For a N.I.P. with a total tube length of 206ram, the above effect is important for aperture radii of less than 5.21 ram, and for a N.I.P. with a total tube length of 412 ram, the effect is important for aperture radii less than 6.17mm. As shown in Table 1, the changes in the N.I.P.s geometry has large effects on the steering accuracy required to maintain the entire solar disk within the field of view of all points on the receiver and, hence, maintain a receiver with uniform illumination. Given a certain field of view for the center of the receiver, the required steering accuracy is greater for a short tube and narrow aperture than for a long tube and wide aperture. This is why in this experiment the restriction of the field of view was affected by the addition of collimator tubes instead of narrower aperture stops. A graph of both the average percent of the sun visible to the receiver of a N.I.P. and the actual percent of the solar intensity measured by that N.I.P. for various steering accuracies is given in Fig. 3. The discrepancy between the actual measurement and the theoretical measurement may I

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Fig. 3. Per cent of solar intensity measured by an Eppley N.I.P. for varioussteeringaccuracies.,

Table 1. Theeffcctsofgeometryaltcrationsonapyrheliometer'smeasurements HALF ANGLE OF THE S E C T I O N OF THE SKY VISIBLE TO THE CENTER OF THE RECE,VER ( nff~ RF~)

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HALF ANGLE STEERING ACCURACY REQUIRED TO MAINTAIN THE ENTIRE SUN VISIBLE TO ALL POINTS ON RECE,yER (nff~R~ff~/

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INTENSITY AT THE EDGE OF RECEIVER R E L A T I V ETO A UNIT INTENSITY AT THE CENTER OF RECEIVER

,99916 ,99980 ,99979 ,99956

346

T. H. JEYS and L. L. VANT-HULL

be accounted for by the fact that the receiver is not uniformly sensitive, but in fact, is most sensitive in the center. The sensitivity of the receiver is both radially and angularly dependent. In fact, rotating the N.I.P. and repeating the measurements indicated in Fig. 3 resulted in curves which more nearly fit the theoretical curve. Another possible effect of adding a collimator tube to a N.I.P. is an increase in the intensity incident on the receiver due to scattering of direct sunlight off of the aperture stops within the collimator tube. The upper limit of this effect can be estimated on very clear clays on which circumsolar radiation is not measurable. If the scattering within the tube were measurable, it would result in the modified N.I.P. reading more than the N.I.P. Returning to the equations which described how the fractional intensity is determined, this difference would be manifested as a negative a, No such negative & was detected for any of the collimator tubes on any days including those with very clear atmospheres. Thus the effect of scattering within the collimator tubes is less than the random error of the measurements. The percentage of the radiation measured by a N.I.P., between 1.01 and 2.860 from the Sun's center, was found to be relatively small for all cloudless conditions under which measurements were made. Usually the intensity within this annular region was less than 1.5 per cent of the intensity measured by the N.I.P. Both the percentage intensity and the intensity of this annular region are largest in the morning and evening and reach minimums around solar noon. The data of 1 June1" is illustrative of this point (Fig. 4). In general, the amount of scattering is largest for large air masses and smallest for small air

masses. However, the air mass is not the sole controlling factor. The turbidity of the atmosphere also plays an important role. As can be seen in Fig. 5, the atmospheric turbidity times the relative air mass at both 505 nm and 384 nm behave in much the same way as the fractional scattering within 1.01-2.860 from the Sun's center (Figs. 4 and 5). The product of the relative air mass and turbidity are maximum in the morning and evening, but more important than this, note that the minima of these curves occurs at about the same time as the minimum fractional scattering (Figs. 4 and 5). As can be seen in Table 2, there is generally a high weighted~ linear correlation between (1) the atmospheric turbidity times the relative air mass at both 505 nm and 384 nm and (2) the per cent of the radiation measured by a N.I.P. between 1.01 and 2.860 from the Sun's center. A total extinction coefficient defined as T = -lOglO (Direct Radiation/Extraterrestrial Radiation) behaves in much the same way as the turbidity times the relative air mass, although not completely (see Fig. 6). This total extinction coefficient represents the extinction of the total solar spectrum much better than the turbidity times the relative air mass at either 505 nm or 384 rim. The relation between the fractional scattering between 1.01 and 2.86° and the total extinction coefficient is linear as i

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Table 2. Linear correlation between the atmospheric turbidity x air mass, at both 505 nm and 384 nm, and the per cent of the direct radiationscattered within 1.01to 2.86° from the Sun'scenter

HOURS- DST

Fig. 4. Per cent of radiation, measured by a normal incidence pyrheliometer,between 1.01 and 2.86° from the Sun's center. tl June was cloudless but very hazy. In fact during the early morning hours a murky brown haze was evident all around the horizon and persisted until the late morning. ~tWeightingfactor is the reciprocal of the error squared.

505 NM JUNE 2 JUNE i MAY 31 MAY 19 MAY 17 MAY 16 MAY 14 APRIL 3

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347

Measurements of pyrheliometers I

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can be seen in Fig. 7. The weighted linear correlations between the fractional intensity measured by a N.I.P., within the three annular regions discussed here, and the total extinction coefficient are given in Table 3. The correlation of this fractional intensity with the extinction coefficient is generally higher than its correlation with the turbidity times the relative air mass at either 505 nm and 384 nm. The correlation is also generally higher, as might be expected, as the annular region increases (see Table 3).

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4. DISCUSSION

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Table 3. Linear correlation between total extinction coefficient and per cent of direct radiation scattered within the angles indicated DAY JUNE 2 JUNE 1 MAY 31 MAY 19 MAY 17 MAY 16 MAY 14 APRIL 3

1,01-2.86 i, 43-2,86 ,96 ,94 ,35 ,97 ,94 ,91 .97 .60

,93 ,88 ,33 ,99 .90 .78 .41 ,89

2,02-2.86 ,88 .51 ,55 ,98 ,11 .67 ,84 .66

There are basically two important results of the experiment discussed in this paper. The data indicates that the intensity of radiation in the solar aureole has little effect on the intensity measured by N.I.P.s for cloudless conditions. Hence, the measurements of the N.I.P. are, substantially, measurements of the direct beam intensity to within the accuracy of the instrument. A possibly more important result of the data is that there appears to be a linear relation between the percentage of the direct beam radiation scattered into the solar aureole, and the total extinction coefficient. The actual linear equation varied from day to day in both slope and intercept [10]. Attempts to discover other variables (i.e. precipitable water, average turbidity at 505 nm or 384 nm) from which the slope or intercept could be predicted were fruitless. Although the data presented indicates that the intensity of the solar aureole has an insignificant effect upon the measurements of N.I.P.s for cloudless conditions, the effect under cloudy conditions is significant. Data taken in China Lake, California (15 December 1974) on a day with thin uniform cloud cover over the entire sky revealed as much as 11 per cent of the measured intensity was between 1.01 and 2.86° from the Sun's center. The intensity measured by the N.I.P. at this time was 630 W/m 2. An angular intensity, such as this could have large effects on the performance of solar concentrators unless measures were taken to minimize such effects. Because of the large amount of scattering noted under cloudy conditions and the potentially large effect of this scattering on solar concentrators, more data on the solar aureole angular intensity variation needs to be taken under cloudy conditions. REFERENCES

1. R. Eiden, Calculations and measurements of the spectral radiance of the solar aureole. Tellus 20, 380-398 (1%8). 2. B. Herman et al., The effect of atmospheric aerosols on scattered sunlight. J. Atm. Sc. 28, 419--428 (1971). 3. K. Murai, Spectral measurements of direct solar radiation and of Sun's aureole (I). Papers Met. and Geophys. 18, 239-291 (1967). 4. B. Rydfgren, A. photometric study of the solar aureole under various weather conditions. Tellus 20, 55-64 (1968). 5. D. Deirmendjian,Theory of the solar aureole II. Ann. Geophys. 15, 218-249 (1959). 6. D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions. Elsevier, New York (1%9). 7. Eppley Laboratory, Inc., Newport, R.I. 02840, U.S.A. 8. E. Flowers et al., Atmosphericturbidity over the United States, 1%1-66. J. App. Met. 8, 955-%2 (1%9). 9. Philips, Test and Measuring Instruments, Inc., Hicksville,N.Y. 11802, U.S.A. 10. T. H. Jeys, The Contribution of the Solar Aureole to the Measurements of A yrheliometers, Masters Thesis. University of Houston (1975).

348

T.H. JEYS and L. L. VANT-HULL Resumen--Ha sido determinada durante oeho dias la fracci6n de intensidad medida por un pirheli6metro de incidencia normal Eppley (N.I.P.) dentro de tres regiones anulares de la aureola solar. Esta fracci6n fu6 determinada por medici6n de la diferencia de voltaje ajustada entre un N.I.P. y un N.I.P. modificado, dividida por el voltaje de salida corregido del N.I.P. Fu6 determinado que generalmente la fracci6n de intensidad dentro de la aureola tiene un pequefio efecto sobre la intensidad rnedida por el N.I.P. incluso en dias brumosos. Los datos tornados revelan una relaci6n linear entre la fracci6n de la intensidad del haz directo difundida dentro de la aureola y el coeficiente de extinci6n total de la atm6sfera. R6Snln6--On a d6termin6 pendant huit-jours la fraction d'intensit6 ~ l'int6rieur de trois r6gions annulaires de la couronne solaire, intensit6 par un Pyrh61iom~tre ~ incidence normale Eppley (NIP), de fabrication courante. Cette fraction a 6t6 d6termin6e en mesurantla diff6rence de tension ajust6e, entre le NIP et un NIP modifi6, divis6e par une tension de sortie corrig6e du NIP. La fraction d'intensit6 b, rint6rieur de la couronne a ~t6 trouv6e de peu d'effet sur l'intensit6 mesur6e par le NIP, m6me pour des jours brumeux. Les mesures enr6gsitr6es indiquent une relation lin6aire entre la fraction de rayonnement direct diffus6e dans la couronne, et le coefficient d'extinction total de l'atmosph~re.