Sky Brightness and Polarization During the 1973 African Eclipse

Sky Brightness and Polarization During the1973 African Eclipse

Glenn E. Shaw

The absolute intensity, color, and polarization of the sky were measured during the eclipse of 30 June 1973in Northern Kenya. Zenith sky radiance during totality decreased by a factor of 104 from the normal daysky value. The distribution of sky intensity with angle on the celestial hemisphere was approximatelysymmetrical about the local zenith, with this point having the minimum intensity value. The spectral dis-tribution of zenithal diffuse skylight shifted toward the blue during totality, but the horizon reddened.The polarization ratio P decreased from a normal day value of 0.45 to 0.04. There is evidence that the dis-tribution of polarization ratio is strongly affected by variations in surface albedo. The major results arecompatible with predictions based on a radiative transfer model that considers double-scattering processesonly.

1. Introduction

Sky radiance during a total eclipse of the sun re-sults from a combination of multiple-scattered sun-light and airglow emissions. If it were not for theseprocesses, the sky would be completely dark (exceptfor the coronal radiation) during totality. As it is,however, the illumination from the zenithal region ofthe eclipsed sky roughly approximates twilight condi-tions for a solar depression angle of about 570.1Said another way, the sky radiance during totalitycorresponds roughly to civil twilight; it is usuallydark enough to see the brighter planets and a fewstars, generally those brighter than about magnitudetwo. A compendium of interesting observations con-cerning the brightness of the sky during totality isgiven by Silverman and Mullen.'

Although there have been numerous reports on thecolor, polarization, and brightness of the zenith skyduring totality, 2-7 there are only a few reports ofmeasurements of the distribution of these variableswith angle on the celestial hemisphere, that is, thevariation of the Stokes parameters in different view-ing directions.8 In addition, there has been practi-cally no work reported on modeling of the radiativetransfer process that occurs in the geometry of a totaleclipse. Hence, although it is widely recognized thatthere are differences in the sky radiation parametersfrom one eclipse to another, these have only rarely

The author is with Geophysical Institute, University of Alaska,Fairbanks, Alaska 99701.

Received 10 July 1974.

been related to physical variables such as ground al-bedo, solar elevation angle, air turbidity, altitude ofthe observing station, and the like, although Sharp etal. 3 have presented some information in this regard.Because of this, it has been difficult to a priori esti-mate the expected sky brightness for any given ec-lipse of the sun. As a result, solar astronomersstudying the outer corona have had to bracket photo-graphic or photoelectric exposures widely to insurethat the data fall within the dynamic range of thefilm or instruments's reponse. This often means aloss in valuable time during the few minutes that onehas available to conduct ground-based measurementsof the corona.

In this paper we report on measurements, whichwere made during the African solar eclipse on 30June 1973, of sky brightness, color, and polarizationand their variation with angle in both the solar verti-cal plane and in a plane perpendicular to the solarvertical plane. The sky radiation parameters weremeasured at eight narrow-wavelength intervals (AX =10 nm) extending over the 400-700-nm region.

11. Experimental Procedure

A. Eclipse Parameters

The measurements of sky radiation and polariza-tion were made on 30 June 1973 at LoiyengalaniOasis along the southeast shores of Lake Rudolf inNorthern Kenya (latitude 245.7'N; longitude360 42.0'E; elevation 455 m above msl). At this loca-tion, second contact occurred at 12 h, 57 min U.T.,and totality lasted for nominally 294 sec. The maxi-mum magnitude was equal to 1.072, and the terrestri-al coordinates of the sun at midtotality were:. solar

388 APPLIED OPTICS / Vol. 14, No. 2 / February 1975

Eclipse-GeometryLoiyengalani, Kenya12hr,59m,30sec U.T.,30 June,1973

N

M-roloS

35E 36' 37- 38, 39.

I 5.

Fig. 1. Map of the area around Loiyengalani Oasis, Kenya, show-ing the intersection of the umbra with the ground and with a hori-

zontal plane located at an altitude of 50 km at midtotality.

elevation angle, 370; solar azimuth 2970 measuredfrom north. The pathwidth of totality was equal to234 km, and the center line of the eclipse passedwithin 18.4 km of the observation site to the south-west. Figure 1 shows the intersection of the umbrawith the ground and with a horizontal plane at an al-titude of h = 50 km during midtotality. The umbramoved with an apparent velocity of 1270 m/sec alongthe path of totality. Also shown in Fig. 1 are somegeographic features and estimates of surface albedosat a mean wavelength of 0.7 as roughly derivedfrom ERTS satellite photographs of the area.

B. Radiation Instruments

Diffuse radiation parameters were measured withthree photometers; all employed evaporated thin filminterference filters to isolate 10-nm wide wavelengthregions. In this section we describe the individualinstruments that were used to measure radiation pa-rameters.

Photometer A is a filter-wheel photometer with acircular field of view with an angular diameter of 10°.The detector is a 1P21 photomultiplier tube. Anodesupply voltage is derived from an adjustable preci-sion voltage-controlled power supply with stability of1:1000. The anode current is measured with a tem-perature stabilized logarithmic amplifier having a dy-namic range covering 3 orders of magnitude. Filterrotation rate is 3.1 rpm. The filters are centered atthe following wavelengths: 400 nm; 445 nm; 486 nm;500 nm; 575 nm; 610 nm.

Photometer B is a single channel instrument oper-ated at a wavelength of 705.6 nm. It uses a RCA7265 photomultiplier tube with an S-20 response.The field of view is circular with angular diameterequal to 2.50°. Output is derived through a quasi-logarithmic amplifier. It points at the zenith.

Photometer C is a two channel scanning photome-ter/polarimeter with entrance aperture of 37.4 cm2

equipped with P21 photomultiplier tubes. It hasthe capability of scanning in elevation and azimuth.The instrumental field of view is defined by a rectan-gular aperture subtending 1.44° in elevation and5.44° in azimuth. The two photometer barrels arecoaxially aligned and carefully baffled to inhibit lightentering the system from outside the field of view.Anode electric currents are passed through Keithly610R electrometers. Photomultiplier tube voltage issupplied by a precision adjustable power supply.The dynamic range is extended by (a) adjusting thePMT high voltage and (b) inserting vacuum deposit-ed metal neutral density filters. Channel A monitorsradiation at a mean wavelength of 600 nm; channel B,which is equipped with a motor driven rotating polar-izer, is centered at X = 400 nm.

During totality repeated scans were made in thesolar vertical plane and in a vertical plane perpendic-ular to the solar vertical. In addition, almucantarscans were made of the horizon at a mean elevation of20.

C. Direct Sun Photometer

A fundamental parameter involved in radiativetransfer calculations is the total optical depth r of theatmosphere arising from scattering and absorptionby molecules and aerosols suspended in the air. Wedetermined optical depth by measuring the magni-tude of the ground-level solar flux with a small sunphotometer. This photometer employed a solid-state silicon photodetector as a sensing element.Narrow-wavelength regions (10 nm wide) were select-ed by inserting optical interference filters in the opti-cal path. The instrument was carefully calibratedand corrected for temperature. Optical depth wasdetermined by employing Beers law of extinction; themethod used is described in detail by Shaw et al. 9

D. Photometer Calibration

The photometers were carefully calibrated in abso-lute units of irradiance (W cm-2 nm- 1 sr-') byviewing a diffuse white surface (Eastman white re-flectance standard 6091), which was illuminated by a200-W quartz iodine lamp powered by a controlledregulated-current power supply. The calibrationlamps had been previously calibrated by a standardslaboratory, and the calibration was checked periodi-cally for internal consistency throughout our stay inKenya. An error analysis indicates that the photom-eter relative calibration error was approximately0.03. Effort was expended to insure that the pho-tometer output was linearly related to irradiance overa total dynamic range of 5 orders of magnitude.

111. Results and Discussion

A. Distribution of Sky Brightness on the CelestialHemisphere

During pretotality and totality, there were scat-tered small cumulus clouds in the sky. The sky over

February 1975 / Vol. 14, No. 2 / APPLIED OPTICS 389

contact, with the radiation parameters being relative-Sky Intensity-Solar Vertical Plane-Totality - ly more constant during the midportion of totality.

Loiyengolani Site -June 30,1973Xa400nm The varying sky brightness can be inferred in Figs. 2

and 3 from the fact that the repeated scans in the233 solar vertical plane give slightly differing curves.

.D 73 The numerals on the curves in Figs. 2 and 3 refer to135sec 282 23 9 4 \ 17 times (measured in seconds from second contact) at

which the photometer was pointing at the listed ze-nith angle. As can be seen, the shape of the curves isreasonably constant, although the ordinate values

0 : e vary somewhat from scan to scan. The spike in Figs.2 and 3 is primarily caused by radiance of the solar

Hizon Horizon' corona, although part of this may also be due to for-I , . Is - I | I12 ward scattering of coronal energy by large aerosols (r

00 -80 -60 -40 -20 0 20 40 60 o (0oo > 10 Am) in the earth's atmosphere. The photome-ZENITH ANGLE (degrees) ter field of view in the scan direction was numerically

Sky radiance at 400 am (ordinate values rInF0 ) in the equal to 1.440, and thus the photometric details ofvertical during totality. Numerals refer to measurement the solar corona are integrated out and do not ap-

times (in seconds) from second contact. pear.Figures 4 and 5 show sky brightness in a vertical

plane perpendicular to the solar vertical at wave-

ZENITH ANGLE (degrees)

Fig. 3. Sky radiance rI/F0 at 600 nm in the solar vertical duringtotality.

the lake, however, tended to be reasonably free ofclouds. At the time of totality a large cumulus deckexisted in the north and east sectors over Mt. Kulal,reaching an average elevation angle of about 10°.The sky near the sun was almost free of clouds, butthere were several remnants of evaporating cumulisubtending an angle of 5-10° within an approximate30° radius from the sun. Total sky cover, exceptinga band near the horizon, was judged to be about 10%.Horizontal visibility was approximately 30 km.

Figures 2-5 illustrate the sky brightness plottedagainst zenith angle during totality. Regions ofcloud interference are marked by dashed lines. Fig-ures 2 and 3 show sky intensity in the solar verticalplane at wavelengths of 400 nm and 600 nm, respec-tively. As the umbra moved across the observationpoint, the sky intensity and color varied somewhatdue to the changing scattering geometry. The majorchanges, of course, occurred during the first few sec-onds following second contact and just prior to third

.- 5

a 148 sec

l0-5

- - - - Clouds

South North5 Horizon Horizon

-100 -80 -60 -40 -20 0 20 40 60 80 100


Fig. 4. Sky radiance 1I/F0 at 400 nm in a vertical plane perpen-dicular to the solar vertical during totality.

lo-,

5

2

10-n

5

Sky Intensity-Perpendicular Solar Vertical-Totality

Loiyengalani Site - June 30,1973X = 600nm

148 sec

\ /,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

208 sec

North -Horizon

I 2 l I I l l l

-100 -80 -60 -40 -20 0 20


-SouthHorizon

- - - - Clouds

40 60 80 100

Fig. 5. Sky radiance 7rI/Fo at 600 nm in a vertical plane perpen-dicular to the solar vertical plane during totality.


2

5

2

arn

10-

5

-II

Fig. 2.solar

�11

0

Y

Sky Intensity-Solar Vertical Plane

14.in prior to 2nd contact

Loiyengalani Site

'I.S .

Z° Horizon

C ,:-100 -80 -60 -40 -20 0 20

ZENITH ANGLE degrees)

ace _ /iJ~~~~~~~~~~~~~~~~~~~~~~~~~~horizon X 600nm~~~~~~~~~~~~~~~~~Clouds.

40 60 80 100

Fig. 6. Sky radiance inI/Fo at 400 nm (solid) and 600 nm

(dashed) in the solar vertical during the partial phase of theeclipse.

lengths of 400 nm and 600 nm. These data were ac-quired near the midpoint of totality when the skyconditions were relatively constant.

One can see immediately that the distribution ofsky radiation during totality is remarkably smoothand tends to be approximately symmetrical aroundthe local zenith direction. This is in great contrast tothe distribution of sky radiation that occurs duringthe daytime for noneclipse conditions. Figure 6 il-lustrates the sky intensity in the solar vertical planeat wavelengths of 400 nm and 600 nm made 14 minprior to totality. A comparison with the curves madeduring totality (Figs. 2 and 3) shows that the shape ofthe curves differs substantially. Worthy of specialnote is the enhancement of diffuse radiation near thesun. In addition, one should note the relative mini-ma in intensity that occurs approximately 90° fromthe sun. Comparison between measured sky radia-tion data during noneclipse conditions to curves ofsky brightness calculated for a pure molecular scat-tering atmosphere without aerosols10 shows that theatmosphere aerosols strongly perturb the radiationfield which results in (a) the sky being several timesbrighter than a pure Rayleigh scattering atmosphereand (b) the occurrence of an aureole or whitish glowsurrounding the sun and extending outward from thesun for 20-30°. This aureole is due to the near-for-ward scattering of sunlight by aerosols in the tropicalatmosphere. There is no tendency for the day skyradiation field to be symmetrical about the zenith, indistinct contrast to the sky brightness distributionobserved during totality.

B. Temporal Changes in Sky Intensity

Apart from the changes in the relative distributionof diffuse sky radiation, the magnitude of the intensi-ty values at totality are also, of course, very much re-duced from what they would have been for anyequivalent day sky. Figure 7 shows the course of skyradiance (in the solar vertical, 900 from the sun) as a

function of geometric obscuration of the sun's disk(not corrected for limb darkening). Also shown forcomparison in Fig. 7 is a curve of sky brightness (at600 nm) during normal clear sky conditions forequivalent solar elevation angles. According to thedata shown in Fig. 7, the sky brightness decreased bya factor of 7.6 X 103 at X = 600 nm. Figure 8 illus-trates the variation of zenith sky intensity at X = 445nm throughout totality. We speculate that theslightly asymmetric shape of the curve about themidpoint of totality may be due to a combination of(a) changes that occur in the eclipse scattering geom-etry as the umbra passed over the observer, andhence in the nature of the radiative transfer -pro-cesses, and (b) slight variation in the circular profileof the moon and by the topographic variations of thelunar surface. We have not analyzed these asymme-tries quantitatively, but we remark that they havebeen noted by other investigators.3 12

C. Polarization Measurements

The change of sky polarization that occurs duringtotality is complex and depends on the distributionand magnitude of numerous parameters. Amongthese we mention variations in ground albedo, solarelevation angle, eclipse shadow diameter, opticalthickness of the atmosphere, and the distributionand extent of the cloud cover. In view of the com-plex geometry and the number of mitigating parame-ters (many of which are unknown), we have not at-

zI-

zn

2L-0.4 -0.6 -0.8 -1.0 1.0 0.8 0.6

GEOMETRIC OBSCURATION0.4

Fig. 7. Sky radiance irI/Fo as a function of solar geometric ob-

scuration ratio at 400 nm (solid) and 600 nm (dashed). Sky ra-diance during normal noneclipsed conditions (X = 600 nm) is

shown for comparison.


5

2

loo

5

2

10''

I , . . . . . . . . .

- I

0.7

0x

I-LUz

z

Cn

I-z

I , , , I

60 120 180 240 300TIME FROM 2ND CONTACT

(SECONDS)

Fig. 8. Zenith sky radiance rI/Fo at 445 nm during the totality.

tempted to explain or interpret the polarization de-crease, except in a very general and qualitative way.

One would expect that the polarization ratio Pshould diminish during totality because of the ran-domizing effects of multiple scattering (m.s.). In-deed, as Fig. 9 shows, the polarization ratio did de-crease as expected. The data in Fig. 9 were taken atan angular distance of 900 from the sun in the solarvertical plane at a mean wavelength of 400 nm.

As can be seen, the polarization ratio decreasedfrom an approximate preeclipse value of P = 0.45 toa value of P = 0.04 during midtotality. This agreesreasonably well with other reported observa-tions47 11; for example, Rao et al. 7 measured a de-crease from P = 0.45 to P = 0.005 at an altitude of12.3 km on 30 May 1965 and at X = 475 nm (thin ciclouds reported). They also report a decrease from P= 0.59 to P = 0.19 at an altitude of 10 km in Novem-ber 1966 and at X = 436.5 nm (clear sky conditions).Our measurements fall roughly halfway betweenthese values. Figure 10 shows the manner in whichthe polarization ratio is distributed across the skyboth 14 min prior to totality and during midtotality.The course of polarization P with zenith angle 14 minprior to totality (solid line in Fig. 10) is what onewould expect for a Rayleigh scattering atmospherethat is degraded by aerosols that generally act tocause a decrease in the maximum polarization ratio.13The maximum polarization for a pure Rayleigh scat-tering atmosphere for the appropriate conditions (ZO= 510, Z = -39°, A = 0.12, r = 0.364) is equal to0.67. As mentioned, the observed maximum of 0.39is smaller due to aerosol scattering effects (and alsoperhaps due to some rise in multiple scattering inthis instance since the geometric obscuration ratio is76%).

The curve of sky polarization in the solar verticalplane changes dramatically during totality (see dot-ted line in Fig. 10). Interestingly, the polarizationratio reaches a minimum near the zenith and in-creases with increasing zenith angle to a maximum atZ = 60-70°, then falls sharply as the horizon is ap-proached. The asymmetry in the curve may be dueto variations in ground albedo. If one looks in thedirection of the sun's azimuth, one passes over thewaters of Lake Rudolf. The water surface has aspectral albedo (as computed from the Fresnel for-mula) of approximately 2.5% for the appropriatevalue of solar elevation. In the antisun direction(1800 from the sun), one passes over arid terrain and,at a distance of 70 km, over the Chalbi Desert whichis composed of white gypsum sand with a high reflec-tivity estimated at 10.4.14 ' ERTS satellite photo-graphs of the area also show a high albedo. Thehigher surface albedo in the antisun direction, alongwith cumulus cloud decks over Mt. Kulal to the east,no doubt resulted in additional high order scatteringfrom the reflected radiation with an attendant de-crease in polarization ratio.' 5 This hypothesis is

70 I I IICIIX: 400 nm

Solar Vertical Plane60 Z=-39° (l0 =90°)

0

8 40Sotality

CO 30

20

10

0800 400 0 0 400 800 1200 600

TIME PRIOR TO 2ND CONTACTFOLLOWING 3RD CONTACT (seconds)

Fig. 9. Sky polarization ratio at 400 nm in the solar vertical 900

from the sun.

Solar Vertical Plane40 Y 400 nmr

z Pre Totality0 ~~~~~~~~(T2 -14mi.)

'~20

a: ~-." Totality/

o 10 /0~~~~~~~~

0.00-90 -60 -30 0 30 60 90


Fig. 10. Sky polarization ratio at 400 nm in the solar vertical dur-

ing pretotality (solid) and totality (dotted).


4x10-

2X10-

1 X10

5X10-

2X10-

0.5 0.6 0.7WAVELENGTH ()

(a)

0.4 0.5 0.6WAVELENGTH

(b)

0.7(IL)

Fig. 11. (a) Spectral distribution of zenith sky radiance irI/Fo atsolar noon on 30 June 1973. Calculated radiance resulting fromscattering in pure molecular atmosphere (r = TR) and for scatter-ing in an atmosphere with r = TR + TD are illustrated. (b) Spec-

tral distribution of zenith sky radiance during midtotality.

consistent with the observed asymmetry in polariza-tion ratio shown in Fig. 10.

D. Wavelength Dependency of Sky Radiation

Many authors have reported that the spectral dis-tribution of zenith sky radiance during a total eclipseshifts toward the blue.2-6 "4 The change in sky coloris due to a change in the ratio of single scattered tomultiple scattered sunlight by the atmospheric con-stituents. Dandekar,16 reports color shifts in termsof an effective blackbody temperature. He reportsvalues for the normal day sky, midtotality, and twi-light as 9100 K, 11,100 K, and 7,800 K, respectively.That is to say that the zenith sky color effectively be-comes bluer during totality than it would be underequivalent normal day sky conditions and considera-bly bluer than under twilight conditions. This, qual-itatively speaking, might at first be expected, sincethe diffusion of blue light would be more affected bym.s. processes than red light. On reflection, how-ever, the problem is complicated by the fact that theprimary-scattering illuminating rays, which comefrom outside the umbra, pass through long, nearlyhorizontal, pathlengths through the atmosphere andhence are considerably reddened (just as at twilight).Thus, it is difficult to say a priori, without recourseto a detailed radiative transfer model, whether thesky radiation during totality would be expected toshift toward bluer or redder wavelengths.

Figure 11 illustrates the wavelength distribution ofzenith sky intensity as observed and as calculated forvarious circumstances. The lower line in Fig. 11(a)shows the expected zenith radiance for local noon fora pure molecular (Rayleigh) atmosphere with opticaldepth TR. The curve was derived from tabulated so-lutions to the equation of transfer which includes allorders of scattering.' 0 The observed sky-radiancevalues at noon on 30 June are shown as dots, and fi-nally we show (upper curve) the sky radiance that

would result from an atmosphere scattering accord-ing to the Rayleigh-scattering mechanism and havingan optical depth r equal to the total observed opticaldepth (Rayleigh plus aerosol), which numerically wasequal to 0.32 at 500 nm. This technique should beexpected to give only an approximation to the ob-served zenith sky radiance because the aerosol scat-tering phase function deviates considerably from aRayleigh-scattering phase function.'7 Nevertheless,a comparison of the upper curve (calculated for anatmosphere having r = R + T-D) and the observeddata give reasonable over-all agreement, especiallyfor the color distribution. If one excludes the anom-alous datum at X = 0.6 gim, the agreement is better,although the theoretical curve seems to give a slightlysteeper falloff of sky intensity with increasing wave-length than was observed. We remark that the ze-nith sky is considerably whitened by the aerosolsover what would have been for the hypothetical caseof a pure Rayleigh scattering by the air moleculesalone. This is also consistent with observations; thesky at Loiyengalani gave the general appearance ofbeing washed out or milky and certainly considerablydifferent than the deep azure sky as seen from moun-tain observatories in the western United States.

At midtotality, the distribution of zenith sky radia-tion on wavelengths falls off rapidly [see Fig. 11(b)].As can be seen by comparing Figs. 11(a) and 11(b),the color ratio indeed shifts toward the blue. Thereis an apparent monotonic increase in the sky red/blueratio as one approaches the horizon. In particular, areddish glow surrounding the horizon to an elevationof approximately 80 was visually very apparent, andthis phenomenon has been commented upon by oth-ers.3 It results from primary-scattered radiationfrom outside the umbra.

E. Relation to Other Eclipses

The sky radiation at totality varies considerablyfrom one eclipse to another. An excellent summaryof comparisons of zenith brightness is given by Sharpet al.3 These authors note that the zenith bright-ness may be considered as attenuated sunlight up to99.8% obscuration. We too have found this to be thecase. Sharp et al. 3 present a curve showing the ratiobetween zenith sky brightness at midtotality Itot andthe zenith sky brightness at a geometric obscurationratio of 98.7%, 19.7, for six different eclipses. Thevalues of Itot/I98.7 ran from a minimum of 0.01 to amaximum of 0.04 for the six eclipses analyzed. Werecorded a value of Itot/I98.7 = 0.02 in the midvisible,rising to 0.03 in the far red (X = 640 Aim). Sharp etal. 3 also have studied the variations of the aforemen-tioned intensity ratio as a function of solar elevationangle. They found a generally increasing trend inthe ratio with increasing solar elevation, that is, Itot!I98.7 is larger for high elevation angles, although thereis considerable scatter. (We note that there is a fac-tor of 10 error in the ordinate scale in Sharp et al.'spaper, i.e., the printed values, 0.003 should be 0.03.)Our measured intensity ratios are very close to Sharp


I-Onzz

On

NNy

5

5 a-_

-I

-6

I -

et al.'s standard curve for the appropriate elevationangle ( = 370); the standard curve predicts a valueof R = 0.030 to be compared to our measured mid-visible value of R = 0.022.

We remark that variation about any standard ec-lipse sky brightness relation will occur due to varia-tion in mean cloud cover, altitude, optical depth, andsurface albedo. In view of the fact that the sky in-tensity had undergone a 4-order of magnitude changefrom normal conditions, we find this agreement is re-markably good and lends credence to the physical re-ality of Sharp et al. 's standard curve of ItotI98. 7.

IV. Concluding Remarks

We have developed a rough radiative transfermodel for the eclipse geometry which treats scatter-ing of order 2. This model will be described in aforthcoming paper. It is of interest, however, topoint out that the major features of the observed skybrightness and color distribution are consistent withthe model results. In a way this is fortuituous sinceone might expect that higher order scattering (n >2), which our model did not include, would be veryimportant in the radiative transfer mechanism. Wetentatively conclude that tertiary and higher ordersof scattering represent something like 20% of thetotal radiative field, and the major features of the ra-diation scattering can be predicted from double-scat-tering theory alone. These remarks are in relation tothe intensity and color balance only. Our modelingefforts were restricted to scalar fields and did nottreat polarization.

To summarize, we point out that our measure-ments of zenith sky intensity are, generally speaking,in accord with other reported measurements. Thedecrease in sky brightness, and its temporal behaviorfollows a standard curve, and up to a point the skybrightness can be considered to result simply fromattenuated sunlight as given by the solar obscurationratio. For high obscuration ratios, greater thane98%, multiple scattering predominates, and thedistribution of color, intensity, and polarization overthe sky hemisphere changes rapidly and dramatical-ly. The zenith sky color shifts toward the blue, butthe horizon, up to an elevation of about 80, reddensconsiderably. The polarization ratio tends to berather symmetric about the zenith and is strongly af-fected by variations in surface albedo, with high albe-dos corresponding to lower polarization ratios.

The distribution of diffuse sky brightness duringtotality is a smoothly varying function with apparentsymmetry about the local zenith. The variation inabsolute intensity from zenith to horizon is a factorof 3 less in the blue (400 nm) than it is in the red (X =600 nm). This means that there is a monotonic red-dening of sky color when one goes away from the ze-nith toward the horizon.

The author expresses his appreciation to all whoplayed a part in the preparation and execution of theexperimental portion of this work. In particular, I

thank the field support group at NCAR for their ex-cellent logistics support. Also, the helpful coopera-tion and friendliness extended to us by governmentofficials of the Republic of Kenya is appreciated. Fi-nally, I am especially grateful to Larry Sweet who ac-companied me on the African eclipse expedition. Hedevoted many long hours working in the intense heatunder difficult conditions, and the success of the ex-periment is in large part attributable to his dedica-tion.

C. Deehr offered many helpful suggestions duringthe preparation of this paper. Support for this studywas provided by National Science Foundation GrantGA-36871.

References

1. S. M. Silverman and E. G. Mullen, "Sky Brightness during Ec-lipses: A Compendium from the Literature," unpublished,June 1972.

2. W. E. Sharp, J. W. Lloyd, and S. M. Silverman, Appl. Opt. 5,787 (1966).

3. W. E. Sharp, S. M. Silverman, and J. W. F. Lloyd, Appl. Opt.10, 1207 (1971).

4. B. S. Dandekar and J. P. Turtle, Appl. Opt. 10, 1220 (1971).5. W. N. Hall, Appl. Opt. 10, 1225 (1971).6. J. W. F. Lloyd and S. M. Silverman, Appl. Opt. 10, 1220

(1971).7. C. R. Rao, T. Takashima, and J. G. Moore, J. Atmos. Terres-

trial Phys. 34, 573 (1972).8. J. G. Moore and D. Lamb, Annal. Geophys. 23, 339 (1967).9. G. E. Shaw, J. A. Reagan, and B. M. Herman, J. Appl. Meteo-

rol. 12, 374 (1973).10. K. L. Coulson, J. V. Dave, and Z. Sekera, Tables Related to

Radiation Emerging from a Planetary Atmosphere with Ray-leigh Scattering (University of California Press, Berkeley1960), p. 548.

11. J. G. Moore and C. R. Rao, Annal. Geophys. 22, 147 (1966).12. C. S. Deehr and M. H. Rees, Planet. Space Sci. 12, 875 (1964).13. E. deBary, Appl. Opt. 3, 1293 (1964).14. K. Ya. Kondratiev, in Radiation in the Atmosphere, Interna-

tional Geophysics Series, J. Van Miegham, Ed. (Academic,New York, 1969), Vol. 12.

15. K. Bullrich, "Scattered Radiation in the Atmosphere," in Ad-vances in Geophysics (Academic, New York, 1966).

16. B. S. Dandekar, Appl. Opt. 7, 705 (1968).17. G. E. Shaw and C. S. Deehr, "On the Relation Between Cir-

cumsolar Sky Brightness and Atmospheric Aerosol," EPA Re-port (1974), in press.


Documents

Sky Brightness and Polarization During the 1973 African Eclipse