Jul 1, 1981 - The changing sky brightness during the Martian twilight as measured by the Viking lander cameras is shown to be consistent with data ...
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 86, NO. A7, PAGES 5833-5838, JULY 1, 1981
The Martian Twilight RALPH
KAHN
AND
RICHARD
GOODY
Centerfor Earth andPlanetaryPhysics, Harvard University, Cambridge, Massachusetts 02138 JAMES
POLLACK
SpaceScienceDivision,NASA AmesResearchCenter,Moffett Field, California 94035
The changingskybrightnessduringthe Martian twilight as measuredby the Viking landercamerasis shownto be consistent with data obtainedfrom sky brightness measurements. An exponentialdistribution of dustwith a scaleheightof 10 kin, equalto the atmosphericscaleheight,is consistentwith the shapeof the light curve.Multiple scatteringresultingfrom the forward scatteringpeak of large particlesmakesa major contributionto the intensityof the twilight. The spectraldistributionof light in the twilight sky may requireslightlydifferentopticalpropertiesfor the scatteringparticlesat high levelsfrom thoseof the aerosol at lower levels.
1.
INTRODUCTION
we regard the results for sol 41 as the most tractable. Moreover, on sol 41, solar attentuation measurements were made
The twilightmeasurements on the Viking landerpermitus to studytheverticaldistributionof scattering properties in the an hour or two beforesunset,and a daytimesky brightness Martian atmosphere. In effect,the combinationof the plan- measurementwas made a few hours earlier. The particle are reportedby etaryshadowand the decreasing numberdensityof particles propertiesdeducedfrom theseexperiments with heightformsthe raysof the suninto a beam which scans Pollacket al. [1979,hereafterreferredto aspaper2]. We beto be of sufficiently lessvalueasnot to to progressively higheraltitudesasthe eveningtwilightwears lievethe otherRescans on (seethe schematicrepresentationof the sourcefunction in justify the labor of reduction at this time. The twilightgeometryis illustratedin Figure 1 for the case Figure 1). In this paper we will discussthe Twilight Rescan Experi- of zero azimuth(A -- 0). Quantitiesare definedas follows: ment performed with the Viking lander cameras. This ex•1 azimuthal angle of the camera direction measuredin periment is a natural outgrowthof earlier work on the terresthe plane tangentto the geoid at the location of the trial twilight [Rozenberg,1966; Volz and Goody, 1962]. The camera (•1 -- 0 is defined as the line of intersection of term 'twilight' refers to the time of day when the disk of the this plane with the plane containingS, O, and D. A sun is just below the local horizon,while the sky overheadis verysmallchangein •1 cantakeplaceduringa twilight illuminatedby directsunlight.We shall refer to the succession run. Althoughof minor significance, this effectis incorof eventsas they occurduring the eveningtwilight; the mornporatedpreciselyinto our calculations.); ing and evening twilights are geometricallyequivalent. We B a point effectivelyoutsidethe atmospherein the direchave introducedthe Twilight Rescan Experiment, together tion of the sun; with the related Viking lander cameraatmosphericopticsexC intersection of the line of sightwith the shadowedge periments,in the work by Pollack et al. [1977, hereafter re(thisisthelocationof thelowestprimaryscattering volferred to as paper 1]. In paper 1 a model basedupon single ume);
scattering wascompared withthedata.In ihispaper weshow CD line of sightof the camera; that multiple scatteringplays a dominant role in the Martian
D O R S
twilightand the 9onclusions mustbe reconsidered. Our overall conclusionis that, with a minor exception,the Martian twilight can be describedquantitatively in terms of dustfrom the lower atmospherewith a reasonableheight distribution.
Thus we are not led to new conclusions about the
SC shadowedgeof the planet (all pointsaboveSC are di-
physicalstate of the Martian atmosphereitself. Nevertheless, the twilight is a cl!•ssicalproblemof atmosphericoptics,and a completelynew set of data on a planet other than earth deservesthe effort to confirm that our theories are soundly
rectlyilluminated, whileall pointsbelowreceiveonly sca•ttered light); Z height above the surface; Zo •]osestapproachof the ray BG to the surface;
based.
Z• heightof pointC abovethe surface, i.e.,the heightof
The analysispresentedhere is for the VL 1 sol41 P.M. Twilight Rescan, which we have selectedas the best and most
the shadowin the line of sight; 8 solardepression angleat the camera(proportionalto
straightforward to ahalyze. Sixcomplete TwilightRescans are
}hetimeelapsed aftersunset);
available. These occurredduring a period in which the total amount of dust (as measuredby solar extinctionexperiments) was increasing.Sol 41 is the earliestand is the occasionof the
e camera elevation angle; *t* angularradiusof the solaraureole;
0 angleof scatterof light from the directsolarbeam into
mosttranspa.rent atmosphere by at leasta factorof 2. Since multiple scatteringis a troublesomefeature of the analysis, Copyright¸ 1981by the American GeophysicalUnion. Paper number 1A0337. 0148-0227/81/001A-0337501.00
location of the camera; centerof the planet; radiusof the planet, equal to 3395 km; location of the sunsetpoint, where the incident solar ray is tangentto the planetarysurface;
the camera.
The naturalindependent variablesfor thisproblemare 8, e, •1(= 0), and Zo,whichcompletely definethe singlescattering
5833
5834
KAHN ET AL.: THE MARTIAN TWILIGHT
••••ource X Gfunction
(B) •• /(B)/•j
sameaccuracy.This translatesinto an uncertaintyin the position of the shadowedge of about 1 km for the largestZ, values used. The data were recorded with VL
I camera 2. Calibration
includesconsiderationof cameratemperature,diode degradation, and vignettingeffects.The resultsreportedby Patterson et al. [1977]and additional calibrationsin the handsof the Viking project indicate an accuracyof ñ 10%in the absoluteintensitymeasurementsand ñ5% in relative intensity.Theseerrors do not affect our conclusionsin any signficantway. In order to minimize errors due to encoding,the twilight sequenceconsistedof three successive picturestaken with different gain settings.The overall level of the noisein the data can be judged from the scatterof points with respectto a smoothcurvethroughthe data in Figures5 and 6. It is only of significancefor the highestdata pointsand doesnot influence our conclsuions.
We give the data in terms of observedbrightness,normalized to that of a Lambert surfacein the orbital position of Fig. 1. The twilightgeometry.Symbolsare definedin the text. Mars illuminated perpendicularlyby the sun (the intensityraThe curve labeled 'source function' is schematic and illustrates the distributionof scatteredlight alongthe line of sight.In a typical ex- tio, Y). Accountis taken of the seasonalvariation of the Marsample with Zl -- 20 km the sourcefunction for singlescattering sun distancein this procedure.The twilight sky brightnessis peaked30 km abovethe shadowedgewith a full widthat half maxi- sufficientlyuniform to allow a linear schemefor interpolation o
mum of 25 km.
of the data in Z, and 19.
The observedbrightnessis comparedwith that calculated
geometry. To derivethetwilightintensity forparticular values from a theoreticalmodel of the twilight. The model assumesa of 8 and F, an integrationis performedoverZo or an equiva- vertical distributionof scattererswhich is sphericallysymmelent variable,sinceZo definesthe pathsBG and GD. In prac- tric about the planet. Recognitionof the presenceof discrete tice,we preferto use,in additionto Zo,theindependent vari- cloudsor obstaclesin the path of the twilight ray will be exablest9(8,F,A • 0) andZl(/•, •, A • 0): theformerbecause it plainedin a later section.We neglectRayleighscattering,airspecifies the scattering phasefunction,the latterbecause it is glow, and atmosphericrefraction.Theseassumptions will be relatedto the heightat whichmostprimaryscatteringoccurs. discussedsubsequently. The modelparametersincludea verticaldistributionof parA slightchangein the azimuthangleallowst9to be held constant while Z, varies.
ticles which determinesthe particle number density at each We assumethat the atmosphericoptical propertiesare a height.We alsospecifythe particlemean radius,the particle functionof Z only (exceptthat we shall considerthe possi- sizedistribution,and the real and imaginaryindicesof refracbility of mountainsor cloudsat the sunsetpoint). This as- tion at eachheight.In selectingthe input valueswe usethe resumptionis commonto all attemptsto interprettwilightdata. sultsof the solar extinctionexperimentsto constrainthe total The Viking camerageneratedusefuldatawith e varyingfrom opticaldepthof the column,and we usethe resultsof the sky about 5ø to 35ø for each/•, so we obtain information for each brightnessexperimentto obtain the particle properties(see Z, value for a number of combinationsof e and & This per- paper2). The opticaldepthin red light from paper I is 0.37 ñ mits the selectionof subsetsof the data for which Z, and 19can
0.04. This differs from conclusionsbased on orbiter data, but,
be variedindependently. For example,we canextractdatafor a rangeof Z• valueswith a constantvalueof 19,therebyobtaining informationabout the vertical distributionof scatterers which is independentof the scatteringphasefunction of
beingbasedupon direct solarmeasurements, we considerit to be more reliable, sinceit is basedon a model independentapplicationof Beer'slaw. The quantitativeresultsin this paper would not be greatlyinfluencedif it were as smallas 0.1. The
the particles.
Thecurves in Figure 2 define theregion oftheZ•-Oplane
5o
for which useful data could beobtained during the VL1sol 41 P.M. TwilightRescanExperimentwith A -- 0. As time in-
I
creases (increasing 8),weprobea regionof theskyat increasing Z• and 19values.If we repeatthe geometriccalculation
withA -- 15ø, the areaof the Z•-19planecovered is smaller than is shownin Figure2, and,in particular,lessof the region
oftheskywithsmall Z, andsmall 19 isaccessible forobserva-z tion.Otheraspects of theexperimental designarediscussed in
20
-
paper 1. 2.
DATA
REDUCTION
AND
ANALYSIS
The relationshipbetweenthe cameradirectionand the sun positionisgivenby theVikinglanderephemeris. Thispermits
m
10
O0
_
10
20
30
40 Z ,•(km)
50
I
60
I
70
80
us to correctfor lander tilt to within a few tenthsof a degree betweenZ•,/•, •, and19forA -- 0. and to determinethe positionof the local horizon with the Fig. 2. Geometricalrelationships
KAHN
ET AL.: THE
assumed particle properties influence the phase function shown in Figure 4. Much of Figure 4 is directly established from empirical data. The strengthof the forward scattering peak is model dependent;its importance is consideredwhen we discussmutliple scattering. Our procedureinvolvesintegrationof the extinctionalong the paths of a sequenceof solar rays BG to produce source functions for single scatteringalong the line of sight of the camera. We use a Mie scatteringprogram to generate cross sectionsand phase functions for the particles. The essential purpose of this procedure is to infer the phase function for small scattering angles for which there are no direct sky brightnessmeasurements.As discussedin paper 1, we can neglectthe effectof particle shapeon the scatteringpropertiesat such angles.Finally, we integrate the sourcefunction along paths GD coincident with the line of sight to evaluate the singly scattered intensity at the camera location. Multiple scatteringwill be discussedlater. We attempt to devisemodelswhich reproducethe shape of the observedintensitycurvesfor each color. We typically plot the intensity ratio (Y) as a function of Z• for a fixed value of 0. The ratio of observedto model intensityfor Z• equal to 20 km is designatedby M; thus if M > 1, the model intensityis lower than the observed intensity. One value is obtained for each
color,and we distinguish thesewith subscripts, Mb, M s,Mr for
MARTIAN
TWILIGHT
5835
wavelength of photons which may be converted into visible light by atmosphericptotochemical processes.At earth this
flux of photonsgivesa skybrightness of 1 megarayl$igh (MR) [Hinteregger, 1970], correspondingto about 0.4 MR at Mars. Accordingto the data given by Huck et al. [1975],this airglow contribution
is far below the detection limit of the camera.
We must also consider resonant scatteringof solar visible photons,which makes an important contributionto the terrestrial airglow. The concentrationof specieswhich could pro-
ducethisscatteringin the Martian atmosphere is now known. Consider sodium, which is a particularly efficient scattererof visible light in the airglow on earth. This light will only affect the green passbandof the Viking lander camera. We follow Chamberlain [1961], adjusting his numerical values to allow for the different distances of earth and of Mars from the sun.
If we selecta column abundancefor sodium of 4 x 109cm-•, a value representativeof the atmosphereof earth, we obtain a maximum sky brightnessof 1.6 MR, which is more than an order of magnitude below the camera detection limit. In summary,none of the likely sourcesof airglow basedon terrestrialexperienceis likely to producea componentof sky brightnesslarge enough to be detectedby the camera. Extended Layers and Obstaclesat the Sunset Point
A layer of dust in the line of sight with a horizontal extent of tensof kilometersor more, or an obstacle(e.g., a mountain We now discussthe importanceof each of the assumptions or a cloud) at the sunsetpoint can both causeinflectionsin a contained in our model. plot of intensity(Y) againstZ,, for a fixed scatteringangle (0). the blue, green, and red light, respectively.We seek a model
for which Mb,s,r= 1 for all Z, values.
AtmosphericRefractionand the Finite Size of the Sun
Since we can select data at constant 0 or constant Z,, it is in principle possibleto distinguishbetween the two causes.The record for sol 41 P.M. showed no significant inflections.On
We calculatethe deflectionof the shadowedge from its unperturbedheight Z, due to atmosphericrefraction.This problem has been solvedin general by Goody[1963]. For a CO2 atmosphereof 7-mbar surfacepressurewith a scaleheight of 10 km, we calculate the asymptoticangle of deviation of a graz-
layers in the line of sight nor obstaclesat the sunsetpoint. In order to make this statementquantitative we have performed numericalexperimentswith modelsof dust layers containing one third of the total atmosphericopacity concentratednear
this occasion,therefore, there was no evidence in favor of dust
Thelayerthickness wasvaried,•lndweconing ray to be 4.76 x 10-3 deg.For the largestZ, valuestreated to40-kmaltitude. here this correspondsto a height uncertainty of less than 60 m. At Mars the solar disk is about 0.25ø in size.For the largest Z, valuesthe shadowedgewill be spreadby about 3 km. Both of these are small in comparison with the full width of the sourcefunction distribution (Figure 1).
RayleighScattering The optical depth for a 7-mbar CO2 atmosphere due to
cluded that a 10-km layer was marginally detectable. Narrower layers, or layers containing less dust, are not inconsistent with our data.
Multiple Scatteringin the Twilight
In paper 1 we attemptedto fit the observeddata to a single
scattering model,i.e.,usingsource functions der•,ved fromthe attenuated direct solar beam incident upon scatterersin the
Rayleighscattering is about1.2x 10-3 at 0.49microns.This is line of sight.For any aerosoldistributioncompatiblewith the more than 2 orders of magnitude smaller than the lowest atmospheric optical depth measured at either lander site throughoutthe Viking mission(paper 2) and is at leastan order of magnitude smaller than the uncertainty in the measured optical depth; assumingthat the atmosphere is well mixed, the Rayleigh contribution to the atmospheric extinction and sourcefunctionscan safely be neglectedfor all Z, values, even when allowance is made for the differences between Rayleigh and dust phasefunctions.
optical depth and aerosolpropertiesdeducedfrom other Viking observationsthe intensity calculated from this model is
far smaller than is observed,showingthat secondaryand higher-order scatteringare of major importance. We shall
neverthelessconclude that the scale height of the scatterers deducedon the basisof a singlescatteringmodel is approximately correct. The problem of multiple scatteringin the complexgeometry of the twilight is well known (seeRozenberg[1966] for an accountof this phenomenonin the terrestrialtwilight). Unlike Airglow the terrestrialcase,the major sourceof atmosphericopacityin We can estimate an upper bound to the magnitude of the the Martian sky is dust with a very large forward peak in the Martian airglow by calculatingthe total flux of solar UV pho- scatteringphasefunction.Viking observations of the daytime tonswithwavelengths lessthan1700A at Marsandby assum- sky brightnessshowthe sun to be surroundedby a bright auing that each one is convertedinto a visiblephoton.From ter- reole. The scatteringphase function deducedfrom these obrestrialexperience, 1700A is a reasonable upperlimit for the servationsis presentedin papers 1 and 2.
5836
KAHN ET AL.: THE MARTIAN
TWILIGHT
0.20
0.9
Z•
0,6
Scale height, km
o.]4ho
o
/ø/ /o\
Mr
20 l0
8.2 23.2
5
232.7
• OlO
o.o.P z - / g
o ' ' ' ' ' ' ' ' ' 14
16
18
20
22
24
26
28
•
0.06
32
SCATTERING ANGLE,
Fig. 3. Skybrightness at 32ødivided byitsvalueat scattering angle
0.04• 0.02• 0.•
t9,for two values of Z!.
In order to treat the problem we must distinguishbetween multiple scattering involving radiation reaching the line of sight which has not been deflectedmore than a few degrees from the direct solar beam (the aureole component)and radiation which is scatteredat large angles (the diffuse component). The diffuse component may originate from single scatteringat large scatteringangles or by many scatterings from the aureole. The origin is not important, for• whatever it may be, a combination of the curved geometryof the surface with the verticaldistributionof scatterers givesrise to a source function in an extendedlayer whosemaximum lies between
the geometricshadowedgeandtheground[Rozenberg, 1966]. Consider first the diffuse component.A rough calculation shows that if it is evenly distributed over a few steradians, multiply scatteredlight would not be detectedin the Viking camera twilight observations.We may confirm this conclusion by a lessprecisebut perhapsmore convincingtreatment,used by Rozenberg. The layered character and low altitude of the diffuse source
5
10
]5
20
25
30
35
40
45
50
Zi (kin)
Fig.5. C/iiculations ofthelightcurve forsingle scattering models
for threedifferentdustscaleheightscompared to thesol41 P.M. measurements (opensquares). Calculations arefor theredcolorbandand t9= 20ø.Opticaldataaretakenfrompaper3 andarede. scribedin the text.In thecaseof thetheoretical curvesthe intensity[atiohasbeen multipliedby Mr, chosento normalizeagainstthe observeddata for Z! = 20 km.
functionof 0, at fixedZi, we canusetheintensityat large0 to placean upperlimit on the multiplescatteringfor small0. Figure 3 showsY(O)/Y(32ø) for Zi = 20 and 50 km. If we
assume thatalLlight at0= 32øis['rom thediffuse component, we anticipatethat this componentis unimportantfor Z! -< 20
km, 0 _
